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Yang? 1:4 V I:90¢lvvlv; V ) OlirrvnkathttlltfifltV-th‘ 2% EPviXS c7. vawrfr‘rlil)19v V V. it v 2.3:} . a t. 3va i:fllswrvr.uh.§zln "Huh?! m .9 V 1 >032?!) lily}... zV . .kv‘a33al1trz; . . V V V. . 1.." vhvrliliAfinflhgh¢n 19.21115": i {#1.}. .V <0 V u c‘. aiL .tlfirwlnw}... f...SC:..a:..-:7.? 52.:sz ...VVV.. .. . V.. V, Z. V . . .. (lulu; L I BRA 7?. Y Michigan State University This is to certify that the thesis entitled SPAN OF CONTROL: r A CRITICAL REVIEKIJ AND SOL-IE I‘IITW CONS DERATIOIIS presented by PAUL NORUIAII Lilli'i'O has been accepted towards fulfillment of the requirements for Ph. D. degree in Education / -\ / ' fi \ / /_<::_.L. ..... 0-169 -__,-_.,_-_,.__! vv 0* ABSTRACT SPAN OF CONTROL: A CRITICAL REVIEW AND SOME NEW CONSIDERATIONS by Paul N. Lehto Statement of the Problem Span of control is a concept in administra— tion that may be defined as the greatest number of persons that can be adequately supervised by another person. The problem of this study was: (1) to identify the factors believed to determine span of control, (2) to establish the extent to which these factors have been precisely and Operationally defined, (3) to report these findings in a context that is cohesive and useful for further research, and (4) to identify the areas within this structure that re— quire additional research or develOpment before the structure can be used as the basis for a more—nearly adequate restatement of the principle of span of control. Methodology This study was undertaken to provide a basis in theory and research for a more-nearly adequate restatement of the principle of span of control. It Paul N. Lehto was felt necessary first to establish that the pres- ent and prevailing conception of it was inadequate. If it were possible to dispose of this notion satis- factorily it would then be possible to substitute another for it which would, hopefully, explain the same phenomena with greater accuracy. In essence, this was the strategy of the study as set out in Chapter I. In Chapter II, a perspective was provided for the critical review of span of control. The historical background of the development of the traditional con— cept was given and the Graicunas—Urwick version of span of control was identified as the object to be examined Their rationale for span of control was described in detail. Chapter III had three objectives: (1) to show that the Graicunas—Urwick version of span of control was not a rigorous proof, (2) to show further that it failed to take into consideration some of the variables regarded to be the determiners of span of control, and (3) to show that, in spite of the dis— satisfaction with the principle as stated, there is a large degree of agreement that something like span of control exists. Paul N. Lehto The objective of Chapter IV should have been to develop a refined version of span of control. It should be noted that the study was begun by making a number of assumptions which essentially declared that span of control was determined by Man's limited abilities to receive, process, and transmit information. To show the plausibility of these assumptions, two models were constructed, the first describing two-way inter— personal communication and the second shwoing Man to be a receiver,processer and tnflmmitter of information. From the communication model, it was possible to con- clude that there is a minimum amount of information that must be received and processed if a supervisor is to keep track of all of the aspects of a changing situation. However, knowledge about the mechanics of information handling has not yet advanced to the point where a satisfactory model of Man as an inform— ation processer may be constructed. When this became known, the objective of the chapter was modified to providing a basis for the eventual refinement of span of control. This was done by first showing how the factors already acknowledged to be among the deter— miners of span of control could be accounted for jointly by the communication and information processing models. The examples of successful supervisory situations having broad spans of control were then reviewed and Paul N. Lehto explained in terms of the models. The chapter was con— cluded by pointing out areas needing further study be- fore the joint communication/information processing model could be satisfactorily established as a basis for a refined notion of span of control. Summary and Conclusions Summary of Contributions Made by This Study This study makes three kinds of contributions. First, it defines communication and information theory as fields which can contribute to the advancement of the study of administration. Second, it reveals to some students of administration a need to increase their fam- iliarity with topics in mathematics and physics so that they may examine more critically some of the ideas that have been developed in this study. Finally, it des— cribes specifically how a basis for the re—definition of span of control can be constructed from some of these ideas that are new to administration. Conclusions The study shows that many areas still need to be deveIOped before Man will adequately understand his own information handling capabilities and the concept of span of control can be adequately and pre— cisely restated. More must be known about how the Paul N. Lehto brain handles simultaneously received messages. The input and transducing capacities of the several sens— ory receptors must be measured as well as the relative importance of the channels to which they are sensitive. Coding efficiency must be increased and the optimum rate of auditory reception should be established. An understanding of monitoring and the interruption of processing would shed light on what information the mind attends to and regards as worth processing. The various processing operations need to be analyzed so that