SOCIAL CHOKEE BEHAVMR: A THEORETICAL AND EMPIRQCAL STUDY flissertation fer the Degree of Ph, D. WCHIGAN STATE UNWERSSTY JAMES WELLIAM BALK‘NEL 1973 mm mm In III! M mm fill 1le 1m 1!! M” will! Ill!) ll L ’ 3 1293 ABSTRACT SOCIAL CHOICE BEHAVIOR: A THEORETICAL AND EMPIRICAL STUDY BY James William Balkwell Over the past thirty years, one of the most inten- sively investigated fields of social science has been dECir sion making. _As a recent review article noted, ". . . the literature of decision theory is vast, and its boundaries are ill-defined. Even a very restrictive definition of the limits of that literature would produce several thousand titles . . ." (Edwards and Tversky, 1967: 396). The socio- logical relevance of behavioral decision making theory is unmistakable: the axioms of decision making, whatever they may be, describe a procedure for combining and using infor- mation, a procedure that unquestionably plays an important part in buying behavior, voting behavior, interpersonal bar— gaining behavior, and so on. The basic principle of decision making is presumably at the heart of many sociological phe- nomena. But what is that basic principle? James William Balkwell Perhaps two candidates are most prominent. The first is what might be called a "balancing" principle. Ac- cording to it, the chooser,given a repetitive choice situa- tion, selects alternatives in proportion to their associated gains--that is, if the gain from A1 is twice the gain from A2, then Al will be selected twice as often as A2. The second is what might be called a "utility maximizing" prin- ciple. According to it, the chooser selects the strategy that maximizes his total gain, which is conceived as the sum of the gains from the alternatives plus the gain from vari- ability--that is, from avoiding monotony and the like. This dissertation seeks to determine which principle more ade- quately accounts for observable social choice behavior, par— ticularly social influence decisions. We select from the literature two mathematical models of behavioral decision making, one that takes the balancing principle as a basic postulate, the other that takes the utility maximizing principle as a basic postulate. The balancing model is by Camilleri and Berger (1967), and the utility maximizing model is by Siegel §£;gl, (1964). The two are comparable in both scope of application and degree of empirical confirmation. After setting forth some concepts and notation in terms of which both models can be stated, we proceed to ex— plicate both models somewhat more completely than they were explicated by their original authors. In the course of this, James William Balkwell we derive some conflicting implications that are amenable to empirical testing. Specializing these to social influence decisions, we arrive at the concrete empirical hypotheses of this dissertation. By way of indicating these hypotheses, let us de— scribe the experiment that was conducted. Basically, each experimental session entailed a sequence of twenty—five two-step decision episodes having these characteristics: (1) each of two persons makes an initial task-relevant deci- sion, there being two possible responses; (2) each person subsequently receives information that the other person has made the opposite judgment; and (3) each person, after re- ceiving this information, makes a final decision. We are not interested in a subject's actual responses; rather, we are interested in whether, for his final decision, he stays, changes, or (in half the experimental conditions) withholds judgment. Decisions in this sense generate the primary data. The dependent variable is the "response vector" (ns,nc,nw), the vector of frequencies with which the focal actor stays, changes, and withholds judgment. In half the conditions, by definition, nw equals zero, since the subjects are not offered the "withhold judgment" alternative. In the usual research terminology, ours is a 2 x 2 x 2 factorial experi- ment, the three factors (independent variables) being a sub- ject's ability compared to his partner's (high or low), a subject's number of response options (two or three), and a James William Balkwell subject's sex (male or female). The central hypotheses con- cern the relationship between the two-alternative decisions and the corresponding three-alternative decisions. The Camilleri model implies that the third alternative will act as a progressive tax on the other two, taking at least pro— portional amounts of probability mass from them. The Siegel model, in contrast,implies that the third alternative will act as a regressive, or flat—rate, tax, taking equal amounts of probability mass from the other two. Our 23 = 8 experi- mental conditions allow for four separate comparisons that bear upon these conflicting implications. Other hypotheses are also tested, using a variety of statistical and analyti- cal techniques. But these conflicting implications are the central focus. To extract a meaningful conclusion from the collat- eral analysis, we turn to a procedure based upon Bayes' Theorem. Under the assumption that one model or the other is true--or at least is a good approximation to the truth-- the question becomes: what is the probability, in the sense of rational belief, that the true model is the Camilleri model? That it is the Siegel model? Before the present research, we assumed that the two models' credibilities were 1/2 and 1/2. After the present research, however, based on a Bayesian analysis, the credibility of the Camilleri model is 3/8, that of the Siegel model is 5/8. illlll‘ [ilk [ll James William Balkwell But what about the two underlying principles? This is the initial concern of the final chapter. There, two new models, developed by the author, are set forth. The first, Model A, which is a utility maximizing model, is shown to yield as a theorem schema the balancing principle. The implication of this is that balancing and utility maxi- mization are not separate basic principles. The second new model, Model B, which is based on the principles of utility maximization and diminishing marginal utility, is shown to have the very same implications for our research as the fiiegel model,1although the two models are substantively very different. The existence of Model A and Model B inevitably forces us to ruminate on what is required for decision making research to bear the sociological fruits we seek. Clearly, more research designed to test implications shared by vir- tually every model in existence is not required. What we need, now more than ever, is research addressed to matters where one credible model takes issue with another. And research must be judged by its potential to alter the bal- ance of credibility. This, we submit, is the straightest, if not the only, road to further scientific progress. SOCIAL CHOICE BEHAVIOR: A THEORETICAL AND EMPIRICAL STUDY BY James William Balkwell A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Sociology 1973 Copyright by JAMES WILLIAM BALKWELL 1973 ACKNOWLEDGMENT S Whatever defects remain, this dissertation is surely a sounder document than it would have been without the criticisms and suggestions of others. Thomas L. Conner, my committee chairman, and Hans E. Lee read and reacted to several earlier drafts. Santo F. Camilleri, Bo Anderson, and James L. Phillips also provided useful feed- back at various points in the dissertation process. To all of them I offer my sincere thanks. Thanks are also due for help with my research. In this day and age, when most sociological dissertations draw upon data banks, the expenditure of time and effort required to actually gather data tends, I think, to be vastly under- appreciated. For more than two academic terms, the experi- ment reported herein was the dominant fact of life at 920 H Cherry Lane; and it might well have been even longer. I wish to express my deepest appreciation to Carolyn Balkwell for the hour upon hour, month after month, spent on the telephone, scheduling and reminding subjects. Without this tremendous gift of time and energy, I could not possibly be {writing retrospectively at this time! J. W. Balkwell East Lansing, Michigan August, 1973 ii TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . . . . . . v LIST OF FIGURES . . . . . . . . . . . . . . . . . vi LIST OF SYMBOLS . . . . . . . . . . . . . . . . . Vii Chapter I. STATEMENT OF THE PROBLEM . . . . . . . . . 1 ABehavioral Decision Making Theory +An Unsolved Theoretical Problem Decision Making and Social Influence Coordinating Analysis II. ALTERNATIVE MODELS . . . . . . . . . . . . 23 A Basic Conceptual Scheme The Siegel et a1. Model The general case The social influence application The Camilleri et a1. Model The general case The social influenCe application Empirical Consequences that Disagree 'LThe Hypotheses of this Dissertation +~Summary and Conclusion III. +THE RESEARCH: DESIGN AND PROCEDURES . . . 44 A Brief Overview The Experimental Procedures Statistical Analysis First stage Second stage Third stage IV. THE RESEARCH: RESULTS AND DISCUSSION . . 71 Preliminary Notes The Models' Parallel Implications The Models' Divergent Implications An A Posteriori Assessment iii Page V. EPILOGUE ON POST—1971 DEVELOPMENTS . . . . . . 87 The Demise of a Distinction An Alternative to the Siegel et al. Model Conclusion APPENDIX A: THE EXPERIMENTAL MATERIALS . . . . . . . 98 Part One Instructions: All Conditions Part Two Instructions: Conditions 1 and Part Two Instructions: Conditions 2 and Questionnaires Interview Schedule Substance of the Debriefing .Bw APPENDIX B: THE LOGIC OF THIS DISSERTATION . . . . . 124 LIST OF REFERENCES . . . . . . . . . . . . . . . . . 128 iv Table 1. LIST OF TABLES Page Competence-status and influence: Camilleri- Berger data I O I O I I O O O I O I O O I O O 15 Competence-status and influence: Moore data . . l7 Observed values of the response vector (nS,n ,nw) by condition . . . . . . . . . . . 76 c ANOVA of the change-response component . . . . . 78 ANOVA of the stay-response component . . . . . . 78 Observed reSponse proportions by experimental condition . . . . . . . . . . . . . . . . . . 80 Chi-square goodness-of-fit values . . . . . . . 81 Theoretical and observed values of L1 and L2 . . 82 LIST OF FIGURES Figure Page 1. The matrix of outcome-sets . . . . . . . . . . . 25 2. The experimental room . . . . . . . . . . . . . 47 . 47 3. A subjet panel . . . . . . . . . . . . . . . . vi LIST OF SYMBOLS A document that uses logically tight arguments expressed via mathematical notation tends to be difficult to read, partly because logically tight arguments are inher— ently demanding, but perhaps even more because the system of mathematical notation employed is apt to be unfamiliar to everyone except the author. To mitigate the latter obstacle, so far as this dissertation is concerned, we have collected here the most important symbols employed in the text, to- gether with brief indications of their meanings. A = {A1,A2, . . . , Am} is the set g£_alternatives available to the focal actor in an arbitrary decision making situation. Ak = The kth member of A, where k is an arbitrary integer, l i k i'm. Pr(Ak) = The probability of the event that the focal actor selects alternative A given that k, his potential choices are the members of A. oi = An arbitrary elementary outcome, an event that the focal actor believes will occur with a probability that depends upon the alternative he selects. vii ui = u(oi) is the ratio-scale utility to the focal actor of 01's occurrence; that is, if oi occurs, the focal actor receives an amount of satisfac- tion having the value u(oi), a real-valued magnitude. If ui > O, ui is called an element- ary gain; if u. < O, ui is called an elementary 1 loss; if ui = 0, the elementary outcome Qi is irrelevant--the focal actor is indifferent to its occurrence. For any alternative Ak e A, pk = The sum of the elementary gains that are poss— ible if Ak is selected, each weighted by its subjective probability of occurrence. -qk= The sum of the elementary losses that are poss- ible if Ak is selected, each weighted by its subjective probability of occurrence. gk = pk - qk IS the expected net gain for the focal actor if he selects A . k m Qm = Z qi is the absolute value of the sum of the i=1 the expected losses from A1,A2, . . . , Am. At one very important point in our argument, we compare the probabilities of choices from an m-alternative choice-set with the probabilities of the respective choices from this m-alternative choice-set augmented by one additional alter- native. In that context, viii Tm = {A1,A . . . , Am} is the m-alternative choice- 2! 5811. T = {A1,A2, . . . , Am'Am+ m+l 1} IS the augmented (m+l)-alternative choice-set. Prm(Ak) = The probability of the event that the focal actor selects alternative Ak’ given that his potential choices are the members of Tm. Prm+l(Ak) = The probability of the event that the focal actor selects alternative Ak’ given that his potential choices are the members of Tm+l' For research purposes, we consider a particular application of the general development. The specializations of Tm and Tm+1 to what we call "the social influence application" employ the following notation. T2 = {C,S} and T = {C,S,W}, where 3 C = The change-response; S The stay-response; W The withhold judgment response. At two points, one in connection with each model under investigation, we demonstrate that the model in question yields an explicit social influence proposition that is consistent with the known experimental evidence, reviewed in Chapter I. In the context of these "plausibility argu- ments," the following notation is employed. u , u , and u are the particular elementary gains 3 o t associated, by hypothesis, with social influence ix [I l'l‘ ‘(Jll‘lnlllllllfl’ {i {fl [(l decisions. The first, us, is the utility to the focal actor of approval for choosing in accord- ance with his own initial judgment; uO is the utility of approval for choosing in accordance with his partner's initial judgment; and ut is the utility of approval for choosing in accord- ance with objective truth. Z = The focal actor's subjective probability that his initial choice is correct when he and his partner disagree on their initial choices. Z is also interpreted as a standardized measure of the focal actor's competence-status relative to his partner's. For both theoretical and methodological reasons, sequences of decisions are often of interest. In discussing such sequences, we employ the following notation. n = (nl,n2, . . . , nm) is the "response vector," the vector of frequencies with which the focal actor selects the members of a given m- alternative choice-set. The expected value of the kth component, E(nk), is the number of res- ponses in the sequence multiplied by Pr(Ak). (ns,nc,nw) is the particular instance of n that pertains to the research of this dissertation. It is the vector of frequencies with which the focal actor stays, changes, and withholds judgment. Given twenty-five decisions, an example would be (13,07,05). Three of the four models presented, including both of those invented by the present author, are utility maximizing models. In discussing utility maximizing models, T = The total utility accruing to the focal actor from his sequence of choices. T depends upon the response vector n, the assumption being that the focal actor's choices tend to produce the unique value of n that maximizes T. Finally, in connection with our statistical analysis, we introduce the following notation. In this context, we are comparing Model 1, the Siegel et_al. model, with Model 2, the Camilleri et_al. model. L1 = A linear combination of sample means whose expected value, E(L1), is at issue. According to Model 1, E(Ll) = 0; according to Model 2, E(L1) > 0. L = A linear combination of sample means that, in 2 a sense, is the "mirror image" of L1; that is, according to Model 1, E(L2) > 0; according to Model 2, E(L2) : 0. Cr(M1) and Cr(M2) are the prior credibilities of Model 1 and Model 2, respectively, relative to each other. Cr'(Ml) and Cr'(M2) are the posterior xi credibilities, the revised credibilities after new evidence has been analyzed. There are many other symbols employed for various special purposes--this list is by no means exhaustive. Those pre- sented here, however, are perhaps the most important and most frequently recurring ones. xii CHAPTER I STATEMENT OF THE PROBLEM Decision making is incontrovertibly ubiquitous. Indeed, viewed abstractly, social life consists of little else. Not surprisingly, therefore, decisional phenomena are increasingly becoming recognized as the junction where_so- ciology, political science, psychology, and economics come Atogether. Currently, a number of scholars in these fields are investigating the possibility that ". . . all decision making is guided by an abstract set of axioms which vary only in the manner in which they are operationalized in specified situations . . ." (Ofshe and Ofshe, 1969: 337). Should this turn out to be true, the implications for social science would be great indeed. Without attempting to pre- judge this bold possibility, the present dissertation will investigate whether certain kinds of social choice behavior are guided by‘a "balancing" or a "utility maximizing" prin- .gip1e. This distinction arises in the context of the theory and research to which we will now turn our attention. Behavioral Decision Making Theory Since 1944, when J. von Neumann and O. Morgenstern published their seminal treatise, Theoryiof Games and Eco- nomic Behavior, the accumulated work in this area has become immense. As a recent review article noted, ". . . the literature of decision theory is vast, and its boundaries are ill-defined. Even a very restrictive definition of the limits of that literature would produce several thousand titles . . ." (Edwards and Tversky, 1967: 396). Yet the accomplishments of that literature are less vast. Indeed, if an earlier review paper by Edwards (1954) is accurately indicative, then the first decade after von Neumann and Morgenstern's treatise is important mainly for having dis- pelled certain common-sense notions. It was learned, for example, that persons do not choose so as to maximize ob- jective utility, as a perfectly rational "economic man" would. Thus, although game theory may describe how persons nght to behave, it does not accurately describe‘fibw they do behave. It was also Learned that a person' s preferences are frequently not transitive. Thus, a person may prefer "A to B, B to C, yet C to A. Furthermore, it became clear. that a person's preferences are frequently not even consis- tent: he may prefer_A‘to~B sometimes, B to A other times. These difficulties, especially the last two, apparently dashed the sense of euphoria that many felt about the applicability of game theory to social science, for the second decade after von Neumann and Morgenstern's treatise witnessed a pronounced shift in interest toward stochastic conceptions of decision making.' In retrospect, this was probably inevitable, for it does circumvent the problems arising from the undeniable intransitivities and inconsis- tencies found in almost all empirical data. An especially notable theory of stochastic choice behavior appeared in 1959. There were other theories pre— sented before this, of course, and there have been still others presented since; but the theory of R. D. Luce must be considered a milestone in the "stochastic era." Luce's well known Axiom 1 can be stated as follows: Suppose that T is a set of alternatives, that S is a subset of T, and that R‘is a subset of S. \Then the probability of selecting a_member of R, given that the members of T are presented, equals the product of the following two quantities: (1) the probability of selecting a member of R, given that the membershngS are presented, and (2) the probability of_se+ lecting a member of S, given that the members of_T are pre- sented3_ A direct test of this axiom would require two separate experimental conditions. To illustrate the axiom's meaning, Luce asks us to ". . . suppose that T is the set of entrees on a certain menue, S is some proper subset of T that includes roast beef, and R is the single element set of roast beef. The heart of the axiom is that when, for whatever reason, the restaurant has only the entrees S, the probability of selecting roast beef is the same as the condi- tional probability of selecting it from S when the whole menue is available" (Luce, 1959: 7-8). A surprising variety of consequences follow from this axiom. One is that the value, or attractiveness, of each member of T, the choice- set, is measureable on a ratio scale of utility; and, assum- ing a fixed scale factor, the utility of an alternative depends only upon the characteristics of that alternative itself, not upon inter-alternative relationships. This is a strong assumption about the way in which persons combine and use information. Supporting the axiom is a certain amount of empirical evidence (see, for example, Atkinson, Bower, and Crothers, 1965: 143-150). On the other side of the ledger, ". . . abundant evidence . . . shows that Axiom l is not always correct. \Many , . . decision theorists consider it too strong . . ." (Edwards, 1961: 484). As the present author sees it, however, a convincing test would have to involve a credible alternative theory and a situation such that this alternative theory and the Luce theory implied clearly dis— ;inguishable outcomes. -Insofar as we can determine, there have been no tests of this kind.“ Becker et_al. (1963) use Luce's Axiom 1 for classi- fying models of decision making. Either a given model satisfies the "strict utility" property derivable from the axiom or else it does not; hence, it can be classified as "Luce" or "non-Luce," based upon that criterion. Whether Luce or non-Luce, stochastic conceptions of ‘decision making are now dominant. lOne discomfitting thing about this is that anyone can think of choice behavior that is transparently not stochastic. A_satisfactory theory must be able to predict this behavior too. It must be able to specify the conditions under which decision making will be apparently non-stochastic. This problem is not quite as easily solved as one might imagine--in fact, it is not clear that it has been solved. Naturally, after the fact, one can always find ways in which particular stochastic choice situ- ations differ from particular non-stochastic choice situa- tions; and there is an understandable inclination to couch Qne's observations in an abstruse nomenclature and offer them as general principles, which clearly define the neces- sary and sufficient conditions for choice behavior to be stochastic (or non-stochastic). To a greater or lesser degree, most discussions of the issue carry this impression. .An exception, however, can be found in the paper by, Begkerflet_al. (1963). They postulate that most--though not a11--a1ternatives can be compared on more than one dimension. For example, the prospective car buyer can compare Fords and Chevrolets on the dimensions of styling, performance, gasoline mileage, comfort, workmanship, price, "status value,‘ and so on. The gist of their explanation is that, if the chooser focuses upon a fixed set of dimensions, his choice will be fixed. But the attending process is probabilistic. Therefore, in a second-order sense, the decision making process is probabilistic. But how, one might ask, does this solve the problem of specifying the conditions under which decision making will be apparently non-stochastic? Becker gt_§l. would reply that if the alternatives rank the same on each dimension-~a trivial case being where there is only one dimension--the ensuing choice behavior will be determin- istic. Likewise, if the chooser focuses upon the entire set of dimensions. But the assumption is that, typically, he cannot "consider everything," so he randomly focuses upon some subset of "everything." The notion of one alternative ranking higher than ‘another on all dimensions brings to mind the concept of .dominance from game theory. But the two are not the same. Suppose that one were offered the choice between a Ford with probability one and a Chevrolet with probability one. Ac- cording to the game theory perspective, either the two would be equivalent or else the preferred one would dominate the other. In either case, the prediction would differ from that of the Becker et_§1. theory. And this is not an excep- tional case. Think about almost any mundane decision--say, the choice between Wheaties and Oaties for breakfast, both available with probability one if selected. If he acted in accordance with the Becker et_gl. theory, the chooser might focus upon taste and crunchiness, hence choosing the one, or he might focus upon iron and riboflavin content, hence, choosing the other. The dominance prediction would be that the chooser would select the one with greater utility all the time. The Becker et_al. theory is not without its own weaknesses, however. Indeed, it glosses over one of the most important questions. The idea of multidimensionality suffices to explain why some choice behavior is deterministic but not why the rest is probabilistic. Simply postulating that the attention process is stochastic seems a facile answer. "The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil" (Russell, 1919: 71). That any human be- havior should be stochastic cries for an explanation. After all, few of us feel that we are stochastic automata. One possible explanation is that our feelings of free will are delusions-~that the attending process is isomorphic with electrical activity within the brain, which is wholly explic- able in terms of the probabilistic laws of physics. It is noteworthy that a prominent psychologist likens the belief ‘in free will to primitive beliefs about the solar system (see Skinner, 1953: 6-7). But an equally prominent astron- omer disagrees, claiming that free will is one of the most self-evident facts of nature: "If I can be deluded over such a matter of immediate knowledge-—the very nature of the being that I myself am--it is hard to see where any trust- worthy beginning of knowledge is to be found" (Eddington, 1957: 260). A second possible explanation is that persons often behave "quasi-randomly on purpose," so to speak, due either to personal or to normative considerations. It has been suggested that a chooser ". . . has some utility of avoiding monotony, of maintaining variability" (Siegel et 31., 1964: 29). Along similar lines, it has also been sug- gested that a justice principle may give rise to the appear- ance_of_randomness: "There is evidence that an equity norm causes a utility of choice variability" (Ofshe and Ofshe, 1969: 339). An equity norm could easily be operative in social situations, whereas a desire to avoid monotony could easily be operative in both social and non-social situations. This second explanation is compatible with--a1though it does not depend upon--the doctrine of free will, of individual responsibility, and so on. The practical consequence of subscribing to the first explanation is that the scientist will be inclined to view a sequence of decisions as a stoch— astig_progess, seeing the dynamic aspect as primary, the stable-state, or static, aspect as secondary. The practical consequence of suscribing to the second explanation is that the scientist will be inclined to view a sequence of deci— sions as a goal-directed process, seeing the stable-state aspect as primary, the dynamic aspect as unimportant. Sequences of decisions are, from a sociological standpoint, without question the most interesting decisional phenomena” Traditionally, sociologists have been concerned more with recurrent behavior than with that which is unique. When a person makes recurrent choices, his behavior can be conveniently described in terms of a "strategy," in terms of a vector (Pr(Al),Pr(A2), . . . , Pr(Am)). As this suggests, a strategy is defined as a probability distribution over alternatives. To illustrate, if, for breakfast, a person ate Wheaties three days per week and Oaties four days per week, then his strategy, defined over Wheaties and Oaties, would be (3/7,4/7). To study decision making in terms of strategies, however, requires one further distinction: when a repetitive choice process commences, two separate phenomena arise. First, there is a transitory learning period; then, a relatively stable pattern develops. Ofshe and Ofshe ex- plain as follows: "Stable-state choice strategy refers to an individual's decision strategy after he has 'adjusted' to the situation. In choice experiments, . . . it is typi- cally observed that subjects adopt a stable choice strategy after [such] a learning period . . ." (Ofshe and Ofshe, 1969: 333). Sociologists have been principally concerned with the stable-state period, whereas learning theorists (for example, Estes and Burke, 1955) have been principally concerned with the learning period. 10 In bringing this discussion to a close, we should disclaim any intention to discuss every important issue or to give an exhaustive review of the literature. Our aims have been more focused. We have tried to indicate the social scientific importance of analyzing decisional phenomena in the abstract, some of the more salient impediments to such analyses, and some of the more insightful responses to those impediments. There is one additional issue, to which we heretofore only alluded, that will be our point of departure. To this issue we now turn. An Unsolved Theoretical Problem Two themes seem to run through the published theo- retical studies of decision making. One is that the chooser, given a repetitive choice situation, selects alternatives in proportion to the respective gains associated with those alternatives--that is, if the gain from choosing A1 is double that from choosing A then the former will be selec- 2! ted twice as often as the latter. Lghe second theme is that the chooser selects a strategy so as tomaximize his total subjective gain, which is conceived as the sum of the sub- jective net gains from the alternatives, plus the subjegtive gain from variability--that is, from avoiding monotony and the like. On the face of it, these principles are different. If they are in fact different, then at least one of them 11 must be false: "Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity and affects not the pomp of superfluous causes" (Sir Isaac Newton, 1686: 398). The objective of this dissertation can be viewed broadly or narrowly. At the broad level, we will attempt to pinpoint which of these two principles is the "superfluous cause." We will investigate whether man is essentially a "balancing" or a "utility maximizing" organism. Does he balance his choices vis-a-vis the gains from the respective alternatives, or does he select a strategy so as to maximize his total gain? A more fundamental social scientific ques- tion is difficult to imagine. At the more narrow level, we will attempt to assess the relative merits of two decision making models--models formalizing the "balancing" and "util- ity maximizing" principles. Perhaps it is now time to relate decision making to the sociological context within which our work will take place, to the more concrete sociological problem. Decision Making and Social Influence Decision making is always embedded in a sociological context. The axioms of decision making, whatever they may be, describe a procedure for combining and using information, a procedure that presumably plays an important part in buying behavior, voting behavior, interpersonal bargaining behavior, llll‘.llll"uf(l 12 and so on. The basic principle of decision making is pre- sumably at the heart of many sociological phenomena. To study it, of course, one must study one of these phenomena. The research context of the present dissertation is social influence in small groups, which, in the author's judgment, is an important sociological phenomenon in its own right. In particular, we shall investigate the following proposition: -In a social interaction situation, the greater a person's competence—status, the greater his influence-- that is, the more often his advice is taken, the more often he wins arguments, and so on. But having stated this asser- tion, it is clear that some elaboration is required. What precisely does it mean? And, given that meaning, what reason is there for believing it is true? These questions are per- haps best answered by pointing to some appropriate research studies. This will define by extension (Carnap, 1958) the concepts entailed, and it will also indicate the proposi- tion's degree of empirical confirmation. So let us do this now, following which we can draw together this substantive problem and the abstract theoretical problem described in the preceding section. The first study to which we would like to point is * by Camilleri and Berger (1967). They reported results from *The purpose of Camilleri and Berger's study was to test a formal model of decision making; however, it is the strictly empirical aspect of their work that concerns us at this time. Their model is obviously relevant to our overall objective, but we shall postpone discussion of it until Chapter II. 13 a controlled experiment in which competencefstatus and in- fluence figured prominently. Let us first dexcribe the design of their research and then relate that design to these two variables. Their research design was such as to produce, in each experiment, a sequence of twenty to twenty-two episodes hav- ing the following characteristics: (1) each of two persons makes an initial task-relevant decision, there being two possible responses; (2) each person subsequently receives information that the other person has chosen the opposite response; and (3) after receiving that information, each person makes a final decision. Their dependent variable was the number of times a subject stayed with his initial deci- sion--that is, the number of times his initial and final decisions were in agreement. This will henceforth be refer- red to as a subject's number of "stay-responses." Their research entailed twelve experimental conditions, obtained by crossing four "expectation states" with three control arrangements. By a manipulation, each subject was induced to think that he had high or low task ability, and he was also induced to think that his partner had high or low ability. Thus the four ability combinations or, from a subject's perspective, "expectation states." The subjects worked together as a team, trying to maximize their "team score," which was a weighted sum of their individual num- bers of "correct" final choices, each person's number 14 "correct" weighted by his degree of control. A subject could have full control, half control, or no control, as prearranged by the researchers. To sum up, then, Camilleri and Berger's was a 4 x 3 factorial experiment, the two fac- tors being expectation state and control, the dependent variable being number of stay-responses. They reported their data in the form of relative numbers of stay—responses, aggregated over subjects and trials, for each of the twelve conditions. Now let us relate the Camilleri-Berger experi- mental design to the two variables in which we are inter- ested: competence-status and influence. Competence-status in this case is relative task ability as induced by the researchers. Let the symbol "(H,L)" denote the expectation state where the referent actor was induced to think that he had high ability, his partner low ability. Similarly, let "(H,H)" denote "high self, high other," and so on. Then the four levels of the expectation state factor--vis., (H,L), (H,H), (L,L), and (L,H)--represent three values of competence-status: (H,L) represents a large value, (H,H) and (L,L) represent medium values, and (L,H) represents a small value. Now let us con- sider the second variable. The referent actor's influence is manifested by-- and can therefore be indexed by--his partner's proportion of change-responses, a change-response being a final decision that differs from the antecedent initial decision. Aggregate 15 proportions of changes-responses can be computed from Camilleri and Berger's reported data, since these are simply one minus the corresponding proportions of stay-responses. Now that competence-status and influence have been operationalized in terms of Camilleri and Berger's experi- mental design, let us examine their data. Three separate cases must be examined, so as to avoid confounding compe- tence-status with control. The data are presented in Table 1. Table l. Competence-status and influence: Camilleri-Berger data. Level 1 of Control Level 2 of Control Level 3 of Control Com-Sta Influ Com-Sta Influ Com-Sta Influ High .57 High .56 High .76 Medium .27 & .29 Medium .35 & .33 Medium .48 & .40 Low .18 Low .22 Low .27 It can be seen that, within each level of control, the re- lationship between competence-status and influence is in agreement with our social influence proposition. By competence-status, however, we have in mind more than simply task ability. A second facet of this concept can be seen in a study by Moore (1968). The notable differ- ence between Moore's research and Camilleri and Berger's was that Moore manipulated prestige instead of ability. His 16 subjects were recruited from a junior college. In half of his experimental conditions, the subjects were told that their partners were from a local high school; in the other half, they were told that their partners were from Stanford University. The first experimental factor, then, was a subject's "prestige-by-association" relative to his partner's. The second factor was called "relevance," the levels being "implicit relevance" and "explicit relevance." In the for- mer conditions, the subjects were left to decide for them- selves whether prestige was a relevant clue to ability; in the latter conditions, they were told point-blank that ". . . ____ students consistently do much better than students" (Moore, 1968: 52). The names of schools were inserted so as to indicate a congruence between prestige and ability. In sum, then, Moore's was a 2 x 2 factorial experiment, the two factors being prestige and relevance, the dependent variable being number of stay-responses. This experimental design can also be related to our two variables. Competence-status in this case is relative prestige; and, as before, influence is indexed by the referent actor's partner's proportion of change-responses. Moore's data are presented in Table 2. The numbers in parentheses are the proportions after Moore eliminated the data from subjects who did not perceive a status discrepancy. It can be seen that, within each level of relevance, the relationship be- tween competence-status and influence is in agreement with Ill!!!) 17 Table 2. Competence-status and influence: Moore data. Level 1 of Relevance Level 2 of Relevance Com-Sta Influence Com-Sta Influence High .37 (.37) High .41 (.41) Low .30 (.25) Low .31 (.25) our social influence proposition. The relationship within the first level, "implicit relevance," is especially note- worthy, showing that a relatively weak prestige manipulation has, by itself, much the same effect on influence as an ability manipulation. In real life, of course, persons generally have more than one piece of competence-status information about the others with whom they interact. A study by Berger and Fisek (1970) sheds light upon the question of how such pieces of competence-status information are combined in a social in- fluence situation. Using essentially the same experimental procedures as those of the studies already discussed, Berger and Fisek showed that two pieces of information will be reconciled by averaging the levels of competence-status that would have been inferred from the pieces individually. The author believes that the Camilleri-Berger, Moore, and Berger-Fisek studies, and others related to these three, suggest a simple, compact conceptualization; and this con- ceptualization constitutes the meaning of our original social 18 influence proposition. Let a status characteristic be de- fined as a characteristic of a group member, the states of which are differentially evaluated by the group in question (cf. Berger et_al., 1972: 242). For example, age might be a status characteristic in a certain group, older members being evaluated more highly than younger members. This would be a "diffuse" status characteristic. An ability clearly related to the group's purpose, on the other hand, would be a "specific" status characteristic. Let I = the referent actor's degree of influence within a given social interaction situation; Z = the referent actor's relative competence-status, as perceived by the group; 81,82, . . ., Sn be status characteristics (all diffuse, all specific, or whatever combination applies); and a and b be empirical parameters that are constant over group members, the first being positive. Then the conceptualization suggested by the studies cited can be summarized as follows: Z = 0 (81,8 . . .,Sm), where 0 is some function whose form is 2, probably roughly linear; and I z a Z + b. In words, all the competence-status information that is available in a given situation is combined into a single evaluation, which then guides the social influence process. The greater a person's competence-status, the greater his influence. That the social influence proposition we have been discussing can be conceived as an application of behavioral l9 decision making theory is intuitively clear enough. And that some authors have so conceived it is also clear (see, for example, Camilleri and Berger, 1967). Nevertheless, the precise coordinating statements have not been explicated to the present author's satisfaction; and, since these state— ments are crucial links between the theoretical ideas dis- cussed in the previous section and the research to be conducted by us and reported in this dissertation, it is only prudent that such an explication be made. To this important undertaking we now turn. Coordinating Analysis At the outset, we must state more carefully the relationship between competence-status and influence. To this end, let Ixy = the influence of person x over person . = I _ - l . = y, ny x s competence status relative to y s, and exy a random disturbance of x's influence over y such that E _ _ 2 (exy) — 0 and Var(exy) — o . As above, let a and b be empirical parameters that are constant over group members, a being positive. Then I xy aZXy + b + exy' (l) Essentially, what we must do is transform equation (1) into an equivalent form that is more favorable to analysis in terms of behavioral decision making theory. 