the time it takes to perform each elementary opera— tion, such as the decoding of a symbol or the addition of two one—digit numbers, can be distinguished. Know— ledge about the structure and the operation of storage and retrieval as well as storage capacity would help administrators to avoid the design of situations that would be beyond a supervisor's span of control. SPAN OF CONTROL: A CRITICAL REVIEW AND SOME NEW CONSIDERATIONS BY Paul N. Lehto A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY COLLEGE OF EDUCATION 1966 ACKNOWLEDGEMENTS I wish to express my appreciation to Dr. William H. Roe, Guidance Committee Chairman, for assistance during this study and throughout the doctoral program that led to it. Gratitude is also extended to Dr. Charles A. Blackman, Guidance Committee member, for reading and re—reading the drafts that eventually yielded this document and for otherwise acting as Guidance Committee Chairman after Dr. Roe left Michigan State University. I wish to thank Dr. Floyd G. Parker and Dr. Frederick B. Waisanen for their encouragement, under— standing and support throughout my doctoral program. A special word of appreciation goes to Dr. J. Allan Beegle for substituting for Dr. Waisanen at the oral, examination. Had not their names been mentioned here, my wife and sons would have been unsung heroes of this campaign. To Lillian, my wife, I give a note of ap— preciation for the sacrifices she has made, measured by extra work and hours not spent together, during the nearly five years of study that were demanded by circumstances and the requirements of the program. To my sons, Kenneth, Bruce, David, Richard, Timothy ii and Steven I give the gratitude they deserve for still recognizing their father and for attempting to under- stand and appreciate what he has been trying to do. Last but not least, to my father and mother, Mr. and Mrs. W. A. Lehto, go a special note of thanks for their consistent support and encouragement. iii TABLE OF CONTENTS CHAPTER Page I INTRODUCTION. . . . . . . . . . . . . l A. The Importance of this Study. . 2 B. The Problem and Its Limiting Assumptions . . . . . . . . . 6 C. Design and Procedures . . . . . 9 II THE HISTORY OF SPAN OF CONTROL. . . . 16 A. Earliest References . . . . . . 16 B. Span of Control in the Twent— ieth Century. . . . . . . . . 20 III A CRITICAL ANALYSIS OF SPAN OF CONTROL . . . . . . . . . . . . . . 30 A. Evaluation of Graicunas' Work . 31 B. Additional Factors Affecting Span of Control . . . . . . . 41 C. Present Status of Span of Control . . . . . . . . . . . 50 IV SOME NEW CONSIDERATIONS . . . . . . . 53 A. A Communication Model . . . . . 55 B. An Information—Processing Model . . . . . . . . . . . . 75 C. The Mechanism of Control. . . . 96 D. A Re-Statement of the Principle of Span of Control. . . . . . 104 V CLOSING REMARKS . . . . . . . . . . . 114 A. A Review of Developments. . . . 114 B. The Contribution Made by this Study . . . . . . . . . . . . 117 C. Conclusion. . . . . . . . . . . 117 BIBLIOGRAPHY. O O O O O O O O O O O O O O O O 119 APPENDIX. 0 O O O O O O O C O O O C O C O O O 133 iv TABLE LIST OF TABLES VARIATIONS OF NUMBERS OF RELATION— SHIPS WITH THE NUMBER OF SUBORD— INATES O O O O O O O O O O O O O VARIATIONS OF NUMBERS OF RELATION- SHIPS WITH THE NUMBER OF SUBORD- INATES . C O O C O O O . O C O 0 NUMBER OF EXECUTIVES REPORTING TO PRESIDENT IN 100 LARGE COMPANIES I AS A FUNCTION OF pE . . . . . . OUTLINE OF DETERMINERS OF SPAN OF CONTROL 0 O O O O O O O O O O O RELATIONSHIPS AND PERCEPTIONS OF GRAICUNAS AND LEHTO . . . . . . Page 25 37 49 68 108 143 LIST OF FIGURES FIGURE Page 1 A DIAGRAM OF SHANNON'S COMMUNICA- TION MODEL. . . . . . . . . . . . . 56 2 A MODEL OF TWOJMAY INTER—PERSONAL COMMUNICATION . . . . . . . . . . . 6O 3 ENTROPY AND CHANNEL CAPACITY OF A SUPERVISORY SITUATION . . . . . . . 74 vi CHAPTER I INTRODUCTION Span of control is a concept in administration that is defined as the number of persons being supervised by another person.1 It is also defined as a limit; that is, as the greatest number of persons that can be ade— quately supervised by another person.2 As a limit, span of control was chosen as the subject of this study for two reasons. First, if such a limit exists and can be accurately determined, either as a number or a range of numbers, its effects upon organizational planning and structure would be felt everywhere. However, it was ob— served that, although this limit had been declared to exist and had been stated as a range of numbers, it has been widely ignored by administrators and organizational planners and strongly criticized on both theoretical and practical grounds throughout its history. A desire to resolve this dissonance first prompted the selection of this topic for study. Second, although the notion of 1Stephen J. Knezevich, Administration of Public Education (New York: Harper & Brothers, 1962), pp. 68—69. 2Rudyard K. Bent and Lloyd E. McCann, Administration of Secondary Schools (New York: McGraw—Hill Book Co., ' 1960), p. 57. 2 limit suggests that the key to span of control might be found in research on human limitations, the demonstration that has been offered as a "proof" of the principle is entirely mathematical and has not been related to any empirical findings.3 Observing that thirty years of criticism have not yet totally discredited span of con— trol——for it is still discussed in current books on ad— ministration—-it was then anticipated that research in the intervening years had produced findings that would either support the present principle or provide the evid— ence needed to restate it with greater accuracy. Although this hope finally proved false, it was for some time the principal reason for the study. It was not until the study was in progress that its justification was shifted to providing a basis in research and theory for a future restatement of the principle. A. The Importance of this Study This study is important for three reasons: (1) it identifies fields outside of administration that have significant contributions to make to administration, (2) it stresses a need for an inter—disciplinary approach in the development of a science of administration, and (3) it describes specifically how developments in other fields might be used in administration. 