20 First, let us propose that, for each x and y, ny + Zyx dgf 1.0, where 0.0 s ny s 1.0. This definition is consistent with our interpretation in the foregoing section that competence-status is a relational concept; moreover, it puts ny on a standardized numerical scale, which is easily interpreted. Second, recall that we have operation— alized Ix as y's proportion of change-responses. Observed Y values of Ix are assumed to be the observed values of an Y underlying random variable. For heuristic purposes, we might imagine that Ixy has a scaled binomial distribution (but, of course, assuming a particular distribution is per ripheral to the argument). Now, let Cy = the event that y makes a change—response on an arbitrary trial. Then the probability of Cy is the first moment of the theoretical def E(I ). Paren— XY thetically, it is worth noting that if the distribution of distribution of Ixy' That is, Pr(Cy) Ixy arises from Markov dependent trials, as some authors have posited (see, for example, Cohen and Lee, forthcoming), then Pr(Cy) is the unconditional probability of the event that y makes a change-response on an arbitrary trial. But let us return to the problem of transforming equation (1) into an equivalent but more convenient form. With the definitions now at our disposal, the conversion is straightforward: 21 P C = I ; r( y) E( xy) = E(azxy + b + rxy) ; = aE(ZXy) + E(b) + E(exy) ; = aZxy + b ; = a(1 - Zyx) + b ; = -aZyx + (a + b) . If we now switch perspectives, letting y instead of x be the referent actor, we have an equation that relates the (new) referent actor's theoretically expected behavior to his own competence-status. Since the focus is now upon a single actor, there should be no confusion if we suppress subscripts, writing simply Pr(C) = -aZ + d, (2) where d = a + b, and where it is understood that the refer- ence is to a given actor in a social influence situation such as that of the Camilleri-Berger, Moore, and Berger- Fisek studies. Verbally, this proposition states that, in a social interaction situation, the greater a person's competence- status, the legs his probability of making a change-response. The important point, however, is that this proposition is readily amenable to analysis as an application of behavioral decision making theory. In the coming chapter, and also at other points where our focus is upon abstract decision mak- ing theory, equation (2) will be referred to as "the social influence application." Let us file this equation in our 22 minds, so to speak, along with the concomitant discussion of this section and the preceding section. We will return to social influence and the social influence application of behavioral decision making theory at numerous subsequent points, most notably in connection with our own empirical research, to be reported at a later point. This brings to a close the work of this chapter. In summary, the problem, stated succinctly, is to determine whether decision making is guided by a utility maximizing principle or by a balancing principle. For research pur- poses, we shall focus upon social influence decisions, which, as we have just seen, can be conceived as a subclass of all behavioral decisions. The next segment of our work will involve the presentation of two decision making models-- models that formalize the utility maximizing and balancing themes. Once these models have been presented, and once they have been suitably specialized to the social influence application, the outlines of an empirical test will begin to emerge, and such a test will then become our paramount concern . CHAPTER II ALTERNATIVE MODELS The relatively complex business of this chapter will be tackled in five steps. First, we will set forth some concepts and notation in terms of which behavioral decision making can be further discussed and analyzed. These concepts and notation are similar--but not identical--to those used by Camilleri gt_al. (1972). Second, we will present, in terms of our conceptual scheme, a model by Siegel et_al. (1964), a model that incorporates the utility maximizing principle. Third, we will present, also in terms of this scheme, a model by Camilleri gt_al. (1967; 1972), which incorporates the balancing principle. Fourth, we will iden- tify some logical consequences of these two models that disagree. And finally, specializing and coordinating these disagreeing consequences to a concrete empirical situation, we will arrive at and state the concrete empirical hypotheses of this dissertation. With this plan in mind, let us begin. A Basic Conceptual Scheme Let A = {A1,A2, . . .,Aé} be a well defined choice- set. By well defined, we mean that the alternatives are mutually exclusive, exhaustive, and relevant. A relevant 23 24 alternative is one the chooser accepts as viable, one that is not dominated. Put negatively, an alternative the chooser would never seriously consider is not relevant. For example, given the choice between Wheaties, Oaties, and raw fish for breakfast, many persons would consider at least one offering to be irrelevant. Generally, the choice situations of interest are characterized by imperfect information. That is, certain information upon which the choice outcomes are contingent may be known only within limits. To be more precise, for the choice situations of interest, we posit the existence of a set of "contingencies" C = {C1,C2, . . .,C§} that dif- ferentially affect the attractiveness of the alternatives; one and only one is the true state of affairs at the time of any given choice; and the chooser has only probabilistic information about which one that is. We can think of the contingencies as Nature's alternatives, the chooser's prob- abilistic information as his conception of Nature's strategy. Let AxC be the cartesian product of A and C. Asso— ciated with each member of AxC, by hypothesis, is a well defined outcome-set. Let Oij denote the outcome-set asso- ciated with alternative A1 and contingency Cj' Then Oij is the set of social outcomes for the chooser if he selects Ai and Nature "selects" Cj' The relationships among these basic concepts are illustrated in Figure l. 25 Cl C ... C 2 n (21) (22) (Zn) A1 O11 012 "° 0in A2 O21 O22 '°° OZn Am 0m1 0m2 ' Omn A1 = the ith alternative; Cj = the jth contingency; and zj = the probability of the event that Cj is operative. Figure l. The matrix of outcome-sets. The array of Oi.'s will be called the matrix of outcome-sets, J and, as suggested, it will enter into both models. We assume that the elementary outcomes, members of the Oij's, are differentially valued by the chooser—-that is, that some are more attractive to him than others. Given an elementary outcome 0, let u(o) denote the ratio-scale utility to the chooser if that outcome occurs. That is, if 0 occurs, the referent actor receives u(o). Now u(o) may be either an "elementary gain" or an "elementary loss." For any elementary outcome 0, u(o) is an elemetary gain iff u(o) > O; and u(o) is an elementapy loss iff u(o) < O. Whenever u(o) = O, of course, 0 is an irrelevant outcome-- that is, the referent actor is indifferent to it. There is a class of outcomes having diametrical 26 opposites. For example, gaining five dollars is the dia- metrical opposite of losing five dollars, and social approval is the diametrical opposite of social disapproval. More abstractly, "generalized reinforcers," pecuniary or other- wise, have diametrical opposites. In contrast, such out- comes as pellets of food or electric shocks do not. The principle about to be stated applies only to the class of outcomes having diametrical opposites. OPPOSITES RULE: Let u(o) be an elementary gain, and let 6 be the diametrical opposite of 0. Then u(6) = -ru(o), where r is a positive real number that does not depend on o. The gist of this rule is that, subjectively, avoiding the loss of five dollars has r times as much utility for the chooser as getting five dollars. Moreover, it does not matter who or what gives or takes the money. In other words, more generally, the incentive value of not losing is r times the incentive value of gaining, irrespective of the particu- lar outcomes or from where they come, so long as the pairs in question are diametrical opposites. In general, r # 1. It will be possible to simply our subsequent expo- sition enormously by employing some shorthand notation. It should be emphasized, however, that these definitions do not affect the arguments to be made in any way--they are merely conveniences. For future reference, let us call them our auxiliary definitions. 27 AUXILIARY DEFINITIONS: For any alternative Ak e A, Pk dgf the sum of the elementary gains that are possible if Ak is selected, each weighted by its subjec- tive probability of occurrence; -qk dgf the sum of the elementary losses that"are poSsible if Ak is selected, each weighted by its subjec- tive probability of occurrence; gk dgf pk - qk dgf the expected net gain from Ak; and Qm dgf the absolute value of the sum of the expected losses from A1,A2, . . .,Am dgf iEl qi . These definitions will be very useful, simplifying certain parts of our presentation considerably. In conclusion, we have presented a conceptual scheme that, in many ways, resembles that of one-person game theory. In addition, we have presented one substantive principle-— the Opposites Rule--and four auxiliary definitions. With these various results available for future reference, let us turn to the two models themselves, presenting the Siegel et a1. model first. The Siegel et a1. Model The general case.--Although the exact scope of the model is not known, it is assumed to apply to a fairly broad class of choice behavior. We assume a repetitive choice context. Moreover, we assume that the decisional process has settled down to a stable-state. The model is intended to predict a single actor's stable-state strategy; it is not concerned with the transitory adjustment process, the learning 28 period. This focus of concern has been succinctly expressed as follows: "Our interest . . . is not in learning, but rather in stable-state strategy behavior after the subject has learned . . ." (Siegel et_al., 1964: 151). Let GV be the chooser's gain from variability, and let T be his total gain from the strategy (Pr(Al),Pr(A2), . . .,Pr(Am)). Then the following utility function is posited. m AXIOM 81: T = z g.Pr(A ) + GV i-l 1 1 Note that gi is the expected net gain from Ai’ which was defined in the preceding section. The following is also posited. AXIOM SZ: GV = b ‘ Pr(Ai)[1 - Pr(Ai)] 1 ll MB 1 The intuitive rationale for Axiom 82 is this: Let Xi be an indicator random variable, equaling one if the chooser selects the ith alternative, zero otherwise. Then the gain from choice variability is seen as being proportional to the sum of the variances of the indicator variables Xi’ (i=l,2, . . .,m). The greater the sum of the variances, the greater the gain from variability (cf. Siegel et_al., 1964: 36). It is easily shown that GV is maximal when, for all i, Pr(Ai) = l/m. Now, the distinctive principle of this model is that the chooser selects (Pr(Al),Pr(A2), . . .,Pr(Am)) so as to maximize T. Mathematically, this can be stated as follows. 29 AXIOM 83: Pr(Ak) equals the kth component of the solu- tion vector of the set of m-l linear equations in m-l unknowns determined by Z Pr(Ai) = l and 8T/8Pr(Ai) = 0, (i=l,2, . . . , m). That is, when, for each Ai, the instantaneous rate of change of T with respect to Pr(Ai) equals zero, given the constraint that 2 Pr(Ai) equals one, there is a unique strategy, a unique set of probability values. At the point determined by these values, T is maximized. For a rigorous statement of the mathematical principles that justify this conclusion, see Cronin-Scanlon (1967: 119-124, 264-267). With some mathematical ingenuity, it is possible to derive an analytic expression of Pr(Ak) from Axioms $1, $2, and $3. This we will state as a theorem schema. 1 mgk". gi THM SCHEMA Sl: Pr(Ak) = - + 1 1 , (k=l,2, . . . , m) m 2 b m This completes our presentation of the Siegel et a1. model IIMB in its general form. Now let us turn to the social influ- ence application, discussed in Chapter I. At the outset, we should note that applying the model requires specifying the alternatives, contingencies, and outcomes associated with each alternative-contingency pair. In addition, for those elementary outcomes having diametrical opposites, it requires specifying which are to be regarded as the elemen- tary gains and which the elementary losses. Typically, certain substantive assumptions will be required before a detailed application will be possible. 30 The social influence application.--The objective here is to derive a theorem schema that gives an explicit theoretical characterization to equation (2) of Chapter I, that specifies the parameters a and d in terms of theoreti- cally meaningful quantities. Recall that in the social influence experiments described in Chapter I, each subject made a sequence of two-step choices. On each trial, he made an initial choice; he then received information that the other subject had made the opposite initial choice; and, after receiving that information, he made a final choice. For his final choice, he could stay or change; and it was the decision to stay or change that was of interest. Equa— tion (2) involved the probability of the event that the referent actor would change on an arbitrary trial. Adopting the standpoint of a focal actor, we can coordinate this situation to the two-alternative, two- contingency case of our basic conceptual scheme. Let C1 = the contingency that the referent actor's initial choice was correct, hence that his partner's was incorrect; C = the contingency that the referent actor's initial choice was incorrect, hence that his partner's was correct; 2 = the referent actor's subjective probability that Cl is the true state of affairs (henceforth to be denoted "Z"); 2 = the referent actor's subjective probability that C2 is the true state of affairs (henceforth to be denoted "1-Z"); 31 Al the change-response (henceforth to be denoted "C"); and A2 = the stay-response (henceforth to be denoted "8"). Notice that 21 = Z is a measure of the referent actor's competence-status, a measure that satisfies the definition of Chapter I. Now we must specify the elementary outcomes associ- ated with this situation. The immediate outcomes are ap- proval and disapproval, coming from various sources for various reasons. Interestingly, for most purposes, the sources are wholly irrelevant. They would probably include the actor himself, the other subject, the experimenter, and perhaps even physically absent "significant others" (cf. Israel, 1963). They could even include "posterity" or God. But none of these potential sources needs to be explicitly acknowledged in deriving a general theorem schema. The reasons for getting approval or disapproval fall into three categories: (1) acting in accordance or disac- cordance with one's own initial choice, (2) acting in ac- cordance or disaccordance with one's partner's initial choice, and (3) acting in accordance or disaccordance with objective truth. Altogether, then, we can, at this level, distinguish six elementary outcomes: oS = approval for acting in accordance with one's own ini- tial choice; as disapproval for acting in disaccordance with one's own initial choice; 32 o = approval for acting in accordance with one's partner's initial choice; 6 = disapproval for acting in disaccordance with one's partner's initial choice; ot = approval for acting in accordance with objective truth; and OI ll disapproval for acting in disaccordance with objec- tive truth. The matrix of outcome-sets is constituted as follows: Initial Choice Initial Choice Correct Incorrect Z l - Z Change-response {68,00,0t;} ‘{§s’oo’°€}' Stay-response . {IS'OO’OE} {bs,oo,o€} Now the quantities defined by our auxiliary definitions can be computed. They are given below. Notice that the Oppo- sites Rule has been applied. pC = qu + (uo+ut) (l - Z) = uO + ut(l - Z); PS = (us+ut) Z + us(l - Z) = uS + utZ; -qc = (-ruS -rut)Z + (—ruS)(1 -Z) = -r(us+utZ)' -qS = (-ruO)Z + (-ruO -rut)(l - Z) = -r(uo+ut(l -Z)); 90 = pc -qC = -rus + 110 + (1 -Z - rZ) ut; and gs = PS -q8 = us -ruO + (Z - r+rZ)ut. From this point, it is only necessary to substitute the ex- pressions for 9C and 9S into Theorem Schema 51. Writing the result in a suggestive form, we have: (l+r)ut (l+r)(ut+uO-us) + 2b THM SCHEMA 82: Pr(C) = - ——————— Z + 2b 4b 33 It is worth pausing to reflect upon what the result of this analysis has been. By applying the Siegel et_al. model of behavioral decision making, we have specified the parameters a and d’of equation (2) in terms of theoretically and sub- stantively meaningful quantities. Now obviously we still have some unspecified parameters; but the point is that we have derived a proposition from the Siegel et_al. model that is consistent with what is known about empirical reality. This lends credibility to the Siegel et_al. model and, there- fore, to the utility maximizing principle that it represents. It would be imprudent, however, to draw further conclusions until we have presented the Camilleri et_al. model, which represents the balancing principle. Let us do that now. The Camilleri et a1. Model The general case.--The exact scope of this model is unknown, but it too is assumed to apply to a fairly broad class of choice behavior. Again we assume a repetitive choice situation, and again we assume that the stable-state period has been reached. Like the first model, this one is intended to predict a single actor's stable-state choice strategy, his strategy after he has adjusted to the situation. Camilleri ep_al. note that their model ". . . has many features in common with Luce's" (Camilleri §t_al., 1972: 27). Nevertheless, they depart from Luce's work in an 34 important respect; namely, they define the attractiveness of an alternative--which they call the "expected positive utility" of an alternative--in a novel way: The expected positive utility of a response is the sum of the values of the utilities of the positive elemen- tary outcomes associated with the response minus the values of the utilities of the negative elementary out- comes associated with the remaining responses, each weighted by its subjective probability of occurrence (Camilleri et al., 1972: 24). The authors do not attempt to state this formally, but there is clear advantage in doing so. Let G(Ak) denote the ex- pected positive utility of alternative Ak' Then G(A ) = p — Z (-q.) ; [this is the direct translation] k k . i i¢k = p + 2 q. = P — q + q + Z q.. From this formalization, it can be seen that the expected positive utility of an alternative equals the expected BEE gaip from that alternative plus the absolute value of the sum of the expected losses from all alternatives. Let us state this as axiom one. AXIOM C1: G(Ak) = 9k + Qm' (k=1,2, . . .,m) Expected positive utility is related to choice behavior according to the balancing principle—-that is, the probabil- ity of choosing a given alternative is proportional to the expected positive utility of that alternative. Since the probabilities of the alternatives must sum to unity, this is equivalent to the following. 35 m AXIOM C2: Pr(Ak) = G(Ak) /i:l G(Ai) , (k=1,2, . . .,m) It is a relatively simple matter to derive an analytic ex- pression of Pr(Ak) from Axioms Cl and C2. In order to pre- serve a parallel with our presentation of the Siegel et a1. model, we will state this as Theorem Schema Cl. g=Q = THM SCHEMA c1: Pr(Ak) = k m , (k 1:2: - . + QO .,m) i This completes our presentation of the Camilleri et_al. model in its general form. Now let us turn to the social influence application. Applying this model requires, as does applying the first model, that we specify the alterna- tives, contingencies, and elementary outcomes associated with each alternative-contingency pair. Moreover, for each eler mentary outcome, it requires specifying whether the utility from that outcome is to be regarded as an elementary gain or an elementary loss. The social influence application.--The objective here, as in the corresponding subsection earlier, is to derive a theorem schema that gives an explicit theoretical characterization to equation (2) of Chapter I. The prelim- inary analysis presented there applies here as well, of course. Recall that we had the following: gC = -ruS + u0 + (l-Z-rZ)ut and gS = uS -ruO + (Z-r+rZ)ut. It is easily verified that Qm (Q2 in this case) is the 36 following: 02 = r(us + u + u From this point, it is o t)' only necessary to substitute these expressions in Theorem Schema Cl. Writing the result in a suggestive form, we have: ut uo+u THM SCHEMA C2: Pr(C) = - u +u +u Z + s o t t + + us 110 u t Notice that again we have partially specified the unspeci- fied parameters of equation (2), this time by applying the Camilleri et_al, model of behavioral decision making. Once again the parameters a and d have been given explicit char- acterizations in terms of substantively meaningful quanti- ties. Just as the corresponding earlier derivation lent credibility to the Siegel et_al. model, this derivation lends credibility to the Camilleri et_al, model. Before pursuing this matter further, however, it is appropriate to remark upon an unobvious but nonetheless important point. When the sources of approval and disapproval are explicity stated, let us call the formula that results a "variant" of the theorem schema in question. Then the theorem schemata of the Siegel et_al. model and the Camil- leri et_al. model represent quite an array of separate theorems. Let n = the number of possible sources, and let V = the number of possible variants. Then it can be shown that V = 8n (eight to the nth power). For n = 3, V = 512; and for n = 5, V = 32,768. One reason for dealing with theorem schemata instead of particular theorems, therefore, 37 is obvious. Still, there is an even more compelling reason. Let us.take the perspective of a subject in a social influ- ence experiment of the kind described in Chapter I. Let u1 = the utility of approval from oneself; u2 = the utility of approval from one's partner; and u3 = the utility of ap- proval from the experimenter. Now consider the following "source-analysis" of us, uo, and u . Suppose uS = ul; t u0 = zero; and ut = u2 + u3. Making these substitutions in Theorem Schema C2, and subtracting the result from unity, we get the equation for Pr(S) that Camilleri and Berger tested via the research described in Chapter I. Out of 512 possible variants, they selected this one and set out to test it. Now it is easily shown that a large number of alternative variants produce exactly the same predictions as those they tested. But the important point is app that they selected an unreasonable variant--in fact, they may have selected the most reasonable one of all 512. The point, however, is that a much stronger test could have been ob- tained if the authors had designed their experiment to focus upon the distinguishing features of the model as opposed to the unexacting features of a variant. This distinction is of fundamental importance. Empirical Consequences that Disagree As we have seen, both the Siegel et al. model and the Camilleri et a1. model yield equations that are consis- tent with the known empirical evidence from social influence 38 experiments. Although these equations are superficially different, they are, we believe, empirically indistinguish- aple. Camilleri and Berger, in evaluating their model, state: " . . . the ordering implications of our model are consistent with the data" (Camilleri and Berger, 1967: 376). It so happens, however, that the ordering implications of the Siegel et_al. model are equally consistent with the data. But the decisive point is this. Suppose that the parameter "b" of the Siegel etpal, model were to have the following value: b = (l/2)(l + r)(us + u0 + ut). Then Theorem Schema 82 would reduce to Theorem Schema C2. And to prove that b does not have this value would probably be impossible. This state of affairs is disconcerting, for the two models do represent different substantive principles. The question naturally arises: is it e323 possible to empiri- cally distinguish between the two models? There does not exist an algorithm for finding the answer to this question; however, one possible road to an answer might be to explore the deviations from Luce's Axiom 1 that each model implies. In particular, let us inquire about what happens to the probability that an alternative will be selected if the choice-set is enlarged by adding one alternative. Let Tm = {A1,A ... ,Am} and Tm ... ,Am,A 2' +1 2’ m+l}° We will indicate which choice-set a given selection is from = {A1,A by subscripting the probability in question with "m" or "m+l." Notice that Tm+1 is identical to Tm except that the 39 former has an added alternative. Now, the Luce axiom implies the following: Pr m(Ak) = Prm+l(Ak) / [l - Pr Wm+l( +1)], (k= 1, 2, . . .,m). The analogous statements implied by the Siegel et al. model and the Camilleri et al. model are given below. (Ak) + l Pr THM SCHEMA s3: Prm (A m m+l (Am+l)' k) = Prm+1 (k=1,2, . . .,m) Prm+l(Ak)/[l - Prm+1(Am+l)] + 3k. (k=1,2, . . . ,m), where THM SCHEMA C3: Pr m(Ak) V (a) 6k _ O if Prm(Ak) > l/m; (b) 6k = 0 if Prm(Ak) = l/m; (c) 5k 5 O if Prm (A < l/m. k) These theoretical relationships can be verified by direct substitution, using Theorem Schema 81 and Theorem Schema Cl, respectively. In Theorem Schema C3 above, it should be noted that whenever Qm+1 > Qm, the inequalities involving 6k are strict. Whenever Prm(Ak) # l/m, the predictions of the two models disagree. Moreover, the direction of the disagree- mgpt depends upon the direction of Prm(Ak)'s departure from l/m. Herein lies the basis of a strong empirical test. Research designed to test models based on a balancing principle has produced a fair amount of evidence that has been interpreted as supporting this principle (see, for example, Olin, 1966; Camilleri and Berger, 1967; Balkwell, 40 1969; McMahon, 1970). At the same time, research designed to test models based on a utility maximizing principle has also produced a fair amount of evidence, but this latter evidence has been interpreted as supporting this second prin- ciple (see, for example, Siegel and Goldstein, 1959; Siegel §E_al., 1964; Ofshe and Ofshe, 1970a, 1970b). It is not clear that any of this evidence is more compatible with one principle than with the other. Thus, on evidential grounds, neither principle can be considered more credible than the other. "How and why," asks the philosopher Karl Popper, "do we accept one theory in preference to others? . . . We choose the theory which best holds its own in competition with other theories" (Popper, 1959: 168). We would add only that someone must arrange for the theories to "compete." The Hypptheses of this Dissertation Let us specialize these disagreeing empirical con- sequences to the social influence application. Recall that the choice-set of that application.is.{C,S} . The subject must make either a change-response or a stay-response. To apply Theorem Schemata S3 and C3 to social influence deci- sions, it is necessary to find a second choice-set that includes C and S and one additional option. The author's experience in conducting social influence experiments sug- gested that a natural addition would be a "withhold judgment" option, for it was clear that subjects often decide to change 41 or stay only with the greatest reluctance. The chance to say, in effect, "it is too close to call," seemed like one that might have some appeal. The details of this option will be presented in Chapter III; for now, let us just note that in half our experimental conditions, the offered choice- set is {C,SL}, and in the other half, the offered choice-set is {C,S,W} . The concrete hypotheses of this dissertation are straightforward applications to these choice-sets of Theorem Schemata S3 and C3. In terms of the notation intro- duced in the preceding section, the first set is a particular instance of T2, the second set is the corresponding T3. For future reference, let us call the social influence applica— tions of Theorem Schemata 83 and C3 our "basic hypotheses," and let us record them. BASIC HYPOTHESES Model 1: Pr2(C) Pr3(C) + 1/2 PR3(W). Model 2: Pr2(C) = Pr3(C) / [l - Pr3(W)] + 6c, where (a) 6c (b) 6C IV 0 if Pr2(C) > 1/2; IA 0 if Pr2(C) < 1/2. Model One, of course, is the Siegel et_al, model, and Model Two is the Camilleri ep_al. model. Regarding Model Two, the case where 6C = O is irrelevant, because research must be designed so that Pr2(C) # 1/2 if it is to have any chance of distinguishing between the two models. Finally, these hypotheses could be stated in terms of Pr(S) instead of Pr(C). 42 From a research standpoint, the choice is entirely arbitrary-- the two statements lead to the same tests and the same re- sults. But stating the hypotheses in terms of Pr(C) makes better sense vis-a-vis our original social influence propo- sition. Summary and Conclusion The aim of this chapter has been to present alterna- tive models of behavioral decision making, one representing the utility maximizing principle, the other representing the balancing principle. We began by setting forth a basic con- ceptual apparatus in terms of which the two models could be stated. Then, in succession, we presented the Siegel et_al. model and the Camilleri et_al. model, which rest upon the respective principles. Specializing these models to the social influence application, we observed that both yield propositions that specify, in terms of substantively mean- ingful quantities, the previously unspecified parameters of Chapter I's equation (2). But to our dismay, we discovered that the two models' specifications were empirically indis- tinguishable. Turning to the published experimental evi- dence, we found that all the tests that have heretofore been conducted have been somewhat feeble—-that none have borne directly upon the two models' distinguishing properties. As if to prove that consternation can be constructively 43 channeled, we commenced a search for empirical implications of the models that disagree. This effort bore fruit. Find- ing such implications, we proceded to specialize them to social influence decisions; and this is where our presenta- tion now stands. Until now, our concern has been chiefly theoretical; however, we have arrived at a point where further empirical knowledge is sorely needed. So let us turn to some original research that may be able to answer some of the questions that have been raised, some research designed to test our "basic hypotheses," stated above. CHAPTER III THE RESEARCH: DESIGN AND PROCEDURES Various aspects of the experimental design and pro- cedures have already been mentioned, but until now they have not been described fully and systematically. This is the aim of the present chapter. We shall begin with a brief overview; then we shall describe the experimental procedures in some detail; and, finally, we shall describe the statis- tical analysis, the ways in which the data are to be anal- yzed, relating these ways to our basic hypotheses. Let us commence . A Brief Overview Basically, each experimental session entails a se- quence of twenty-five two-step decision episodes that have the following characteristics: (1) each of two persons makes an initial task-relevant decision, there being two possible responses; (2) each person subsequently receives information that the other person has made the opposite judgment; and (3) each person, after receiving that information, makes a final decision. It should be emphasized that we are not interested in a subject's actual responses; rather, we are interested in whether he stays, changes, or (in half the 44 45 experimental conditions) withholds judgment. Thus, decisions in this sense are the primary data. An example of a datum from a single subject might be: s,s,w,w,s,c,c,w,s,s,s,c, w,c,c,s,s,s,c,s,s,w,s,c,s. Here the subject stayed 13 times, changed 7 times, and withheld judgment 5 times. These fre- quencies are the components of our dependent variable, which can be thought of as the "response vector" (ns,nc,nw). For each subject in each condition, we get one value of this vector; and, theoretically, that value depends upon the values of the independent variables to be described. Using standard research terminology, ours is a 23 factorial experiment, the three factors (independent vari- ables) being a subject's competence-status relative to his partner's (high or low), a subject's number of response options (two or three), and a subject's sex (male or female). The first two factors relate to our two models, but sex does not. The reason for adding sex as an independent vari- able is to obtain insight into the degree to which the other variables operate invariantly across groups with different socialization experiences. Needless to say, "socialization invariant" findings are of greater scientific importance than findings that apply only to certain groups--only to males, only to Chinese, or whatever. As noted, we have 23 = 8 experimental conditions. The mean values of the response vector for these eight con- ditions should be related to each other in accordance with 46 the implications of Model One if Model One is correct or the implications of Model Two if Model Two is correct. In a nutshell, our analysis will involve examining the relation- ships among cell means and drawing conclusions, based on this examination, about the relative merits of Model One and Model Two. The precise statistical and analytical procedures will be described in the third section of this chapter; but, before getting into this somewhat technical presentation, let us describe the experimental procedures that were em- ployed, the concrete details of an individual experimental session. The Experimental Procedures Each experiment begins with two subjects being seated in a small groups laboratory. The arrangement of the experimental room is illustrated in Figure 2 (next page). The two subjects are seated side by side, but they are sepa- rated by an opaque partition. There is a large screen at the front of the room, behind which is a Carousel slide projector. The experimenter operates mainly from an adjacent room, observing the subjects through a one-way mirror, en- tering and exiting the laboratory as required. This is explained to the subjects with the statement that "the con— trols for the slide projector are in this room back here," which seems to be all the explanation that is necessary. When he is in the adjacent room, the experimenter communi- cates with the subjects through an intercom system. 47 L l—————J r ~>\‘\~--screen w | Q’1a—table E] J. partition-——’F”? [30/2— chair Figure 2. The experimental room. top INITIAL CHOICE bottom 0 . your choice . 0‘.\ light 0 his chOice 0 FINAL CHOICE . . . RflUSh- top withhold bottom button judgment Figure 3. A subject panel 48 All communication between the two subjects themselves takes place by means of panels, which are part of an ICOM (interaction control machine) system. Unknown to the sub- jects, the experimenter is able to manipulate the content of this communication (cf. Berger et al. 1972: 249). One of the subject panels is illustrated in Figure 3. (It should be noted, of course, that the withhold judgment button is not present in the two-alternative conditions). As indicated earlier, what are purported to be the subjects' initial decisions are communicated to their partners; however, their final decisions are private. All decisions, both initial and final, are recorded by an Esterline Angus event recorder, which is wired into the ICOM system. With this as background, let us indicate the organ- ization of an experimental session. This organization can be outlined as follows: I. Part I (competence manipulation) a. Part I instructions b. Part I test c. Part I questionnaire II. Part II (social influence decisions) a. Part II instructions b. Part II test c. Part II questionnaire III. Part III (interview and debriefing) We will describe the main features of each part in order. The part one instructions have two purposes, one being to explain how the equipment works, the other being to provide an explanation of what the subjects will be asked to do and why we are interested in such activity. The 49 ostensible purpose of part one is to study something referred to as "contrast sensitivity." Let us note at this time that copies of all the experimental materials, including the part one instructions, can be found in Appendix A. Following the presentation of the part one instruc- tions, the subjects are given a "test," which purportedly measures their respective levels of contrast sensitivity. Twenty trials make up the part one test. On each trial, the subjects are asked to judge which of two rectangular, "scrambled checkerboard" patterns projected on the front screen is "slightly more black than white." The patterns are arranged vertically; thus, the possible answers are "the top one" and "the bottom one." The subjects are told that one pattern is 50 percent black and 50 percent white, but that the other is 53 percent black and 47 percent white. (Actually, both patterns are 50-50). After the twenty trials have elapsed, the experimenter purports to add up each sub- ject's correct answers, and then he presents fictitious scores. On the wall are posted scoring standards, comprised of intervals labeled "high," "high average," "low average," and "low." It purportedly turns out that one subject got 17 correct, which is "high," the other subject 8 correct, which is "low." Showing a faint touch of practiced embar- rassment, the experimenter remarks upon how "unusual" this is, and then he passes out the part one questionnaire. 50 The part one questionnaire is designed both to check the success of the competence-status manipulation and to reinforce it, the latter by inducing the subject to rehearse its results. He is asked to estimate how well he and his "partner" (by this time we have begun to refer to the two subjects as "partners") would do if they were to take "a second Contrast Sensitivity test like the one given today." The questionnaire has two Likert-type items and one open- ended item, the latter designed to elicit possible suspicion. When the questionnaire has been completed, it is collected, and we procede to part two. Part two, introduced as "the more sociological part of our work today," is of course the heart of the experiment. In the part two instructions, the subjects are told that we are interested in their abilities to make correct decisions in a "cooperative choice situation." To explain what a "cooperative choice situation" is, we draw an analogy with a physician making a difficult medical diagnosis, who asks the advice of a second doctor before making his final de- cision. It is emphasized that the doctor ". . . shouldn't care whether he himself thinks of the right answer, or whether he recognizes the right answer after this consul- tation process. The only thing that's important is that he make the correct final decision" (experimental instructions). 51 At the completion of the part two instructions, the second test is begun. This test involves 25 critical trials and 5 non-critical trials. On each critical trial, the sequence of events is as follows: (1) the experimenter pre- sents a contrast sensitivity problem, (2) each subject is asked to make an initial choice, (3) each subject is given ostensibly accurate feedback that the other subject has made the opposite initial choice, and (4) each subject is asked to make a final choice. On each non-critical trial, the sequence of events is the same except for the third item. Instead of being led to believe that his partner made the opposite initial choice, he is led to believe that his part- ner made, on these trials, the same initial choice. For purposes of analysis, these trials--numbers 4, ll, 15, 19, and 26--are simply disregarded. Their sole function is to lend plausibility to the experiment. The crux of each criti- cal trial, as we have indicated before, is what the subject chooses to do with his final choice. In the two-alternative conditions, he may stay or change; in the three-alternative conditions, he may stay, change, or withhold judgment. His pay for participating ostensibly depends upon his final de- cisions, a "correct" choice being most rewarding, an "in- correct" choice being least rewarding, and (in the three- alternative conditions) a "withhold judgment" choice being intermediate in reward value. To add effectiveness to this 52 pay-off structure, the subjects are told that they are work- ing together as a team. The "team score" is explained to them as follows: Each time a person makes a correct final choice, the team will gain two points; each time a person selects the 'Withhold Judgment' alternative, the team will gain one point; and each time a person makes an incorrect final choice, the team will gain nothing. Or to put it another way, each final choice you make will be scored +2, +1, or 0, depending upon whether you're correct, whether you withhold judgment, or whether you're incor- rect, in that order. . . . In accordance with our standard policy, each of you will be paid the same amount for taking part in today's study, and that amount will depend on your final team score (experimental instruc- tions). All mention of the "withhold judgment" option is of course deleted from the instructions of the two-alternative condi- tions. Before leaving the part two test, there are three miscellaneous points that should be mentioned. First, the ostensible pay range is $1.00 to $2.20, each subject's pay depending upon the team score; actually, each subject re- ceives $2.00 whatever his choices. Second, it was mentioned earlier that the subjects' final choices are private. This is true, yet it does not mean that the subjects are completely unaccountable for their behavior: they are told that, at the end of the test, each person's contribution to the team score will be announced. Finally, it should be emphasized that, in designing part two, our number one priority was to make the two-alternative and three-alternative conditions 53 identical except for the presense or absense of the withhold judgment option and the instructions pertaining specifically to that option. Following this second test, each subject is asked to fill out a second questionnaire. This questionnaire asks him to indicate his concern with getting correct answers (one Likert-type item), his concern with avoiding incorrect answers (one Likert-type item), his degree of nervousness (one Likert-type item), his conception of his final choice performance (one Likert-type item), and his general thoughts about the test (two open-ended items). The purposes behind these questions are to elicit possible suspicion and to pro- vide leads for the post-session interview. While the sub- jects are filling out this questionnaire, the experimenter is purportedly totaling up the team score. As soon as the questionnaires are completed, the experimenter collects them and announces that he would like to speak with each subject individually for a few minutes. He then leads them to sepa- rate interview rooms and commences to interview and debrief the first subject. We have indicated in passing that the experiment entails two deceptions: the fictitious scores of part one and the fictitious disagreements of part two. From a prac- tical standpoint, it is important to learn whether these deceptions were successful; from an ethical standpoint, it is important to undo the injury to truth that is unfortunately 54 entailed. The concluding interview and debriefing is addres- sed to both these matters. Suggestions by Aronson and Carlsmith (1968: 70-73) were relied upon heavily in design- ing this third and final part of the experiment. These, then, are the essential features of an in- dividual experimental session. As noted earlier, it is a subject's final choices in relation to his initial choices that make up the primary data. The example of a datum from a single subject given before was: s.s.w.w.s,c,c,w,s,s,s,c, w,c,c,s,s,s,c,s,w,s,s,c,s. Here the response vector (ns, nc,nw) = (13,07,05). For each subject--there were 80 in all--we obtain one value such as this, where nw dgf 0 in the two-alternative conditions. Thus, the raw material for our analysis is eighty values of the response vector (ns, nc,nw). The question becomes, what are we to do with eighty values of a random vector? How are the data to be analyzed? How are conclusions about the two models to be reached? It is to such questions that we now turn. Statistical Analysis Perhaps the prime virtues of a statistical analysis are thoroughness and systematization. The object is to sum- marize and evaluate every aspect of one's data that bears upon the hypotheses being tested. Given a data-set, there is a finite collection of non-overlapping questions that 55 can be asked. A subset of these is relevant to a preselected group of hypotheses, and the complementary subset is irrele- vant, although it may be relevant to other purposes. So the problem is to identify and concentrate upon the first subset while, at the same time, avoiding irrelevant forays into the second. The place to begin is with a conception of just what it is one wishes to find out. Once that is decided, the rest practically falls in place. In the present case, we should first be concerned with whether either model is con- sistent with the gross features of the data, whether either model predicts correctly in those ways in which their pre- dictions are parallel. The models' parallel predictions are of course what Camilleri and Berger (1967) referred to as the "ordering implications" of their model, which were restricted to relatively gross ordering implications. Now assuming that such ordering implications are borne out--that both models are "in the right ballpark," so to speak--we should become concerned with whether the data conform better to the implications of Model One or Model Two where those implications diverge. And finally, we should become con- cerned with the degree of rational belief one can have that the better fitting model is in fact the more valid model. After all, we are examining but one data-set, and no one would deny that there is statistical variation in the data. Thus, the question becomes: what is the degree of rational 56 belief that the observed pattern of results, insofar as that pattern supports one model over the other, represents a true empirical regularity and not just a statistical anomaly? These three concerns define the three stages of our statis- tical analysis; let us consider each in turn. First stage.--The first concern, in the present author's judgment, is best dealt with in conjunction with the usual, well known procedures of statistical inference. Since ours is a 23 factorial experiment, it is natural and appropriate to ask what might be learned by performing an ordinary three-way analysis of variance on the change- response component and the stay response component, respec- tively. Let us list the seven pairs of hypotheses that each ANOVA entails. Then we can consider how they bear upon mat- ters of substantive significance. With regard to the change- response component, these hypotheses are the following. H10: There is no difference in frequency of changing between high competence-status subjects and low competence-status subjects. *Hl : There is at least some difference. H20: There is no difference in frequency of changing between subjects allowed to withhold judgment and subjects not allowed to withhold judgment. *H2a: There is at least some difference. H3O: There is no difference in frequency of changing between male subjects and female subjects. H3a: There is at least some difference. H4O: There is no 2-way interaction between competence- . status and number of alternatives. H4a: There is at least some such 2-way interaction. H5 : There is no 2-way interaction between competence- status and sex. HSa: There is at least some such 2-way interaction. 