3Waino W. Suojanen, "The Span of Control——Fact or Fable?" Advanced Management (November, 1955), pp.5-l3. Reprinted in Max D. Richards and William A. Nielander (eds.) Readings in Management (Cincinnati: Southwestern Publishing Company, 1958), p. 550. 3 During the study it was observed that mathematicians and scientists had produced many theoretical, scientific and technological advances in the decade from 1940 to 1950. These included the successful Operation of the first stored—program digital computer, the quantification of the concept of information and the development of mathematical 4 theories of communication (Shannon) and decision (Wald). The word cybernetics was coined (Wiener) and with it came the realization that there were many analogies between control and communication mechanisms in automata and men. Then, it was noted that, while some researchers, notably psychologists, have adopted the ideas inherent in these advances, writers in administration have not yet begun to reflect their acquaintance with them. If, in fact, they have not yet become acquainted with these ideas, unfortun— ate consequences follow: they can neither apply these ideas correctly to administration nor can they contribute to their further development. Thus, it was felt that, if span of control were investigated in terms of somecf these new ideas, it might help administrators to identify new fields in which they would need to extend their acquaint— ance . Robert E. Machol (ed.) Information and Decision Processes (New York: McGraw—Hill Book Co., 1960), p. vii. SIbid. 4 This study is also important for it underscores the need for the developers of ideas pertinent to admin- istration to examine the areas between the field of ad— ministration and other fields such as information theory, communication, decision theory and psychology. For many years the separate developments of fields of study were assured by the tendency toward ever—increasing specializa- tion of workers in those fields until, as Wiener wrote in 1948: Today there are few scholars who can call them— selves mathematicians or physicists or biologists without restriction. A man may be a tOpologist or an acoustician or a coleOpterist. He will be filled with the jargon of his field, and will know all its literature, and all its ramifications, but, more frequently than not, he will regard the next sub— ject as something belonging to his colleague three doors down the corridor, and will consider any in- terest in it on his own part as an unwarrantable breach of privacy. 6 Yet, the no—man's land between the various established fields offers rich opportunities to the qualified researcher for it is out of this limbo that many of the advances of the 1940's came. At the same time, this area is the most re- fractory to the accepted techniques of mass attack and division of labor. For, if the difficulties of a problem in education are mathematical in essence, a corps of 6Norbert Wiener, Cybernetics (New York: The Tech— nology Press, John Wiley & Sons, Inc., 1948), p. 8. 5 educators ignorant of mathematics will get as far and no farther than one educator ignorant of mathematics. Sim- ilarly, if a mathematician who knows no education is teamed with an educator who knows no mathematics, the ed— ucator will not be able to state his problem in terms which the mathematician can manipulate nor will the mathe— matician be able to translate his answers so that the educator can understand them. However, the treasures that are being found in these areas by some are motivating others to acquire new skills in fields seemingly but re— motely related to their primary interests and to develOp new techniques of research which they hope will permit them to share in these discoveries. It is hoped that this study will stimulate a greater number of adminis- trators to acquire the additional skills that they will need before they may adequately investigate the no—man's lands that surround their field. Still, the greatest contribution that this study can make is to show how ideas from information theory and other advances in communication can be used in ad— ministration. This is done by constructing a model using components from those disciplines that can be used to explain span of control. Examples are given that show how the model may be applied. Those research findings are reviewed which either support the model or define quantitatively some limitations on human abilities to communicate or to handle information. That which emerges 6 is an incomplete but relatively cohesive body of theory and research which, it is asserted, could be used as a starting point for further research that could lead to an overall theory of administration and allow a more nearly adequate restatement of span of control in the process. B. The Problem and Its Limiting Assumptions The problem of this study which finally emerged was: (1) to identify the factors believed to determine spancf control, (2) to establish the extent to which these factors have been precisely and operationally defined, (3) to report these findings in a context that is cohesive and useful for further research, and (4) to identify the areas within this structure that require additional re— search or development before the structure can be used as the basis for a more nearly adequate restatement of the principle of span d5control. Four major assumptions were made about this study. The first of these is that supervision and control were developed to meet Man's need to reduce the degree of un— certainty he perceives in his environment. This uncer- tainty may be of two kinds: (1) uncertainty about the present status of some aspect in that environment, and (2) uncertainty about what change may take place in an aspect. The first of these implies a need for knowledge about something whereas the second implies a need to pre— dict that an event will occur or to cause it with a prob— ability greater than chance. h-___‘. 7 The second assumption about supervision and control is that both are primarily sets of two-way communication and information—processing procedures. That is, to know what some aspect of the environment is like or is likely to do implies having received at least one information- bearing communication about it and being able to recall and perhaps otherwise process the received information. To be able to cause an event to occur implies having in— formation and being able to transmit a communication back to the environment. It is recognized that Man has developed SOphisticated manifestations of these procedures ranging from the manipulation of simple and predictable machines to the supervision and control of complex cooperative human endeavors such as our nation's space program. How— ever, the assumption is only that, if each of these man— ifications were analyzed, the analysis would reveal a set of simple procedures for receiving, processing and transmitting information. A third assumption recognized the fact that Man is not omnipotent. He has physical limitations imposed upon him by his very nature and cultural limitations that re- flect the level of civilization of his society. These limitations place bounds on Man's actions as well as on his thinking. The assumption that was made postulates the existence of limitations on Man's ability to receive, process and transmit information and, therefore, on his ability to supervise and control subordinates. Examples 8 of physicallimitations on information—processing ability might be the inability of the brain to receive two or more messages simultaneously, its limited span of immediate memory, or the maximum rate at which it can process a unit of information. An example of a corresponding cul- tural limitation is a clumsy coding system, such as Roman numerals, which does not lend itself to the process of multiplication. This forced the Romans to adopt the abacus as a device to speed up the process of multiplication which was needed in commerce and industry. A fourth and final assumption was that a super— visor may spend a significant portion of his time doing non-supervisory tasks. There are two extremes of thought about supervision, one claiming that there are as many kinds of supervision as there are kinds of activities to be supervised, and the other asserting that supervision consists of but a single set of skills, those involved in getting peOple to work together effectively and ef- ficiently. Quite probably, the truth lies somewhere be— tween these two extremes. Hoffman7 (1963) analyzed the dichotomy and concluded that no such thing as an all— purpose manager exists. He reasoned that there are at 7F. O. Hoffman, "The All-Purpose Manager: Does He Exist?" Personnel, 1963, Vol. 40, No. 1, pp. 8-16. 9 least two aspects to a manager's job: (1) the specialized training and experience needed to build skills required to manage a particular field of work, and (2) the common denominator of all managerial jobs -- the responsibility for seeing to it that the organizational machinery runs at peak efficiency. This kind of a central position sug— gests that the supervisor must spend some time using his "common core" skills. However, any amount of time de- voted to the use of specialized skills will reduce the amount of time left for supervision and it is reasonable to conclude that, other things being equal, it will re- duce his span of control. This assumption serves to define the span of control as but a part of the super— visor's total capability for work. C. Design and Procedures Both the research design and the procedures of this study were simple. To achieve its objectives, it was felt necessary to establish three points: (1) that something on the order of span of control really exists, (2) that the Graicunas—Urwick explanation of it is inade— quate, and (3) that new ideas adapted from fields out- side of administration can provide the basis for an event- ual restatement of span of control in terms that are more-nearly adequate. It had to be shown that authorit— ies in administration still feel that something on the order of span of control exists and is Operating in super— visory situations because of the possible contention that 10 span of control has been totally discredited. Also, such a demonstration supplies justification for pro- ceeding with the investigation. In lieu of empirical evidence of span of control, which does not exist, the testimony of contemporary writers in administration was cited to provide at least circumstantial evidence in favor of span of control and to give this study a reason for being. If the Graicunas-Urwick explanation for span of control were valid, this fact would also render such a study as this redundant. However, there are two good reasons for believing otherwise. First, the principle has been often ignored in practice with no apparent ad— verse effects. Second, neither Graicunas nor Urwick were able to relate their explanation of the phenomenon to observable reality. In Chapter IV are to be found the beginnings of a rationale that, it is asserted, could lead to a more— nearly adequate restatement of span of control as well as to provide stimulation and direction for those interested in developing a research—based theory of administration. The third point to be established was to show how the new ideas that were incorporated into the rationale could lead to such a theory. Again, circumstantial evidence has been resorted to for it is impossible to predict the