57 H6 : There is no 2—way interaction between number of alternatives and sex. H6 : There is at least some such 2-way interaction. H7 : There is no 3-way interaction among competence- status, number of alternatives, and sex. H7 : There is at least some such 3-way interaction. The hypotheses marked with asterisks represent predictions of 22th_models. Hypothesis Hla’ of course, is our original social influence proposition; hence, we would expect this hypothesis to be strongly confirmed; and, indeed, were such confirmation not in evidence, serious doubt would arise about the efficacy of the experiment. Hypothesis H2a is also an implication of both models under the assumption that the withhold judgment option attracts any responses at all. Both models imply that an added alternative will take proba- bility mass from each other alternative. This is not, of course, logically necessary: if it is true, it is an em- pirical truth. But the important point for us is that if it is false, then neither model is predicting correctly-- and we should know this before proceeding to what would then be a dubious question of which model is best. The other hypotheses are theoretically relevant, but they are relevant in a different way. They pertain to "the nature of the givens," so to speak. Consider H30 and H3a' Neither model says whether we should expect to find a dif- ference between males and females. If there is a difference, however, then the models must be applied to each group sepa- rately, for both models assume homogeneity of the subject 58 samples. "Homogeneity," of course, means sameness with re- spect to pertinent characteristics, not with respect to every conceivable characteristic. So the question becomes: is sex a pertinent characteristic? Similar questions could be asked about age, race, cultural background, and so on. As science seeks general, widely applicable propositions, it is clear that a model is more valuable if it does not depend upon the ascribed and achieved characteristics of the groups to which it is applied. But if a model is dependent upon such characteristics, this only makes it more complicated, not false. A similar point should be noted in regard to the interaction hypotheses entailing sex. An "interaction" means that the rate of change of the dependent variable with respect to an independent variable is non-constant over dif- ferent values of the other independent variab1e(s). For example, if our basic social influence proposition were stronger for males than for females, this would imply an "interaction" between competence-status and sex--it would imply that the parameter s of equation (2) was different for males than for females. Again, however, the issue is whether the models' unspecified parameters depend upon the ascribed and achieved characteristics of the persons to whom they applied, or whether the models' unspecified parameters are independent of such characteristics. This is a scientific- ally important issue, to be sure, but it should not be con- fused with the issue of whether a model is true. 59 The interaction hypothesis about competence-status and number of alternatives also concerns the "nature of the givens." In this case, however, the issue has to do with how the matrix of outcome-sets, discussed in Chapter II, should be constituted, with the nature of the elementary outcomes associated with the withhold judgment alternative. Were we to find an interaction in this case, it would sug- gest that Pr(W), the probability of withholding judgment, is a function of competence-status, which would place con- straints upon the two outcome-sets associated with this alternative. In sum, then, this first stage of our analysis should yield three kinds of useful information. Most basically, it should indicate whether either model is worth pursuing fur- ther; it should also indicate, or at least give insight into, the extent to which our main findings are what the author likes to call "socialization invariant," the extent to which they are independent of the ascribed and achieved character- istics of the subjects. And finally, it should indicate some things about how the withhold judgment option is per- ceived by the subjects who take part in this study, what the "pros" and "cons" of this option are. At this point, let us consider the second state. Second stage.--The second question raised at the outset--that pertaining to the models' divergent predictions-- is amenable to the technique of planned comparisons, applied 60 to theoretically meaningful functions of the response vector (for discussions of this technique, see Hays, 1963: 459-483; Guenther, 1964: 50-54; Blalock, 1972: 330-334). Consider first the following function, which we will call ¢l° ¢l(nS’nC'nW) = ns + 1/2 nw In the two-alternative conditions, the value of this function dsf 0. Now, according is simply the value of ns, since nw to Model One, the mean value of O1 in each two-alternative condition should equal the mean value of ¢1 in the analogous three-alternative condition. This is easily established by means of our basic hypotheses, stated in Chapter II. But according to Model Two, no such equality should exist. Moreover, the inequalities implied by the second model be- come reversed as we move from the (H,L) conditions to the corresponding (L,H) conditions. To simplify our exposition, let us disregard sex and diagram the second model's predic- tions as follows: 2 alternatives 3 alternatives (H,L) 61 > ‘31 (LB) 61 < 51 Let L1 = the sum of the two larger values in this diagram (upper left and lower right) minus the sum of the two smaller values (upper right and lower left). Then Model One's im- plication is L1 = 0, whereas Model Two's implication is 61 L1 > O. This is a planned comparison, and it can be evalu- ated using standard techniques based upon the t-distribution. The null hypothesis represents Model One. But a partisan of Model Two might object that such a test favors Model One, since beta, the size of the Type II error, would almost certainly be larger than alpha, the size of the Type I error. Granted. So let us supplement this comparison with one that reverses the roles of the two models. Consider the following function, which we will call ¢2° In this expression, N is the number of trials. ¢2(ns,nc,nw) = N nS/(ns+nc) In the two-alternative conditions, the value of Oz is simply the value of ns, since N = ns+nC in this case, which cancels with the denominator. Model Two implies that ¢2 of the mean value of the response vector in the two-alternative condi- tions compares with OZ of the mean value in the three- alternative conditions as follows: in the (H,L) case, the first is greater than or equal to the second; and, in the (L,H) case, the first is less than or equal to the second. Model One implies strict inequalities in the opposite direc- tions. For all practical purposes, the two models' impli- * cations are equivalent to the situations diagrammed below. *This is extrapolating from ¢ of the response vec- tor's mean values to the mean values of O. In the two- alternative conditions, the two are the same, since ¢ is linear; however, in the three-alternative conditions, the two differ slightly. Looking ahead to the data, in the (H,L) case, ¢ of the mean values is 20.15, the mean value 62 Model One Model Two 2 Options 3 Options 2 Options 3 Options (H,L) ¢2 < 62 52 3 ¢2 (L,H) ¢2 > ¢2 52 5 ¢2 Paralleling the approach taken before, let L2 = the sum of the two larger values minus the sum of the two smaller values according to Model One. Then Model Two's implication is L2 5 0, whereas Model One's implication is L2‘> 0. Again,this is a planned comparison that can be evaluated using standard teChniques. Here the null hypothesis represents Model Two. These "mirror image" planned comparisons cut right to the center of the differences between Model One and Model Two. Just as an additional check, however, we will also do an ordinary chi-square goodness-of-fit test of each model. Although the goodness-of-fit technique is not as robust with respect to underlying statistical assumptions as the planned comparisons technique, it should nevertheless provide use- ful supplementary information. In particular, if the two approaches should produce contradictory conclusions, this would alert us to the need for additional analysis. In all probability, however, by the time this second stage of the analysis is completed, one model or the other will have a of O is 19.95; in the (L,H) case, ¢ of the mean values is 7.32, the mean value of O is 7.38. It should be noted that this slight bias favors the null hypothesis of the test to be employed. 63 clear edge in apparent tenability; and this brings us to the third question raised at the outset: Given the result, whatever it may turn out to be, what is the strongest iEEEiI fiable conclusion about the relative merits of the two models that can be extracted? Third stage.--The problem can be viewed as that of meaningfully translating Neyman-Pearson type conclusions into the language that working scientists actually speak. That a given model has, let us say, been rejected at the .10 level of significance is evidence to be considered in drawing a scientifically meaningful conclusion, but the statement of such a result is not itself a scientifically meaningful conclusion (cf. Camilleri, 1962). For the record, the present author favors the use of "significance tests." But it must be conceded that the conclusions from such tests, to a considerable degree, "beat around the bush," as it were. They do not cut to the center of what the scientist really wants to know, which is the credibility of his hypoth- esis in light of the new evidence he has just examined. Not that they are irrelevant to this, mind you--their fault is perhaps more non—trenchency than irrelevance. It is to circumventing this fault that the third stage of our analysis is directed. The technique to be used is not new, although it may be unfamiliar to some sociologists. It is based upon Bayes' Theorem, which has long been recognized as an aid to the 64 derivation of unobvious but correct conclusions. Consider a non-scientific example. Suppose one percent of the United States population has tuberculosis. A certain tuberculin test comes out positive ninety-five percent of the time if the person actually has tuberculosis and Ehrss percent of the time if the person is in fact free from the disease. Suppose person x takes this test and it comes out positive. What are the chances that x has tuberculosis? The answer is a surprisingly low twenty-four chances out of a hundred. Now, the scientific uses of the theorem are directly anal- ogous to this: given certain probabilistic information, one computes the chances that a certain conclusion is valid. Now let us be carefu1--in fact, a scientific conclusion is either true or false, just as, in fact, x either has or does not have tuberculosis. But the point is that, on the basis of given evidence, a certain degree of confidence in a con- clusion is optimally rational. More confidence is unwar- ranted, and less confidence is equally unwarranted. An analysis based upon Bayes' Theorem is very well suited to "crucial experiments" involving stochastic models. To see why, let us review the features of a so-called "cru- cial experiment." Suppose there are two models, M1 and M2, that yield empirically indistinguishable predictions in most cases, that account for the relevant, known evidence equally well. For example, several variant models of "learning theory" yield empirically indistinguishable 65 "learning curves." Suppose that, at a given date, there is no solid basis for preferring either model to the other. In time, however, someone discovers discrepant implications. An experiment is designed whose outcome can be compatible with M1 or M2 but not with both. Such an experiment would be "crucial." In principle, its execution would lead to the rejection of one model, the acceptance of the other. Unfortunately, research is never quite this swift and clean: "In sober fact the crucial experiment does not conclusively establish one alternative while making the [second] absolutely untenable; at most it only alters the balance of probabilities" (Kaplan, 1964: 152). Going into a crucial experiment, the two models must be considered equiprobable, since they have always tied in head-to-head competition, so to speak. But coming out, one or the other must ordinarily be accorded the edge, for remaining aloof to the evidence is "a form of insanity in which truth is by fiat," to borrow an apt phrase from R. D. Luce. The problem is how to fairly express that edge, and this is where Bayes' Theorem enters. A Bayesian analysis eschews categorical conclusions-- for example, that M is now tenable and M2 is not, or vice l versa. Instead, its conclusions relate how the "balance of probabilities" has changed--from .5-.5 to .3-.7 or whatever. This is clearly in the spirit of Kaplan's remarks: a cru- cial experiment only alters the balance of probabilities. 66 Of course, given a sequence of tests, covering the range of the two models' divergent predictions, this balance will indeed converge to 0.0-1.0 or l.O-0.0; but the point is that we are not put in the indefensible position of deciding bee tween models on the basis of a single test. Let Cr(Ml) and Cr(M2) denote the credibilities of Mod- el One and Model Two relative to each other. Cr(Ml) + Cr(M2) dgf 1.0. Now Bayesians distinguish between prisr and pssssr risr credibility, the temporal reference being to a given consideration of new evidence--say, to the analysis of new experimental data. To distinguish between credibilities of the prior and posterior varieties, let us prime the latter. That is, let Cr(Mi) and Cr'(Mi) denote prior and posterior credibilities, respectively. Finally, let Pr(D: Mi) denote the probability of the event that the focal data--the new evidence--will have the observed characteristics siyss the event that Mi is true. Then the relationship between prior and posterior credibilities can be expressed as follows: Pr(D : Mi)Cr(Mi) Cr'(M.) = ’ Pr(D : M1)Cr(Ml) + Pr(D : M2)Cr(M2) (i=l,2) (3) For a classical crucial experiment, Cr(Ml) = Cr(M2) = 1/2; thus, the only problem in using this application of Bayes' Theorem is to compute Pr(D : M1) and Pr(D : M2). Needless to say, computing exact probabilities re- quires exact knowledge of the pertinent distributions. In the present case, we would have to know the exact distribution 67 of the response vector (ns,nc,nw). We do not. One alter- native would be to attribute to this vector a certain dis- tribution and proceed from there. For instance, we could attribute to it a multinomial distribution--or the distribu- tion arising from a specified summed Markov process. But this would have the disadvantage of confounding our calcula- tions with a rather strong auxiliary assumption. There is a better way. Recall L and L l 2' section. Both are asymptotically normally distributed, defined in the preceding since both are functions of sample means (see Wilks, 1962; 259). Thus, whatever the response vector's distribution, these quantities computed from it have distributions that are more or less known. It is instructive to recall in this connection that, in the second stage of our analysis, we put to use the fact that Lland L2 conform closely to the t- distribution with 76 degrees of freedom. Now, save far out in the tails, the t density function, given 76 degrees of freedom, is virtually indistinguishable from the normal density function with the same mean and variance. Their corresponding values might differ at, say, the tenth decimal place, but, for all practical purposes, they are the same. This confers plausibility upon the following result, although this result draws it primary justification from normal approximation theory: — - 1 x - E(Li) fi(X) = ¢ S. S. l 1 68 where fi is the density function of Li’ ¢ is the standard normal density function, and si is the estimated standard E(L deviation of Li' Under M = 0; and, under M2, E(L2) 1' 1) z 0. In the latter case, if we are willing to tolerate a slight bias in favor of the Camilleri 2E_El- model, Model Two, we can assume that equality holds. Now it is clear that there is some connection between fi(x) and Pr(D : Mi). Let Da and Db be two data-sets, and let xa and xb be cor- responding values of Li (i = l or 2, arbitrarily). Then it is intuitively clear that fi(xa)/fi(x = Pr(Da : Mi)/ b) Pr(Db : Mi). That is, the probability of getting the observed data-set is proportional to the height of the density func- tion. In making comparisons across different normal density functions, however, it must be remembered that such functions differ in average height. For example, a normal density whose standard deviation equals ten will be much shorter than one whose standard deviation equals one. More precisely, if c1 and c2 are the upper .05 critical values of the re- spective distributions, then the former density at C1 will be one-tenth as tall as the latter density at c2. (The choice of .05 is, of course, immaterial.) So to make the comparisons valid, it is necessary to multiply each density by its standard deviation. The principle this leads to, in the present case, is the following: Pr(D : Ml) z ¢(xl/sl) Pr(D : M2) ¢(s2/s2) , (4) 69 where x1 and x2 are the observed values of L1 and L2. We might note that if Model One and Model Two were to "compete to a standoff" in the second stage of our analysis, then the right hand ratio would equal one; and this is certainly what we would expect the left hand ratio to equal in such a case. Although the value of this ratio does not tell us the values of Pr(D : M1) and PR(D : M2), it does tell us all we need to know to use equation (3). Therefore, we have at our disposal a way to circumvent the seemingly intractable problem of computing the quantities necessary to use a Bayesian analysis. It is instructive to apply equations (3) and (4) to a hypothetical case, as this gives some understanding of the relationship between the second and third stages of our analysis. Suppose that, in the planned comparisons of the second stage, one model were to mispredict its L (Ll for Model One, L2 for Model Two) badly enough that it could be rejected at the .05 level of significance; and suppose that the other model were to be right on target in predicting its L. Then the calculated probability ratio of equation (4) would be .2565 or 3.899, depending upon which model were which; and the posterior balance of credibilities would be .2-.8 or .8-.2, again depending upon which model were which. Thus, even in this relatively extreme case, we would be cautioned not to be more than eighty percent confident that the seemingly better model were in fact the model of 70 greater promise. Perhaps the most important function served by a Bayesian calculation of the kind indicated here is to restrain the investigator from making either too little or too much of his results, to restrain him from weighing the evidence either too lightly or too heavily in assessing the relative merits of the opposing models. This concludes a reasonably detailed description of the present research: its design, its experimental procer dures, and its statistical procedures. This description has been merely preparation, of course, for what is still to come. In Chapter IV, to which we shall now turn, the actual data will be examined, the actual performance of each model will be scrutinized. Without further delay, let us now proceed to this climactic chapter. CHAPTER IV THE RESEARCH: RESULTS AND DISCUSSION Preliminary Notes The experiment, for the record, was completed on May 31, 1973. A total of forty-eight sessions had been con- ducted, in which ninety-five naive subjects and one confed- erate had taken part. Immediately following each post-session interview, the author decided whether the subject in question should be included in, or excluded from, the sample. Since we were aiming for ten subjects in each experimental condi- tion, eighty subjects in all, it can be seen that, for one reason or another, fifteen subjects were excluded. Before analyzing the data, it might be well to indicate the criteria upon which judgments to exclude subjects were based. First, a subject was excluded if he volunteered being suspicious about either the part one competence—status manipulation or the part two initial choice disagreements-- that is, about the fictitious aspects of the experiment. Eight persons fell into this category, all of whom had had prior experience with studies they perceived to be similar to the present one. The exclusion of these subjects' data seemed advisable, since, strictly speaking, these persons were not naive subjects. 71 72 Second, a subject was excluded if his frame of refer- ence, or definition of the situation, proved to be markedly atypical. In seven cases, the author decided that the per- sons in question just did not meet the assumptions that are necessary if the data analysis is to be valid. This requires some explanation. Both models, as we know, are utility formulations. Each asserts that a subject's behavior will depend upon what he values and disvalues, upon what has utility for him. Now, in an empirical test such as the pre- sent one, it does not matter what a subject values or dis— values--our basic hypotheses are completely general in this respect. But it matters very much, indeed it is crucial, that a subject's orientation, determined by what he values and disvalues, be shared with his fellow subjects. Whenever group data are used to test an explicit utility formulation, homogeneity of orientation, both within and across groups, is an inescapable condition of the analysis. If a subject has a clearly atypical orientation, then he simply does not meet this essential condition. In the present case, it was posited that the focal actor values the approval of his partner, and that he perceives his partner's ability as dif- fering from his own. It will be recalled that there were other assumptions of the social influence application as well, but these two are relatively easy to check in conjunc- tion with the post-session interview. In three cases, sub- jects were eliminated because they thought the part one test 73 was "pure luck." (In fact, these subjects were correct, albeit not in quite the way they imagined: their scores came about with the help of a random number table.) In the other four cases, there was serious doubt about whether the persons in question placed any value whatsoever upon their partners' approval. In these cases, there is obviously a fine line between one decision and the other; yet such judgments must be, and were, made. Our paramount concern, of course, was that these judgments not affect the data preferentially in regard to the two models. To this end, these judgments were made before the data were analyzed--in most cases, weeks before the graph paper of the Esterline Angus event recorder, which unwinds and winds up again like a typewriter ribbon, was even unwound. This should have ensured that there would be no systematic benefit to either model relative to the other; however, just to make sure, the author did recompute the chi-square values to be presented shortly with the suspect data included. It turned out that, as might have been an- ticipated, neither model fitted quite as well as it did without the suspect data thrown in; but the worse fitting model lost additional ground to the better fitting model, dispelling any lingering suspicion that the better fitting model might owe its better fit to the selection of the sub- ject groups. 