develOpment of any theory with absolute accuracy. The theory and the research from which the rationale was ll constructed were chosen with two criteria in mind: (1) the items used should relate to each other to a great degree so as to provide as large a measure of internal consistency as possible, and (2) the entire structure should be based upon the same few principles to lend credibility to that basis. Procedures in the study included the following: (1) searching the literature to find probably relevant writings, (2) scanning the located materials quickly to determine their value to the study, (3) reading the valued material carefully and making notes from the articles and books read, (4) organizing these notes into chronological order (for Chapters II and III) and into logical order (for Chapter IV), (5) writing the rough draft of the study from the notes, and (6) re- fining the rough draft into its final form. It was frequently discovered at the times of taking notes, or- ganizing, or rough—draft writing that pertinent points were not adequately covered; additional reading was done to make up these deficiencies where possible. The procedures for searching the literature were organized into several phases. In addition to review— ing the Dissertation Abstracts,8 the basic body of literature to be scanned was identified by reviewing 8Dissertation Abstracts (Ann Arbor: University Microfilms, Inc.). 7 12 apprOpriate categories in the Psychological Abstracts.9 A supplementary list of readings was obtained by not- ing the references in the articles that were carefully read. The actual scanning procedure started with the most recent writings. There were several reasons for scanning backward through time: (1) more recent writ- ings in a given area are likely to be more s0phisticated, (2) later writings supplied lists of relevant earlier studies, and (3) they frequently also provided eval- uations of the earlier work of others. The list of readings for the historical sketch found in Chapter II was generated by starting with one source on span of control, Urwick's "The Manager's Span of Control,"10 and tracing its references as systematically and thor— oughly as possible. In analyzing the present rationale for span of control, a logical flaw was discovered in it, that of the failure of Graicunas to consider all of the pos— sibilities. In examining some of the overlooked cases and trying to count them, it was found to be helpful to develop Graicunas' patterns further using simple algebra. This analysis forms the Appendix. 9Philip J. Siegmann (ed.) Psychological Abe_ stracts (Washington: American Psychological Associa— tion, Inc.) lOLyndall Urwick. "The Manager's Span of Con— trol," Harvard Business Review, Vol. 34, No. 3 (May- June, 1956), pp. 39-47. l3 Readings were evaluated in terms of their relev— ance, validity and the reliability of their findings. A piece of research was considered to be relevant if it could be reasonably shown to pertain to one or more of the factors probably affecting span of control. It was considered to be valid if its research results could be abstractly expressed. This, in effect, is the defini- tion of construct validity that was first enunciated by Cronbach and Meehl in 1955.11 Construct validity is based upon the notion that all abstract concepts are devices which exist only in the minds of men and are, therefore, incapable of being measured directly. Ex- periments designed to substantiate such concepts can do so only through indirect measurements or indices. This means that there is no rigorous method by which an abstract concept pertaining to anything real can be firmly established in one experiment. Rather, a number of different indices in a successioncf experiments must all suggest the validity of a concept before it is thought to be satisfactorily established. Similarly, a concept can be weakened but not demolished by one contradictory finding. Moreover, a contradictory re— sult cannot be attributed to a faulty concept until it has been first determined that the contradiction is 11Lee J. Cronbach, and Paul E. Meehl, "Construct Validity in Psychological Tests," Psychological Bulletin, 1955, Vol. 52, pp. 281—302. 14 not due to a flaw in the experimental design or method. The last consideration in the evaluation of research findings was that of reliability or freedom from the influencesof transitory, outside factors. Such a con- sideration would not be necessary if it were known that validity were high but, in the case of construct valid— ity, there can be no such simple determination. Con- sequently, in the review of research, only such re— search that was relevant to the immediate problem of the study was incorporated. In addition, findings had to appear to be valid and reliable. In fabricating the rationale of Chapter IV, two problems had to be dealt with, that of consistency and that of the disposition of defects. For a rationale to be useful, it must be both externally and internally consistent, externally in the sensethatiione of its com— ponents can produce arguments with contradictory con- clusions. That is, although no rationale needs to be complete, its points must correspond to points in the reality it purports to describe and no pair of its points may be mutually inconsistent. Furthermore, a rationale built from theory as well as research is likely to generate defects in its construction that are of two kinds. The first kind of defect is the area in which no theory or research is to be found. Where such defects occurred, a remedy suggesting a possible ex— planation for the phenomena encountered was offered or 15 an area was defined in which more research was needed. The second kind of defect arises from conflicts between theory and/or research findings. Conflicts between two theories were disposed of most easily, the disposition consisting of rejection of the position that was in— consistent with the rationale being fabricated or, if no inconsistency could be found, rejection of the posi— tion considered to be more complicated. Conflicts among research findings were judged on the basis of construct validity as mentioned above. In cases of theory/research conflicts, resolution depended on the weight of research findings, the greater the weight of respected research, the greater the probability that the theoretical position would be modified. This is not the first time that span of control has been studied. However, it is an approach to it that would relate a formative theory of administration to observed reality and, in so doing, may give theoretic— ians as well as practicing administrators some valuable guidelines to consider. CHAPTER II THE HISTORY OF SPAN OF CONTROL The objective of this chapter is to provide a perspective for the critical review of span of control. More particularly, it is hoped that the reader will ob- serve that the principle of span of control was first suggested after World War I by the military who tend to adhere to it, at least at the higher levels of command and during wartime. It should also be noted that, while it found its way into the literature of management during the two decades following the Great War, there is no evidence to suggest that either military or non- military groups have subjected the principle to empiri— cal testing. A. Earliest References As a discipline, administration or management appeared upon the scene rather lately. There are many reasons for this delay, among which might be included the many centuries during which business was held in low regard, the pre—occupation of business people with profit—making and technology, the tendency to compart— mentalize the inter-related disciplines that comprise the humanities, and the widely—held belief that ad— ministration is incapable of reduction to a science. 16 17 Nevertheless, interest in administration is as old as civilization itself. In addition to the rich contents of Plato's Republic and Aristotle's Politics, concern over administrative problems and attempts at their solutions can be found in Egyptian papyrii dating back to 1169, B.C.,l in the writings of Confucius and his contemporaries (500,B.C.),2 and in the works of Cicero. Roman records leave much less information about their administrative skills than they do of their military history. However, Lepawsky has this to say about Roman managerial ability: There is some evidence to assume that even un— der the supposedly less efficient Republic the Romans knew much about how to administer their own affairs and those of their subject colonies. As for the Roman Empire, until external forces more weighty than administrative deficiencies alone brought about its destruction, it demon— strated a facility for management on a vast scale that has caused the envy of medieval as well as modern men.4 An examination of these writings has revealed that the origins of many of the concepts now employed in adminis— tration are, indeed, very old. Most of these early 1James H. Breasted, Ancient Records of Egypt (Chicago: University of Chicago Press, 1906), Vol. 4. 2Confucius, Analects, Book XIII, World's Great Classics, Oriental Literature, Vol. 4, "The Literature of China-~The Analects of Confucius," Translated by William Jennings (New York: The Colonial Press, 1899.) 3Cicero, De Officiis. 4Albert Lepawsky, Administration (New York: Alfred KnOpf, Inc., 1949), pp. 91-92. 18 sources deal with the more basic ideas such as or— ganization and division of labor, however, and rarely allude to the more SOphisticated concepts such as span of control. Two early sources clearly hint at span of con— trol. The former of these is the Old Testament where, in the book of Exodus, Jethro, Moses' father—in-law, observed that Moses was spending too much time sitting in judgment of the Israelites and made the following comments: The thing that thous doest is not good. Thou wilt surely wear away, both thou, and this peOple that is with thee: for this thing is too heavy for thee; thou art not able to perform it thy— self alone. Hearken now unto my voice, I will give thee counsel, and God shall be with thee: Be thou for the peOple to Godward, that thou mayest bring the causes unto God: And thou shalt teach them ordinances and laws, and shall show them the way wherein they must walk, and the work that they must do. Moreover thou shalt provide out of all the peOple able men, such as fear God, men of truth, hating covetousness; and place such over them, to be rulers of thous- ands, and rulers of hundreds, rulers of fifties, and rulers of tens: And let them judge the peOple at all seasons: and it shall be, that every great matter they shall bring unto thee, but every small matter they shall judge: so shall it be easier for thyself, and they shall bear the burden with thee.5 5Ex. 18:17—22. l9 Evidently Moses did as he was told, for: . . . Moses chose able men out of all Israel, and made them heads over the people, rulers of thousands, rulers of hundreds, rulers of fifties, and rulers of tens. And they judged the people at all seasons: the hard causes they brought unto Moses, but every small matter they judged themselves.6 As national states developed during the Middle Ages, a corresponding develOpment of administrative procedures followed in the fiscal field. The second source which may be said to refer to span of control is dated 812, A.D. and has to do with the manner in which Charlemagne had his estates administered: Let our mayors, foresters, stablemen, cellarers, deans, tollgatherers, and other officers to reg— ular and fixed duties, and let them pay land taxes for their holdings; and for the manual work due to them let them perform their office well. And whatever mayor has a benefice let him find a sub— stitute, so that the substitute may relieve him of his manual work and other services. No mayor shall have more land in his district than he can cover and administer in a day.7 It should be noted that neither of the above writers showed a conscious awareness of the concept or principle. Both were more concerned with the successful accomplishment of a task than they were with the number of persons re- quiring supervision that are necessary to the accomplish— ment of the task. 6Ex. 18:25—26. 