74 We mentioned earlier that the goal was to have ex- actly ten subjects in each experimental condition. This requires only very brief comment. The number ten was based mainly on practical considerations. Each additional subject per condition would have required a minimum of four addi— tional experiments. Life being short and these experimental sessions being quite lengthy, ten seemed like an appropriate number. As we know, the power of the F and t tests goes up as the square root of the sample size. The desire for sqssi sample sizes is much less arbitrary: although the robust- ness of the statistical procedures described in Chapter III is highly gratifying when the sample sizes are equal, it attenuates rapidly when they are not. After discussing such considerations, Hays offers the following succinct advice: ". . . use samples of the same size" (Hays, 1963: 322, italics in the original). Although one hesitates to let methodological considerations dominate his thinking, to dismiss them too lightly is to seriously undermine the in- tegrity of the research process. The issues we have been discussing are not often discussed in research reports. Lest the reader be given the impression that these matters were more troublesome in the present research than in most other research, we wish to reassure him that they were not. In a study of this type that is representative, thirty-four percent of the data were eliminated (Berger et al., 1969: 491). For all reasons 75 combined, sixteen percent were eliminated in the present study, including at least one from each of the eight condi- tions and no more than three from any one condition. The eighty observed values of the response vector are presented in Table 3. The Models' Parallel Implications Our initial concern, as indicated in Chapter III, was with whether either model adequately accounts for the gross features of the data, whether the gross, common "order- ing implications" of the two models are borne out. Based on the models, we would expect, first of all, that subjects in the (H,L) conditions would change less often than sub- jects in the corresponding (L,H) conditions. Second, we would expect that subjects in the two-alternative conditions would change more often than subjects in the corresponding three-alternative conditions. Third, we would expect that subjects in the (H,L) conditions would stay more often than subjects in the corresponding (L,H) conditions. And fourth, we would expect that subjects in the two-alternative conditions would stay_more often than subjects in the cor— responding three-alternative conditions. These four pre- dictions are implications of both models. In each case, we tested the null hypothesis, the hypothesis of no differ- ence, and in each case we had to reject this hypothesis, thus accepting as confirmed the predictions of the two models. 76 Table 3. Observed values of the response vector (n ,n ,n ) by condition. 8 C w 2 alternatives 3 alternatives men women men women (20,05,00) (20,05,00) (18,03,04) (15,07,03) (19,06,00) (21,04,00) (19,03,03) (21,01,03) (20,05,00) (19,06,00) (21,04,00) (23,02,00) (18,07,00) (23,02,00) (10,08,07) (12,07,06) (21,04,00) (18,07,00) (16,03,06) (21,04,00) (H'L’ (21,04,00) (22,03,00) (21,03,01) (15,04,06) (19,06,00) (20,05,00) (20,05,00) (21,03,01) (17,08,00) (16,09,00) (21,02,02) (17,04,04) (16,09,00) (22,03,00) (13,06,06) (09,10,06) (22,03,00) (20,05,00) (21,00,04) (15,05,05) (14,11,00) (15,10,00) (07,13,05) (04,11,10) (06,19,00) (06,19,00) (03,19,03) (09,14,02) (05,20,00) (04,21,00) (11,08,06) (09,15,01) (10,15,00) (10,15,00) (05,18,02) (05,20,00) (15,10,00) (07,18,00) (12,11,02) (03,16,06) (L'H) (16,09,00) (09,16,00) (01,13,11) (01,21,03) (07,18,00) (07,18,00) (08,12,05) (05,17,03) (02,23,00) (12,13,00) (06,11,08) (06,09,10) (12,13,00) (08,17,00) (00,24,01) (07,10,08) (01,24,00) (09,16,00) (05,13,07) (11,10,04) 77 The ANOVA summaries are presented in Table 4 and Table 5. The effect of competence-status is significant far beyond the normally reported levels; and the "number of alterna- tives" effect, although less potent, is still clearly pres- ent. The various questions about "the nature of the givens" raised in Chapter III also appear to be answered. Ssx does notflappear to make anydifferenpe, and_there does not appear to be any interaction among the main effects. .Indeed, the F ratios for sex and the interactions are lpwer than might be expected by chance alone. As an aside, the direct meaning of a low F ratio is that the mean squared error is larger than would be expected on the basis of the between group comparisons. The substantive implication is that there may have been some unanticipated variance causing factor whose effect was somehow equalized across groups. Time of day is one possibility. Another is time of the aca- demic term--perhaps the pressures of pending exams and the like would exert some effect. As with time of day, this would have been more or less equalized across groups but would have been variable within groups, thus increasing the mean squared error disproportionately. There may be other possibilities as well; however, what is less speculative is that the predicted effects did occur, whereas the sex and interaction effects did not occur. This suggests that social influence, as a phenomenon, probably has a relatively simple 78 Table 4. ANOVA of the change-response component. Source SS df MS F (A) Competence-Status 2205.000 1 2205.000 177.46** (B) # of Alternatives 48.050 1 48.050 3.87* (C) Sex 0.200 1 0.200 0.02 AxB 4.050 1 4.050 0.33 AxC 0.000 1 0.000 0.00 BxC 4.050 1 4.050 0.33 AxBxC 4.050 1 4.050 0.33 Error 894.600 72 12.425 TOTAL 3160.000 79 * Significant at the .10 level (p = .06) ** Significant at the .001 level Table 5. ANOVA of the stay-response component. Source SS df MS (A) Competence-Status 2531.250 1 2531.250 189.61** (B) # of Alternatives 130.050 1 130.050 9.74* (C) Sex 0.050 1 0.050 0.00 AxB 1.800 1 1.800 0.13 AxC 0.200 1 0.200 0.01 BxC 3.200 1 3.200 0.24 AxBxC 6.050 1 6.050 0.45 Error 961.200 72 13.350 TOTAL 3633.800 79 * Significant at the .005 level ** Significant at the .001 level 79 theoretical structure with some remarkable invariant proper- ties. It is clear that the well recognized socialization differences between males and females in contemporary Ameri- can society have little or no effect upon the influence phe- nomenon; and this makes it at least tenable that social in- fluence may have some other "socialization invariant" proper- ties as well. The fact that the models' parallel predictions are borne out lends a certain amount of credibility to each model; however, it does nothing to distinguish between the two models. Let us now turn to some findings that bear upon the relative merits of the two models. The Models' Divergent Implications This brings us to what was described in Chapter III as the second stage of our analysis. Before performing the calculations described there, however, it is instructive to examine the observed response proportions by experimental condition. These proportions are presented in Table 6. Since sex was apparently not an important factor in the experiment, we have collapsed the eight experimental condi- tions down to just four, combining the comparable male and female groups. The symbol "(H,L)-2" refers to the focal actor having high competence-status, his partner having low competence-status, and there being two alternatives. The similar symbols have analogous meanings. Now, the estimated 80 Table 6. Observed response proportions by experimental condition. Condition 1 Condition 2 Condition 3 Condition 4 nS/N .788 .698 .350 .236 nc/N .212 .168 .650 .570 nw/N --- .134 --- .194 sizes of the competence-status effect and the "number of alternatives" effect can be determined from this table. To see the former, compare Condition 1 with Condition 3, Condi- tion 2 with Condition 4. To see the latter, compare Condi- tion 1 with Condition 2, Condition 3 with Condition 4. At this point, let us consider the relative fits of the two models. The most easily interpreted measure of fit, on the face of it, is the chi-square goodness-of-fit value. Estimates of the expected cell frequencies under each model must be computed separately for the (H,L) and (L,H) condi- tions. Although chi-square values and degrees of freedom are additive, it is more instructive to see the two values for each model uncombined. After one degree of freedom is subtracted for each linear constraint on the data (the cell frequencies for each condition must add to 500) and for each parameter estimated (there must be two parameters esti- mated in each case), we are left with one degree of freedom 81 in each case. Summaries of the calculations are presented in Table 7. It is found that both models fit quite well Table 7. Chi-square goodness-of-fit values. (H,L) Conditions (L,H) Conditions Model 1 0.8968 0.3728 Model 2 0.4643 3.3290* *Significant at the .10 level (p z .07) in the (H,L) conditions--the empirical frequencies fall be- tween the models' predictions--but that the Siegel st_si. model fits much better than the Camilleri st_si. model in the (L,H) conditions. Although the one departure from the Camilleri st_si. model's prediction appears to be signifi- cant at the .10 level, this should not be accepted uncriti- cally, for the goodness-of—fit test assumes that the under— lying distribution is multinomial and that there is perfect homogeneity of the parameter for each cell. At best, this is only approximately true in the present case (for a good theoretical discussion of this test, see Hoel st_s1., 1971: 91-99). Therefore, the precise level of significance should be viewed with a healthy skepticism, although the chi-square values are nonetheless comparable with each other. Let us now consider the planned comparisons described in Chapter III. It will be recalled that these comparisons were based on divergent inequalities derived from the two 82 models. These comparisons can be regarded as tests of the models' "ordering implications," but these ordering impli- cations are much more trenchant than those considered in the preceding section. They focus sii the data from sii the experimental conditions upon the prime area of disagreement between the two models; therefore, if a coup de grace is possible, these comparisons are the ones to provide it. Carrying out the calculations, we arrive at the i results that are summarized in Table 8. The Siegel st_si. model appears to account for the experimental data very well Table 8. Theoretical and observed values of L1 and L2. Theoretical Other Model's Observed Value‘ Implication Value Model 1 L1 = 0 L1 > 0 0.1500 0.00 Model 2 L2 5 0 L2 > 0 1.6145 1.02* *p 3 .15 indeed; the Camilleri st_si. model appears to account for the data somewhat less well. To compute t in the latter case, we took the liberty of assuming that E(L2) = 0, a conservative assumption to be sure. It is found that neither model is rejectable at the customary levels of significance. What to conclude? That is the question. 83 An A Posteriori Assessment The objective of this dissertation, as stated in Chapter I, is, at the broad level, to shed as much light as possible on whether man is a "balancing" or a "utility maximizing" organism. How does he combine and use the in- formation available to him? Does he balance his choices vis-a-vis the gains from the respective alternatives, or does he select a strategy so as to maximize his total gain? At the more narrow level, the objective is to assess the relative merits of two mathematical models representing these respective principles. These abstract models of behavioral decision making have now been applied to a concrete situa- tion, empirical evidence about this situation has been gathered, and this evidence has been analyzed. At this time, it is incumbent upon us to extract a conclusion, to summar- ize the meaning of what we have found for the questions with which we began, to distill from our work its significance. Let us carry out the Bayesian computation summarized by equations (3) and (4) of Chapter III. This computation goes as follows. Let PR denote the probability ratio of equation (4). Then = ¢(0.10) = .3970 = , PR FTITFET .2371 1°674' . _ (1.674) (1/2) _ . ' Gr (M1) ‘ (1.674) (172) + (1.000) (1/2) " 0°625' and Cr'(Mz) = l - Cr'(M = 0.374. 1) 84 According to this computation, the odds, which were assumed to be even prior to this research, are now five to three in favor of the Siegel st_si, model. On the basis of the evi- dence now available, the Siegel st_si, model must be consid- ered more credible than the Camilleri st_si, model. Correspondingly, the utility maximizing principle must be considered more credible than the balancing principle. To put this conclusion in perspective, however, let us ask what change in status would occur if this study were to be repeated, and if the result the second time were to be (1) exactly the same, or (2) exactly the reverse. In the first case, we would have (l.674)(.626) C'r"(M1) = (1.624)(.626) + (1.000) (.374) = 0°737’ and Cr"(Mz) 1 - Cr"(Ml) = 0.263. Thus, the odds would become roughly eight to three in favor of the Siegel et a1. model. In the second case, PR would equal .597, and we would have ) (0.597)(.626) -_ 1 ’ (0.597T(.626) + (1.000)(.374)' Cr"(M 0.500; and Cr (M2) = l - Cr (M1) = 0.500. Thus, the odds would become even again. These computations underscore the fact that our conclusions, like all scientific conclusions, are tentative and are always subject to revi- sion on the basis of further evidence. 85 It is perhaps appropriate at this time to indicate a few of the directions that further research could take. The most obvious one, of course, is the one taken by the present research. Although the reward structure of sociology does not favor replicational research, there would neverthe- less be clear scientific value in repeating the present study. Perhaps one of Camilleri's graduate students looking for an MA project could take on such a task. This would give a clearer idea of whether the trends present in our data are stable, thus making it clearer whether other di- rections are required. We are thinking in terms of the Camilleri st_si. model at this point, since, as things now stand, the Siegel st_si. model is relatively unscathed. If it became clear that the trends apparent in our data are stable, another possible direction would be to investigate the possibilities of "loosening up" some of the assumptions of the present analysis, most notably the assumption that the utilities us, uo, and ut remain constant when a third alternative is added to the choice-set. This line of in- quiry produced, in a related context, the best showing of the Camilleri st_si. model to date (see Balkwell, 1969). A third possible direction would be to consider applications of one or both models to phenomena other than social influ- ence. Although the social influence application has consid- erable sociological significance, it is not clear that it is the most representative application of behavioral decision 86 making theory. And although it has been suggested that ". . . all decision making is guided by an abstract set of axioms which vary only in the manner in which they are oper- ationalized in specified situations . . ." (Ofshe and Ofshe, 1969: 337), this is hardly a proven fact. Perhaps the Siegel st_si. model is more valid for some kinds of decision making, the Camilleri st_si. model for others. Perhaps different axioms apply to social choice behavior than to non-social choice behavior. Perhaps there are as yet unknown conditioning factors that determine what set of axioms will be operative, even within well defined classes of decision making situations. The possibilities are almost endless, and no one knows many of the answers. But, through research, it should be possible to find some of them. Research com- bined with hard theoretical work, that is. In conclusion, let us merely resubmit the question around which this entire dissertation, our entire theoreti- cal and empirical effort, has been structured: Does the Camilleri st_si. model or the Siegel st_si. model more ade- quately account for observable social influence decisions? Accordingly, are such decisions more adequately accounted for by a balancing principle or by a utility maximizing principle? On the basis of present evidence, the Siegel st_si. model and the utility maximizing principle are the better bet. The odds are five to three. CHAPTER V EPILOGUE ON POST-1971 DEVELOPMENTS Although references have been updated and a few of the arguments have been refined in minor ways, the theoreti- cal analysis of this dissertation is essentially as it was in December, 1971. A finished dissertation proposal was distributed to the Faculty in early 1972, and that proposal was officially approved on February 29, 1972. Chapters one through three of the present document are practically word for word from that proposal. Twenty months have now passed, and, during this period, the author has done some additional theoretical work that is sufficiently important and germane to warrant inclusion in some form or other. We have chosen to present this work in an epilogue. Essentially, we have developed two new models of behavioral decision making; and the implications of these put both the accomplishments and the limitations of our previous work in a truer light. Moreover, they raise questions that must be faced by the present author, by Camilleri, by Siegel, and by anyone else who wishes to do futurecreditable work in this area. Let us begin by reconsidering the distinction be- tween "balance" and "utility maximization," first discussed in Chapter I. 87 88 The Demise of a Distinction A major enphasis of the original dissertation pro— posal was that the proposed research would shed light upon whether man strives for balance or for utility maximization when he make choices. It is now clear that the latter principle is much more general than the former, and, indeed, that it includes the former as a special case. To demon- strate this, it suffices to show that the balancing notion can be derived from a utility maximizing formulation. Before such a demonstration is made, however, it should be empha- sized that this does not in any way undermine our previous work insofar as that work is understood as a comparison of the Siegel stisi, and Camilleri st_si. models. It only undermines the more abstract comparison of balancing and utility maximization as separate basic principles. The first model to be presented, which we will call Model A, assumes a repetitive choice situation like that of a typical decision making experiment. Our concern, as in previous chapters, is with a focal actor's stable-state choice strategy. We assume a choice-set A = {A1,A2, . . ., A@} and N trials. Model A has five axioms which can be stated as follows. AXIOM Al: T = G(l) + G(2) + . . . + G(N) + GV, where T is the focal actor's total gain, G(t) is his gain from the t th decision, and GV is his gain from variability. 89 AXIOM A2: G = 9k + Qm’ where G is the expected positive k k utility of alternative A and where gk and Qm kl are as given by the auxiliary definitions of Chapter II. AXIOM A3: G(t) = log(Gk) iff'Ak e A is selected on the t th trial. AXIOM A4: GV = (l/b)[N log(N) - 2 ni log(ni)], where the summation is over i=l,2, . . ., m, ni is the number of times out of N that Ai is selected, and b is a scale factor. AXIOM A5: Let n = (n1,n2, . . .,nm) be the vector of fre- quencies with which the alternatives A1,A2, . . °’Am are selected. Then E(n) = n*, where n* = (ni,n§, . . .,ng) is the unique solution to the m-l linearly independent equations in m-l unknowns determined by m = 0, i=l,2, . . .,m; and Z ni = N. 3T 8n. 1 i=1 Although it is generally agreed that the axioms of a scien- tific system do not require intuitive justification, we would like to point out that Axiom A4 admits of an interest- ing rationale. The function given by the axiom is a variant of the "uncertainty" function of information theory; and its verbal translation can be put as follows: the focal actor's gain from variability is proportional to the uncertainty of his choices to an observer. That is, what an onlooker ex- periences as uncertainty is experienced by the actor him- self as variability, as the absence of monotony. This function and rationale should not be confused with the 90 corresponding function and rationale of the Siegel st_si. model, although the broad notion that the focal actor values variability is the same. Before proceeding, let us note two things. First, Model A is a utility maximizing model by virtue of Axiom A5. It can be shown that the solution to the equations in- dicated by the axiom does in fact maximize T. Second, if p is the focal actor's strategy, then p = (l/N)n*; that is, for i=1,2, . . .,m, Pr(Ai) = (l/N)n§. Drawing this connec- tion is equating p with the vector of expected relative frequencies, which is congruent with the usual conception of a strategy found in the decision making literature. Now let us turn our attention to deriving the balancing prin- ciple from Model A. For convenience, let Ti be the subtotal of T that results from selecting alternative Ai’ (i=1,2, . . .,m). Then Ti= log(Gi) + log(Gi) + . . . + log(Gi); [ni terms] = ni log(Gi). T itself is as follows. m m T = 2 Ti + GV = 2 n1 log(Gi) + GV; i=1 i=1 J; m i=1ni log(Gi) + (l/b)[N log(N) -i:lni log(ni)] This is Model A's utility function. The next step is to maximize it and thereby determine the vector n*. Unfortu- nately, the usual calculus techniques for maximizing a 91 function cannot be directly applied here, because we have only m-l independent variables, due to the restriction that Zni = N. This problem can be circumvented by algebraically eliminating an arbitrary variable or, equivalently, by in- troducing a Lagrange multiplier A and then applying the usual techniques to the Lagrangian function, which is m m 2 L = nilog(Gi) + (l/b)[N log(N) - '2 ni log(ni)] + A 1 i=1 i ( .: ni-N). i l The unrestricted maximum of L will coincide with the restric- ted maximum of T; therefore, it suffices to find the former. Differentiating L with respect to each ni and setting the partial derivative equal to zero, we get the following: _ 3L = _ (Ill-4 [1 + log(ni)] + A, (i=1,2, . . .,m). This holds for each ni; therefore, for arbitrary i and k, log(Gi) - (l/b)log(ni) = log(Gk) - (l/b)1og(nk). This is equivalent to nk(Gi)b = ni(Gk)b. Holding k constant and m summing with respect to 1 yields nk 2 (Gi)b = N(Gk)b. i=1 m Therefore, n* = N(G )b/ X (G.)b. Now, since Pr(A ) = k k i=1 i k (l/N)n*, we arrive at the following: (Gk)b (k=1 2 m) THM SCHEMA A1: Pr(Ak) = ________,. . . - - .. . (G 1 "bag . k) l )1 92 Notice that, in the special case of b = 1, Theorem Schema A1 is the balancing_principle; and this theorem schema has been derived from a utility maximizing formulation. To summarize this first point, then, the distinction between a "balancing" and a "utility maximizing" principle is not a distinction between separate basic principles. Balance is a special case of utility maximization. Whether the other "balance" concepts employed in social science are similarly reduceable remains to be seen, but the feasibility of this merits exploration. There is also a second point that emerges from con- sidering Model A. Note that, from Axiom A2 and Theorem Schema Al, the following straightforward consequence can be obtained. b (9k+Qm) THM SCHEMA A2: Pr(Ak) = m . (k=1,2, - . .,m). b .2 (gi+Qm) i=1 If this theorem schema is compared to Theorem Schema Cl, presented in Chapter II, the following conclusion seems in- escapable: there is no conceivable evidence that could refute Model A while, at the same time, confirming the Camil- leri st_si, model; however, evidence that would refute the Camilleri st_si. model would not necessarily refute Model A. Model A, therefore, subsumes the Camilleri st_si, model. The relationship between Model A and the Camilleri st_si. model is most noteworthy, however, in regard to their respective highest-level hypotheses. Model A yields as a 93 theorem schema the Camilleri et a1. model's so-called "basic postulate" (Camilleri et al., 1972: 25). In other words, Model A yields as a derivation what the Camilleri et a1. model merely asserts--viz., the balancing principle. An Alternative to the Siegel et a1. Model The results of our research, which were reported in Chapter IV, clearly lend credibility to the Siegel st_si. model. This research provided a stiffer test than others that have been reported in the literature, and the Siegel st_si. model met this test quite satisfactorily. This situ- ation is clouded somewhat, however, by the fact that there is a model, developed by the author, that is very different from the Siegel st_si. model, that contradicts the Siegel st_si. model on substantive points of some importance, but that implies the same empirical consequences with respect to our study. The assumptions of this model, which we shall call Model B, are the same as those of Model A. Model B has four axioms. AXIOM Bl: T = G(L) + G(2) + . . . + G(N), where T is the fo¢a1 actor's total gain, and G(t) is his gain from the t th decision. AXIOM B2: G(t) = (l-d)rexp(gk) iff AR 6 A is selected on the t th trial and Ak has been selected exactly r times prior to the t th trial. The quantity d is the discount rate. 94 AXIOM B3: d = 1 - e-b/N, where b is an empirical parameter. Notice that d + 0 as N + 09; and d + l as N + 0. AXIOM B4: Let n = (n1,n2, . . .,nm) be the vector of fre- ' ' quencies with which the respective alternatives are selected. Then E(n) = n*, where n* is the unique solution to the m-l linearly independent equations in m-l unknowns determined by m = 0, i=1,2, . . .,m; and ,2 n. = N. i=1 1 A closed form expression of Pr(Ak) can be derived from these it: 3n. 1 axioms, the derivation being similar to the one presented in i the preceding section. To ease the notational burden some- what, let Ei = exp(gi); also, let Ti be the subtotal of T that results from selecting Ai' (i=1,2, . . .,m). Then _ _ _ 2 _ n.