7Roy C. Cave and Herbert H. Coulson, "Capitulary of the Imperial Estates of Charlemagne," in A Source Book for Medieval Economic History (New York: Biblo and Tannen, 1936), p. 19. 20 B. Span of Controljin the Twentieth Century In 1922, following the experiences of the first world war, military observers began to focus their at— tention specifically on span of control. Among the first of these was Sir Ian Hamilton, a general of the British army, who wrote that: The average human brain finds its effective sc0pe in handling from three to six other brains. If a man divides the whole of his work into two branches and delegates his responsibility, freely and prOperly, to two experienced heads of branches he will not have enough to do. The occasions when they would have to refer to him would be too few to keep him fully occupied. If he delegates to three heads he will be kept fairly busy, whilst six heads of branches will give most bosses a ten-hour day. Those data are the results of cen- turies of the experiences of soldiers, which are greater, where organization is in question, than those of politicians, business men or any other class of men . . . . Of all the ways of waste there is none so vicious as that of your clever politician trying to run a business concern without having any notion of self-organization. One of them who took over Munitions for a time had so little idea of organizing his own energy that he nearly died of overwork through holding up the work of others, i.e., by delegating responsibility coupled with direct access to himself to seventeen sub—chiefs. Now it will be understood why a Battalion has four companies (and not seventeen): why a Brigade has three or four Battalions (and not seventeen). Organizations are run by rule then; a rule whereby from three to six "hands" are shepherded by one "head," each "head" in turn being member of a superior group of from three to six who are being wheeled into line one by one. . . . 21 As to whether the groups are three, four, five or six it is useful to bear in mind a by—law: The smaller the responsibility of the group member, the larger may be the number of the group and vice- versa. That is to say, one N.C.O. in charge of three private soldiers would be too idle; one lieutenant general in charge of six divisional generals would be too busy. The nearer we approach the supreme head of the whole organization, the more we ought to work toward groups of three, the closer we get to the foot of the whole organiza— tion (the Infantry of the Line), the more we work towards groups of six. 8 The principle also made its first, though rather informal, appearance in management circles in the year 1922 when H. P. Kendall of Boston addressed a meeting of the Taylor Society in the following terms: At a dinner the other evening, I heard the President of the General Electric Company asked how many people should report directly to the President of a large industrial company. He said that eight or nine were reporting at pres— ent, but that it was too many, and he was re— organizing his functions so that only four or five would report directly to himself, and I imagine that four or five is enough. Not that a chief executive should not have contact with others; but that is about as many general func— tions as should regularly and directly lead up to him.9 These two writers succeeded in focusing the at— tention of people in circles of management upon the notion of span of control and in fixing the limit rather firmly in the interval from three to six. However, the 8Sir Ian Hamilton, The Soul and Body of an Army (London: Edward Arnold & Company, 1921), pp. 229—230. 9H. P. Kendall, "The Problem of the Chief Exec— utive," Bulletin of the Taylor Society, Vol. 7, No. 2, April, 1922. 22 question was regarded as an Open one until, mainly through the efforts of two other contribitors, a rationale was built for it and the notion was advanced to its present status. The first of these is Lyndall Urwick, the prominent British management consultant, who has become the chief proponent of the concept and principle of span of control as it is presently stated. Urwick discovered General Hamilton's principle Of or— ganization shortly after its appearance and he mentioned it to some Of his friends who were interested in prob— lems of management. He said that he had found, from experience and from reading, "the ideal number of sub— ordinates for all superior authorities . . . to be four," and "at the lowest level of organization, where what is delegated is responsibility for the performance of specific tasks and not for the supervision of others, the number may be eight or twelve."10 Some time later, he adopted the term "span of control" and applied it to a formal statement of his conception, the wording Of which now stands as "No supervisor can supervise directly the work of more than five or, at the most, six subordinates, whose work interlocks."ll He has lOLyndall Urwick, "Axioms of Organization," Public Administration Magazine (London) October, llLyndall Urwick, Scientific Principles and Or— ganization (New York: American Management Association) Institute of Management Series, No. 19, 1938, p.8. 