-1 . Ti — Ei + (1 d)Ei + (1 6) Bi + . . . + (1 d) 1. E1, = (l/d)[1 - (l-d)ni]Ei. T itself, then, is this: m m m n T = 2 Ti = (l/d) 2 Bi - (l/d) z (l-d) i Ei. i=1 i=1 i=1 It is clear that T attains its maximun when the vector n is such that Z (l—d)niEi is minimized. Let us define the La- grangian function m n m L = 2 (l—d) iE. + A( Z n. - N). . i - . 1 i=1 i=1 It can be shown that the unrestricted minimum of L coincides with the restricted maximum of T; therefore, it suffices to find the former. Carrying out the usual procedure, we get 0 = 3%t-= (1-d)niEi log(l-d) + 1 , (i=1,2, . . .,m). i This holds for arbitrary ni; hence, for any i and k, 95 (l-d)niEi = (1-d)nk Ek; and taking logarithms of both sides, nilog(1-d) + gi = n log(l-d) + gk’ Holding k constant and k summing both sides with respect to i yields m N log(l-d) + X g. = mn log(l-d) + mg . Solving for n ._ i k k k i—l and, by Axiom BB, substituting l - e-b/N for d, we get m n* = N/m + (N/mb)(mg - E g.), (k=1,2, . . .,m). Di- k k i=1 i viding through by N brings us home. m mg - 2 g. l k ._ i _ THM SCHEMA Bl: Pr(A ) = — + 1‘1 ' (k’l'z' ° ° °'m)' k m b m Now this is an interesting result. If it is compared to Theorem Schema 81, presented in Chapter II, it can be seen that the two are alike except for the form of an empirical constant. This minor difference makes no difference in the derivation of the "basic hypotheses," presented at the end of Chapter II; and this means that the results of our re- search support Model B to exactly the same degree that they support the Siegel st_si. model. This fact is not trivial. The two models are based upon very different substantive ideas. For example, accord- ing to Model B, as the number of times the focal actor chooses a given alternative increases, the marginal utility of that alternative decreases; but, according to the Siegel st_si. model, the marginal utility of each alternative is constant. The two models also entail quite different con- ceptions of the utility function--in fact, they share only one thing in common: by virtue of Axiom S3 and Axiom B4, they are both utility maximizing models. 96 The full implications of Model B's existence have not been explored at this time. Quite clearly, however, it clouds the interpretation of the present research, to say nothing of the interpretations of several previous investi- gations. Conclusion In this chapter, we have presented two new models of behavioral decision making. These models unsettle some things that seemed to have been settled when the author's dissertation proposal was accepted by the Faculty. Origin- ally, we proposed a comparison between the Camilleri st_si. model and the Siegel st_si. model, and this comparison was carried out as planned. But we suggested that this was to be more than just a comparison between two particular models: it was to be a comparison between "balancing" and "utility maximizing" as basic principles of human choice behavior. We need not have done any empirical research to settle this--the formal argument presented in this chapter vitiates the assumed distinction. Our Model A is a utility maximizing model from which the balancing principle can be derived. The development of Model A opened Pandora's box. Might there not also be other models with interesting impli- cations? Pursuing a hunch, we developed a second model, 97 Model B, that implies exactly the same empirical implica- tions--at least insofar as the research of this dissertation is concerned--as the Siegel EE_31° model. That this muddies the water need not be labored. All in all, what are we to conclude from the work of this chapter? We have, of course, presented two new models of behavioral decision making, one of which subsumes the Camilleri st_si. model as a special case. Both Model A and Model B merit continued investigation, both theoreti- cal and empirical. But this chapter also carries a broader and deeper implication: new standards of discrimination are required if further scientific progress is to be pos— sible. Studies designed to test a single model of behaVr ioral decision making no longer meet important scientific needs. That is to say, research not bearing upon conflict- isg predictions of at least two credible models can add nothing but chaff to the fund of knowledge. Such research should be discouraged. What we need, now more than ever, is research focusing on matters where one credible model or theory takes issue with another; and research results must be judged by the degree to which they alter the balance of credibility. This, we submit, is the broader and deeper implication of the present chapter. a: - ‘ at ’3 «12' J. x". ‘. I. APPENDICES APPENDIX A THE EXPERIMENTAL MATERIALS Part One Instructions: All Conditions First of all, let me introduce myself. I'm Jim w‘l Jim.fi' Balkwell, and I'll be your host in today's study. On behalf of the sociologists who are conducting this study, I'd like to thank you for joining us. We think you'll find this to be an interesting as well as a rewarding experience. What we're doing is studying the ways persons solve certain kinds of problems. More precisely, we're studying the ways persons solve those problems under two different conditions. In keeping with this, our work today will be divided into two separate parts, which we call "phase 1" and "phase 2". In each part, you'll be asked to solve problems, but the conditions under which you'll work will differ. I'll explain more about both the problems and the conditions as we go along. We'll now turn to phase 1 of our work. Sociologists have known for many years that the ability of persons to accurately perceive the relationships within figures or patterns is quite limited. It's known, for example, that two figures or patterns can differ by as 98 99 much as five percent without this being noticeable to most persons. Differences this small simply can't be seen by most persons. Recently, though, it's been discovered that the variation among persons in this ability is much greater than we once thought. It has become clear that there are persons who can detect differences that are very slight eighty or ninety percent of the time. We call the ability to correctly distinguish two figures or patterns that differ slightly "contrast sensitivity." As of now, no one knows for sure why some persons have more contrast sensitivity than others. Dozens of studies have been done, and it's been found that contrast sensitivity is completely unrelated to such things as artis- tic ability, mathematical ability, and general intelligence. You might think that it would be related to one or more of these other abilities; however, it doesn't seem to be. In spite of that, though, there are certain sociological rea— sons why we want to learn more about it. What we're going to do today, in phase 1, is admin- ister a test that measures this ability. The test has been given to thousands of college students in the past and is known to be a very reliable, valid test of how much contrast sensitivity a person has. The test has twenty items, and for each item we'll proceed as follows: I'll present to you, on the screen in in front, a slide containing a contrast sensitivity problem. 100 (PUT DEMONSTRATION SLIDE #1 ON THE SCREEN.) Your job will be to figure out which rectangle, top or bottom, is slightly more black than white. On each item, one rectangle will be exactly fifty percent black and fifty percent white; the other will be fifty-three percent black and forty-seven percent white. So let me repeat: your job will be to figure out which rectangle, top or bottom, is the one that's slightly more black than white. For about half the items, the correct answer is "top", and, for the rest, the correct answer is "bottom"; and I should add that the slides were put into the projector in a random order. After presenting a slide such as this, I'll give you five seconds to study it. Then I'll ask you to indicate your initial choice, which you'll do by pressing either the button labeled "top" or the button labeled "bottom" in the upper row of buttons on your panel, just below the words "initial choice." (REMOVE SLIDE.) When you've made your initial choice, it'll be reg- istered on my panel back here. I'll compare your answer with the correct one, which I have here, and then give you feedback on whether you were right or wrong. I'll also keep track of your score. Since there will be twenty rounds in all, you'll be asked to make twenty initial choices. Needless to say, practically everyone finds these choices difficult, since 101 the two rectangles are so nearly alike. Still, our previous studies have shown that some persons can make correct de- cisions on the basis of slight, maybe even subconscious, cues and feelings. When the test is over, I'll tell you your score. To help you interpret that score, we've prepared the stand- ards that you can see on the board. Those standards are based upon previous studies in which more than one-thousand college students participated. As you can see, a score of 15-16 correct is high average, and a score of 13-14 correct is low average. The most common score seems to be 14 or 15. A score of 17-20 correct is relatively rare, representing very high ability; and a score of 0-12 correct is also rela- tively rare, representing little or no ability. What I'd like to do at this point, before we start the actual test, is go through a practice round to get you used to our procedure. This round won't count toward your score. The way it works is like this: first, I'll present a slide containing a contrast sensitivity problem. Second, after five seconds, I'll ask you to choose the rectangle, top or bottom, that, in your judgment, is slightly more black than white. You'll indicate your choice by pressing the appropriate button by the words "initial choice." (1) This is Demonstration Slide #2. (PUT SLIDE ON, ALLOW FIVE SECONDS.) 102 (2) All right, now make your initial choice. (WAIT UNTIL S's HAVE CHOSEN, THEN REMOVE SLIDE.) Your choices are now registered on my panel. Number One chose _____J and Number Two chose _____3 During the actual test, as soon as I've announced and recorded your scores, I'll press this button on my panel (CLEAR PANELS), and the lights on all the panels will go off. Then we'll be ready for the next round, and, as I said, there'll be twenty rounds in all. During the test, you shouldn't communicate with each other in any way. Otherwise, the scores won't be valid. Is everything clear? All right, now we'll begin the test. (1) This is slide number _____. (PUT SLIDE ON, ALLOW FIVE SECONDS.) (2) All right, now make your initial choice, (WAIT UNTIL S's HAVE CHOSEN.) (3) Number One is _____; Number Two is _____3 (REMOVE SLIDE, CLEAR PANELS.) CONTINUE FOR TWENTY TRIALS ACCORDING TO THE FOLLOWING SCHED- ULE, WHERE THE HIGH AND LOW SCORES ARE ASSIGNED BY A RANDOM PROCEDURE. SLIDE NUMBER HIGH SUBJECT LOW SUBJECT l RIGHT RIGHT 2 RIGHT WRONG 3 RIGHT WRONG 4 WRONG RIGHT 5 RIGHT WRONG 6 RIGHT RIGHT 7 RIGHT WRONG 8 WRONG RIGHT 103 9 RIGHT RIGHT 10 RIGHT WRONG 11 RIGHT WRONG 12 RIGHT RIGHT 13 RIGHT WRONG 14 RIGHT WRONG 15 WRONG RIGHT 16 RIGHT WRONG 17 RIGHT RIGHT 18 RIGHT WRONG 19 RIGHT WRONG 20 RIGHT WRONG The test is now completed. I'll add up your scores and, as soon as I finish, I'll report them to you. (WAIT TEN SECONDS, THEN ENTER THE EXPERIMENTAL ROOM AND FINISH THE REMAINDER OF THIS SCRIPT BY MEMORY.) Let's see, Number One got _____ correct and _____ incorrect; and Number Two got _____ correct and _____ incorrect. (WRITE SCORES ON THE BLACKBOARD.) You can get some idea of how you did by comparing your scores with the standards here. This is a little bit unusual. Well, what I would like for you to do now is fill out a short questionnaire, which I'll now pass out. (PASS OUT THE PART ONE QUESTIONNAIRE; THEN TAKE DOWN THE INDIVIDUAL SCORING STANDARDS, REVEALING THE CHART THAT RELATES THE TEAM SCORE TO EACH PERSON'S PAY.) (COLLECT THE PART ONE QUESTIONNAIRE AND RETURN TO THE CONf TROL ROOM.) Part Two Instructions: Conditions 1 and 3 (TURN ON INITIAL CHOICE FEEDBACK.) We're now ready to begin Phase 2 of our work. As you may possibly know, psychologists are primarily interested in studying individual 104 behavior. Sociologists, on the other hand, are primarily interested in studying behavior as it relates to a group situation. In terms of this distinction, Phase 1 would be considered the more psychological part of our work today, and Phase 2 would be considered the more sociological part. In Phase 2, to make a long story short, we'll be interested in your ability at teamwork. Accordingly, we're going to allow you to exchange information before making your final choices. Let's see how this works. Would you, Number Two, press one of the buttons on the initial choice part of your panel? Thank you. Now, only after you've made your initial choice, Number One, will you be able to see what Number Two chose. And since you've already made your initial choice, Number Two, you'll be able to see Num- ber One's initial choice as soon as he (she) makes it. Would you now make an anitial choice, Number One? All right, as you can see, Number One chose _____, and Number Two chose _____. Do you see that? (CHECK TO MAKE SURE THEY DO.) Your panels are wired so that both persons' buttons must be pressed before the lights will go on. That is, the exchange of information will take place only after both persons have chosen. Needless to add, the exchange of in- formation lights were disconnected during Phase 1. Now let me tell you a little bit more about our work today in Phase 2. The type of situation we wish to study is a very common one. It's also a very sociologically «a. ' .-A Flt n.- .. A?“ y: I 105 important one. Sociologists have a name for it: it's called a "cooperative choice situation." The most important thing for persons in a cooperative choice situation is to make the correct final decision. Let me clarify what I mean with an example. When a doctor at Sparrow Hospital has to make a difficult diagnosis, he knows in the back of his mind that the patient may die if he makes a wrong final decision. Yet he also knows that, at first, it may be very hard to recognize what the right final decision is; and, as I'm sure you'll agree, this presents a very serious prob- lem. Medical schools teach that, when faced with this kind of situation, the doctor should first study the case very carefully and arrive at an initial decision. Then, before taking action, he should get the decision of a second doc- tor. After that, he should carefully weigh all his informa- tion and only then make his final decision. It goes with- out saying that he shouldn't care whether he himself thinks of the right answer, or whether he recognizes the right answer after this consultation process. The only thing that's important is that he make the correct final decision. At this point, I'd like to direct your attention to our Phase 2 procedure. At the beginning of each round, I'll present a slide containing a contrast sensitivity problem, just as in Phase 1. After five seconds, I'll ask you to make your initial choice, and this will also be just as in Phase 1. Then, after five more seconds, I'll ask you to 106 make your final choice, using the lower row of buttons on your panel. Your final choice may be either the same as, or different from, your initial choice. We're using contrast sensitivity problems in Phase 2 because, in certain key respects, these problems are like many of the problems faced by persons in decision making positions in society. They have correct answers, but those answers may be unclear at first, becoming recognizable only after a process of consultation. I mentioned a few minutes ago that you'll be working together as a team. In accordance with our standard policy, each of you will be paid the same amount for partiCipating in today's study, and that amount will depend upon your final team score. Since this team score determines your pay, let me explain exactly how we compute it. Each time a person makes a correct final choice, the team will gain two points; and each time a person makes an incorrect final choice, the team will gain nothing. Or to put it another way, each final choice you make will be scored +2 or 0, de- pending upon whether you're correct or whether you're in- correct, in that order. There'll be thirty rounds in this phase. Therefore, each person's largest possible contribution to the team score is 60 points, and each person's smallest possible con— tribution is 0 points. The team score itself, since there are two of you, has a largest possible value of 120 points 107 and a smallest possible value of 0 points. On the board we have a table that relates each person's pay for partici- pating in today's study to the final team score. You can see, looking at the table, that if your team were to wind up with a full 120 points, you'd each receive $2.20; on the other hand, if your team were to wind up with 0 points, you'd each receive $1.00. The amount you'll actually earn will probably fall somewhere between these two extremes, and it will depend entirely upon your team's final score, which we'll compute when Phase 2 is over. Before we start the test, I'd like to go through a practice round to get you used to our Phase 2 procedure. This round won't count toward your team score. (1) This is Demonstration Slide #3. (PUT SLIDE ON, ALLOW FIVE SECONDS.) (2) All right, now make your initial choice. (ALLOW FIVE SECONDS.) (3) All right, now make your final choice. (REMOVE SLIDE, CLEAR PANELS.) We'll do this thirty times, and the procedure will be exactly as we've just done each time. In order to help your partner as much as possible, you should make your initial choices carefully; however, I want to emphasize that only your final choices will count toward the team score. 108 There is also one more procedural matter that I should call to your attention. Your choices are being ma- chine scored in this phase. Five seconds after I have asked for your final choice, if you haven't responded, the machine will automatically credit you with an incorrect choice. So if you don't know an answer, it would be in your interests to guess rather than to let the time run out and automati- cally be credited with a wrong answer. Finally, one last thing I should mention is that, although your pay for participating depends solely upon the Eggm score, I'll let you know how many points you as an individual contributed to the team score when the test is over. Is everything clear at this point? (CHECK TO MAKE SURE EVERYTHING IS CLEAR; THEN CHANGE THE ICOM FROM "VERIf DICAL" TO "NORMAL" AND TURN ON THE ESTERLINE ANGUS.) Okay, now we'll begin. (1) This is slide number . (PUT SLIDE ON, ALLOW FIVE SECONDS.) (2) All right, now make your initial choice. (ALLOW FIVE SECONDS.) (3) All right, now make your final choice. (REMOVE SLIDE, CLEAR PANELS.) (CONTINUE FOR THIRTY TRIALS.) The Phase 2 test is now over. What I would like for you to do now is fill out another short questionnaire, which I'll now pass out. 109 (PASS OUT THE PART TWO QUESTIONNAIRE; THEN LEAVE THE EXPERI- MENTAL ROOM FOR ABOUT TWO MINUTES; THEN RETURN WITH POST- SESSION INTERVIEW MATERIALS, WAIT FOR SUBJECTS TO FINISH, AND COLLECT THEIR COMPLETED QUESTIONNAIRES.) Before I tell you your team score, I would like to talk with each of you individually for a few minutes. Would you come this way, please? (LEAD THE SUBJECTS TO SEPARATE INTERVIEW ROOMS; BEGIN THE POST-SESSION INTERVIEW AND DEBRIEFING.) Part Two Instructions: Conditions 2 and 4 (TURN ON INITIAL CHOICE FEEDBACK.) We're now ready to begin Phase 2 of our work. As you may possibly know, psychologists are primarily interested in studying individ- ual behavior. Sociologists, on the other hand, are primarily interested in studying behavior as it relates to a group situation. In terms of this distinction, Phase 1 would be considered the more psychological part of our work today, and Phase 2 would be considered the more sociological part. In Phase 2, to make a long story short, we'll be interested in your ability at teamwork. Accordingly, we're going to allow you to exchange information before making your final choices. Let's see how this works. Would you, Number Two, press one of the buttons on the initial choice part of your panel? Thank you. Now, only after you've made your initial choice, Number One, will you be able to see what Number Two chose. And since you've already made your initial choice, Number Two, you'll be able to see Number One's initial choice as soon as he (she) makes it. 110 Would you now make an initial choice, Number One? All right, as you can see, Number One chose _____, and Number Two chose _____. Do you see that? (CHECK TO MAKE SURE THEY DO.) Your panels are wired so that both persons' buttons must be pressed before the lights will go on. That is, the exchange of information will take place only after both persons have chosen. Needless to add, the exchange of in- formation lights were disconnected during Phase 1. Now let me tell you a little bit more about our work today in Phase 2. The type of situation we wish to study is a very common one. It's also a very sociologically important one. Sociologists have a name for it: it's called a "cooperative choice situation." The most important thing for persons in a cooperative choice situation is to make the correct final decision. Let me clarify what I mean with an example. When a doctor at Sparrow Hospital has to make a difficult diagnosis, he knows in the back of his mind that the patient may die if he makes a wrong final de- cision. Yet he also knows that, at first, it may be very hard to recognize what the right final decision is; and, as I'm sure you'll agree, this presents a very serious prob- lem. Medical schools teach that, when faced with this kind of situation, the doctor should first study the case very carefully and arrive at an initial decision. Then, before taking action, he should get the decision of a second doc- tor. After that, he should carefully weigh all his 111 information and only then make his final decision. It goes without saying that he shouldn't care whether he himself thinks of the right answer, or whether he recognizes the right answer after this consultation process. The only thing that's important is that he make the correct final decision. At this point, I'd like to direct your attention to our Phase 2 procedure. At the beginning of each round, I'll present a slide containing a contrast sensitivity problem, just as in Phase 1. After five seconds, I'll ask you to make your initial choice, and this will also be just as in Phase 1. Then, after five more seconds, I'll ask you to make your final choice, using the lower row of buttons on your panel. For your final choice, you may select "top,' "bottom," or "withhold judgment." Since the "withhold judgment" alternative was not available in Phase 1, let me explain a little bit about it. In a cooperative choice situation, withholding judgment has both advantages and disadvantages. To see what these are, think about our previous example. When a doctor has to make a difficult diagnosis, it's best, naturally, if he makes the correct final choice and begins the correct treatment. On the other hand, it's very unfortunate if he makes an incor- rect final choice and begins an incorrect treatment, because an incorrect treatment could harm, or even kill, the patient. To avoid making an unfortunate mistake, a doctor will some- times withhold judgment, which is without question the second 112 best alternative there is. Many other examples could also be given, but let me just summarize the general principle: In any cooperative choice situation, the best choice involves being right, the second best choice involves withholding judgment, and the worst choice involves being wrong. We're using contrast sensitivity problems in Phase 2 because, in certain key respects, these problems are like many of the problems faced by persons in decision making positions in society. They have correct answers, but those answers may be unclear at first, becoming recognizable only after a process of consultation. I mentioned a few minutes ago that you'll be working together as a team. In accordance with our standard policy, each of you will be paid the same amount for participating in today's study, and that amount will depend upon your final team score. Since this team score determines your pay, let me explain exactly how we compute it. Each time a person makes a correct final choice, the team will gain two points; each time a person selects the "withhold Judg- ment" alternative, the team will gain one point; and each time a person makes an incorrect final choice, the team will gain nothing. Or to put it another way, each final choice you make will be scored +2, +1, or 0, depending upon whether you're correct, whether you withhold judgment, or whether you're incorrect, in that order. 113 There'll be thirty rounds in this phase. Therefore, each person's largest possible contribution to the team score is 60 points, and each person's smallest possible con— tribution is 0 points. The team score itself, since there are two of you, has a largest possible value of 120 points and a smallest possible value of 0 points. On the board we have a table that relates each person's pay for partici- pating in today's study to the final team score. You can see, looking at the table, that if your team were to wind up with a full 120 points, you'd each receive $2.20; on the other hand, if your team were to wind up with 0 points, you'd each receive $1.00. The amount you'll actually earn will probably fall somewhere between these two extremes, and it will depend entirely upon your team's final score, which we'll compute when Phase 2 is over. Before we start the test, I'd like to go through a practice round to get you used to our Phase 2 procedure. This round won't count toward your team score. (1) This is Demonstration Slide #3. (PUT SLIDE ON, ALLOW FIVE SECONDS.) (2) All right, now make your initial choice. (ALLOW FIVE SECONDS.) (3)‘ All right, now make your final choice. (REMOVE SLIDE, CLEAR PANELS.) 114 We'll do this thirty times, and the procedure will be ex- actly as we've just done each time. In order to help your partner as much as possible, you should make your initial choices carefully; however, I want to emphasize that only_ your final choices will count toward the team score. There is also one more procedural matter that I should call to your attention. Your choices are being ma- chine scored in this phase. Five seconds after I have asked for your final choice, if you haven't responded, the machine will automatically credit you with an incorrect choice. So if you don't know an answer, it would be in your interests to guess rather than to let the time run out and automati- cally be credited with a wrong answer. Finally, one last thing I should mention is that, although your pay for participating depends solely upon the team score, I'll let you know how many points you as an individual contributed to the team score when the test is over. Is everything clear at this point? (CHECK TO MAKE SURE EVERYTHING IS CLEAR; THEN CHANGE THE ICOM FROM "VERIDICAL" TO "NORMAL" AND TURN ON THE ESTER- LINE ANGUS.) Okay, now we'll begin. (1) This is slide number _____. (PUT SLIDE ON, ALLOW FIVE SECONDS.) (2) All right, now make your initial choice. (ALLOW FIVE SECONDS.) (3) All right, now make your final choice. 115 (REMOVE SLIDE, CLEAR PANELS.) (CONTINUE FOR THIRTY TRIALS.) The Phase 2 test is now over. What I would like for you to do now is fill out another short questionnaire, which I'll now pass out. (PASS OUT THE PART TWO QUESTIONNAIRE; THEN LEAVE THE EXPERI- MENTAL ROOM FOR ABOUT TWO MINUTES; THEN RETURN WITH POST- SESSION INTERVIEW MATERIALS, WAIT FOR SUBJECTS TO FINISH, AND COLLECT THEIR COMPLETED QUESTIONNAIRES.) Before I tell you your team score, I would like to talk with each of you individually for a few minutes. Would you come this way, please? (LEAD THE SUBJECTS TO SEPARATE INTERVIEW ROOMS; BEGIN THE POST-SESSION INTERVIEW AND DEBRIEFING.) Questionnaires (Note: The part one and part two questionnaires are presented in order, just as they appeared to the sub- jects, beginning on the next page.) 116 QUESTIONNAIRE--STRICTLY CONFIDENTIAL Name Your number 1. Suppose that you were given a second Contrast Sensitiv- ity Test like the one given today. Please make an "X" on the scale below at the point representing your best estimate of how many answers you would get correct. Your Number Correct 2. Suppose that your partner were given a second Contrast Sensitivity Test like the one given today. Please make an "X" on the scale below at the point representing your best estimate of how many answers he would get correct. Partner's Number Correct 0 2 4 6 8 10 12 14 16 18 20 3. If the estimates that you made in answering Question 1 and Question 2 differed by more than one or two points from the actual numbers that you and your partner got correct today, please explain your reasoning in the space below. THANK YOU 117 QUESTIONNAIRE--STRICTLY CONFIDENTIAL Name Your number In our previous studies, we have found that, during Phase 2, some persons are primarily concerned with avoid- ing wrong answers. Other persons are primarily concerned with getting right answers. The two are not necessarily the same. Please make an "X" on the scale below at the point that most nearly represents your own degree of con- cern about avoiding wrong answers. Then do the same for the scale that involves getting right answers. Avoiding Wrong Answers 01%;!LL41L1g13‘m‘—_9__1__1__g__n_ 0 1 2 3 4 5 6 7 8 9 10 Not Moderately Extremely concerned concerned concerned Getting Right Answers M41 L—L—‘JfQ—A! l L-4__1_‘___.__ 0 1 2 3 4 5 6 7 8 9 10 Not Moderately Extremely concerned concerned concerned Many persons who have participated in our previous studies have reported feeling some degree of nervousness during the Phase 2 test. Please make an "X" on the scale below at the point that most nearly represents your own degree of nervousness during this test. Degree of Nervousness 0 1 2 3 4 5 6 7 8 9 10 Not Moderately Extremely nervous nervous nervous 118 3. Now we'd like to get your impression of how well you did on the Phase 2 test. Please make an "X" on the scale below at the point that corresponds to your best esti— mate of your own contribution to your team's final score. Estimated Contribution to Team Score . a 4, A‘___nl . .1 .a n 14 a 41 a, 0 10 20 30 40 50 60 points points points points points points points 4. Please explain why you answered Question 3 as you did. That is, what factors did you take into consideration in arriving at your judgment? 5. If you have any additional remarks that you think might be helpful to us, please indicate them below. THANK YOU FOR YOUR COOPERATION 119 Interview Schedule Before I tell you the results of today's study, I'd like to talk to you to find out some of your thoughts and feelings about it. There are many things that might affect the results of a study such as this, and it's these things that I have in mind. Your name is _____J is that correct? And what is your age, _____? And your major field of study here at Michigan State? (RECORD THESE.) 1. To start off, do you have any general, or overall, feel- ings about the study? 2. Have you ever taken part in any kind of social science research before? (IF YES, PROBE FOR ITS EXACT NATURE.) 3. Have you ever read about studies like the one today? (IF YES, FIND OUT WHAT HE KNOWS ABOUT THEM.) Have you ever heard of the Asch experiment? 4. When the Contrast Sensitivity test was first described to you, how well did you expect to do on it? Why is that? How well did you expect your partner to do? (IF HE SAYS ANYTHING EXCEPT "I DIDN'T KNOW," ASK WHY.) 5. Had you ever met your partner before today? What im- pression did you get of him before we started? 6. In phase 1 and the initial choice part of phase 2, how did you go about figuring out the answers? Did you rely on your intuitive feelings, or did you use some kind of a system? 120 7. When I explained phase 2, and you found out that you'd be exchanging information with your partner, did you anticipate that this would be helpful? Why is that? Was it helpful, do you think? 8. In phase 2, do you happen to remember about how many times you and your partner disagreed on your initial choices? (HE WILL PROBABLY SAY "ALMOST ALWAYS" OR SOMETHING OF THE KIND.) Do you have any idea why? How did you react when you found him disagreeing with you? Whom did you think was right? 9. How confident were you of your final choices during phase 2? Did your confidence change at all as the test went along? (IF YES, FIND OUT HOW.) (AT THIS POINT, IF IT IS CLEAR.THAT THE SUBJECT IS NOT SUS_ PICIOUS AND THAT HE MEETS THE ASSUMPTIONS OF THE ANALYSIS, THE INTERVIEW CAN BE TERMINATED. OTHERWISE, PROBE IN THE APPROPRIATE AREAS UNTIL IT IS CLEAR ONE WAY OR THE OTHER.) Substance of the Debriefing (Note: The debriefing will vary somewhat from one subject to the next. It is important that the debriefing seem like a talk, not a recitation. The following is not a script, it is the essential content of a typical debrief- ing.) Now I'd like to explain more about what we were trying to study in today's tests. The purpose of our re- search is to find out the relationship between a person's 121 ability and the decisions he makes. In particular, we are trying to find out how a person's ability is related to whether or not he will change his decision if another per- son with either more or less ability disagrees with him. We are not interested in Contrast Sensitivity as such. To set up a situation in which this problem can be easily studied, there are two things we need to arrange: your ability and your disagreement with your partner. Con- cerning your ability, the test we gave you in phase 1 didn't really measure your contrast sensitivity. On each slide, each of the two rectangles was exactly fifty percent black and fifty percent white, so there were no right or wrong answers. Your seventeen (or eight) right and the other person's eight (or seventeen) right were both fictitious scores that were prearranged and assigned to you and the other person at random. If you had happened to sit in the other chair today, you would have gotten the other score. We hoped that you would naturally assume that the scores were valid and that you had more (or less) ability than your partner. You might wonder why we gave you a fictitious test--why we didn't give you a real test instead. There are basically two reasons. First, if we gave you a real test, there would be no guarantee that one person would score high, the other low. In fact, the odds are against that happening very often. We could, of course, give a real test to a large number of persons and then select the high and low 122 scorers, pair them up, and bring them to the laboratory. But that would mean that, of all the persons who were inter- ested in participating, only about twenty percent could do so--only the very high scorers and the very low scorers. This would be rather wasteful. Second, and perhaps more impor— tant, if we gave you a real test, some of the low scorers would feel bad about it. With a fictitious test, the per- sons who are told that they got low scores may feel bad about it, but they feel much better again when they learn the true nature of the test and the reasons behind it. Does this make sense? As I mentioned, we also had to arrange your disa- greements with your partner. You said that you and he disagreed on your initial choices most of the time. Actually you probably agreed with him about half the time. The panels were wired so that it would look like you were disagreeing much more often than you really were. The reason for this is that we were interested only in disagreements-~we wanted to see how you would resolve the conflict. Since we weren't interested in the times when you agreed, we arranged not to have very many of them. The alternative would have been to have a much longer experiment. To get the twenty-five dis- agreements that we want, we might have to run through sixty or seventy rounds in some cases. On the average, we would need about fifty rounds to get twenty-five disagreements, since, by the law of averages, you would disagree about half the time. 123 Briefly, then, this is what the study is about, these are the things we had to arrange, and these are the reasons we had to arrange them. We would appreciate your coopera- tion is not telling anyone about the two fictitious aspects of the experiment. As I'm sure you understand, if persons knew about these things, they couldn't take part in the study, and word spreads pretty rapidly. So could I have your word that you won't disclose this information? Thank you. I'm glad you were able to participate in our research. (AT THIS POINT, THE SUBJECT IS PAID $2.00 AND IS EXCUSED.) APPENDIX B THE LOGIC OF THIS DISSERTATION As noted earlier, a document that rests upon logic? ally tight arguments is unavoidably difficult to read. Some- times it may be hard to tell what is central to the main undertaking and what is peripheral. Recognizing that this may well be true in the present case, we shall now attempt to explicate the "bare bones" logical structure of Chapters I through IV, which are the heart of this dissertation. In retrospect, based upon the work of Chapter V, it is clear that our original concern with balance versus utility maxi- mization was misguided. Chapters I through IV, the author now believes, should be viewed as neither more nor less than a comparative empirical test of two abstract behavioral decision making models: the Siegel §t_al. model and the Camilleri gt_al. model. Behavioral decision making is our main focus. For theoretical purposes, we concern ourselves with the general case; for research purposes, we concern ourselves with a particular case. Just as a theory about all ducks might be studied by studying Canadian mallards, so a theory about all behavioral decision making might be studied by studying social influence decision making; and this is the particular 124 ..cF- ‘J 'A- ' “...-‘1'“ u 125 case we select. The essential logical structure of our work consists of two parallel chains of implication, which can be described as follows. The utility maximizing principle conjoined with two other premises (viz., the Siegel eE_§l. model) implies Theorem Schema 81, which implies Theorem Schema S3, which in turn, by the applicative principle, implies our first "basic hypothesis" (page 41). This basic hypothesis implies the null hypothesis of the statistical test regarding L and the alternate hypothesis of the test 1 regarding L in the second stage of our analysis. In a 2 parallel fashion, the balancing principle conjoined with one other premise (viz., the Camilleri et_al. model) implies Theorem Schema Cl, which implies Theorem Schema C3, which in turn, by the applicative principle, implies our second "basic hypothesis." This hypothesis implies the alternate hypothesis of the statistical test regarding L and the null 1 hypothesis of the test regarding L in the second stage of 2 our analysis. Now, the results of the third stage of our statistical analysis are determined by the results of the second stage; therefore, these Bayesian conclusions, by the statistical analogue of modus tollens, feed back through the logical chains just indicated to the two models. In these chains of implication, notice that Theorem Schema 82 and Theorem Schema C2 play no part. It might be asked, what is their logical status? Before answering this question, let us indicate the purposes of these theorem In 126 schemata and the fairly extensive analyses that lead up to them. Those purposes are: (l) to give credence to the claim that either model could account for the social influence data examined in Chapter I, and (2) to provide the rationale for the subsequent, related claim that Cr(M1) = Cr(M2) = 1/2. Regarding this second purpose, we argue that the two models are indistinguishable on the basis of previous re- E search, hence that there is no scientifically justifiable basis for assuming that either model is more credible than the other. To answer the question raised, then, Theorem : Schema 52 and Theorem Schema C2 are tangential to the basic logical structure of our work, although, as indicated, they do serve useful collatoral purposes. In this dissertation, as the above discussion indi- cates, the linkages between abstract theory and concrete research are not mediated by any auxiliary substantive assump- tions whatsoever, save the assumption that "the social influ- ence application" is a legitimate application of behavioral decision making theory. That is to say, we have short- circuited the complex, loophole-ridden linkages that some authors seem to believe will necessarily confound any sub- stantive tests of these models (see, for example, Camilleri g£_al., 1972: 29-30). The methodological significance of this accomplishment should not be overlooked when and if, after an appropriate interval, the argument of this 127 dissertation is dispassionately analyzed, and the scienti- fic contribution of our work is dispassionately assessed. In closing, we might remark that the logical structure of this dissertation is best understood in con- junction with the broad scientific strategy that underlies it. Science progresses most expeditiously, we believe, through comparative empirical research, through research designed in such a way that rival models or theories make different predictions. Now we grant that, in many areas of sociology, rival models do not exist, and that, in such areas, this strategy would be inappropriate; however, when- ever rival models gg exist, the first research priority should be to eliminate at least one of them. Thus, when contemplating a particular study, the researcher should ask himself: "What predictions does each model make with regard to my proposed research?" If the answer turns out to be that they both make the game prediction, he should "go back to the drawing board," as it were, and alter his research design in such a way that they make different predictions. This is precisely what we did with respect to the research reported in this dissertation; and, in View of the recent additions of Model A and Model B to the list of rival models (see Chapter V), this general approach seems almost obliga- tory for the future. Such, at any rate, has been the logic and broad underlying strategy of the present document. iif‘u‘ LIST OF REFERENCES 3““_ - SAL—f ' LI ST OF REFERENCES Aronson, Elliot, and J. Merrill Carlsmith. 1968 "EXperimentation in Social Psychology." Pp. l-75 in Gardner Lindzey and Elliot Aronson (eds.) Handbook of Social Psychology (second edition), Volume II. 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