23 restated this principle a number of times in his writ- ing since its first introduction, and it is referred to, both directly and indirectly, in many textbooks and articles on administration that have appeared since 1938.12 Urwick has taken it upon himself to answer the criticisms that have been leveled at the principle since its introduction into management literature and he regards the concept with paternal fondness.l One of the persons to whom Urwick mentioned the writings of General Sir Ian Hamilton was V. A. Graicunas, a French management consultant, who became interested in it and began to build a theoretical foundation for it in the early 1930's. First published in the Bulletin of the International Management Institute, it was re— printed in 1937 in the Papers on the Science of Adminis— tration, edited by Luther Gulick and Lyndall Urwick, and has become the main support for the existing con— cept.14 Graicunas' rationale is mathematical in nature; it is based on the assumption that effective super— vision depends on the ability of the supervisor to keep in mind simultaneously all of the elements of three l3Lyndall Urwick, "The Span of Control——Some Facts About the Fables," Advanced Management, Vol. 22, No. 11 (November, 1956), pp. 5—15. 14V. A. Graicunas, "Relationship in Organiza- tion," Bulletin of the International Management In— stitute. (Geneva: International Labour Office, 1933) as reprinted in Luther Gulick and Lyndall Urwick (eds.) Papers on the Science of Administration (New York: Institute of Public Administration, 1937), pp. 181-187. 24 distinct sets of human inter-relationships: (l) the direct relationships between the supervisor and each of his subordinates in the absence of any of the other subordinates, (2) the direct relationships between the supervisor and each of his subordinates in the pres— ence of all possible combinations of other subordinates, and (3) the indirect cross-relationships between all possible ordered pairs of subordinates.15 Graicunas noted that, computed on a maximum basis, a supervisor over n subordinates must keep in mind n relationships of the first set, n(n — 1) relationships of the third set, and n(2n/2 - 1) relationships of the second set. For each subordinate added thereafter, the number of relationships in the first set increases by just gn§_ while that of the third set is increased by 2n. How— ever, the number of relationships in the second set is increased exponentially and at a much more rapid rate, being at least doubled for each additional subordinate. He felt that, as the number of such subordinates is in— creased, the corresponding increase in the number of relationships in the second set would soon exceed the capacity of the human mind to keep track of them all simultaneously.16 The sum of the numbers of all of lSIbid., p. 184. l6Ibid., p. 184. 24 distinct sets of human inter—relationships: (l) the direct relationships between the supervisor and each Of his subordinates in the absence of any of the other subordinates, (2) the direct relationships between the supervisor and each of his subordinates in the pres— ence of all possible combinations of other subordinates, and (3) the indirect cross—relationships between all possible ordered pairs of subordinates.15 Graicunas noted that, computed on a maximum basis, a supervisor over n subordinates must keep in mind n relationships of the first set, n(n — 1) relationships of the third set, and n(2n/2 — 1) relationships of the second set. For each subordinate added thereafter, the number of relationships in the first set increases by just 233 while that of the third set is increased by 2n. How- ever, the number of relationships in the second set is increased exponentially and at a much more rapid rate, being at least doubled for each additional subordinate. He felt that, as the number of such subordinates is in— creased, the corresponding increase in the number of relationships in the second set would soon exceed the capacity of the human mind to keep track of them all simultaneously.16 The sum Of the numbers of all of lsIbid., p. 184. l61bid., p. 184. 25 these relationships, taken together, is: N = n(2n/2 + n — 1). (1) The following table shows dramatically how the number N,of relationships increases as the number n of subord— inates increases: TABLE 1 VARIATIONS OF NUMBERS OF RELATIONSHIPS WITH THE NUMBER OF SUBORDINATES n lst Set 2nd Set 3rd Set N l l 0 0 1 2 2 2 2 6 3 3 9 6 18 4 4 28 12 44 5 5 75 2 100 6 6 186 30 222 7 7 441 42 490 8 8 1016 56 1080 9 9 2295 72 2376 10 10 5110 90 5210 11 11 11253 110 11374 12 12 24564 132 24708 These data were given by Graicunas as being the maximum numbers of relationships in each set for a given number n of subordinates.l7 They could as well have been de- rived from Equation (1) and Unathnxeexpressions given on page 24 of this study. Equation (1) can also be l7Ibid., p. 186. 26 used to Obtain the total number of relationships N for any n larger than twelve. The thinking of two other men needs to be men— tioned to round out the present picture of span of control. The first of these is C. I. Barnard who, in The Functions of the Executive, had the following to say about it: Under most ordinary conditions, even with sim— ple purposes, not many men can see what each is doing or the whole situation, nor can many com- municate essential information regarding or govern— ing specific action without a central channel or leader. But a leader likewise is limited in time (and capacity) in communicating with many per— sons contemporaneously, especially if they are widely separated so that he must move about. In practice a limit of usually less than fifteen persons Obtains, and for many types of COOpera- tion five or six persons is the practicable limit . . . . . . . The complexity of the relationships in any group increases with great rapidity as the number of persons in the group increases. If the simplest possible relationship between two per— sons is that of "knowing" each other as accom— plished by a mutual introduction, then the re— lational complexity at the very least increases as follows: 27 Increase in Number of Relationships With Number in Group Relationships Each Addition to Group 2 3 4 5 10 6 15 7 21 8 28 9 36 10 45 15 105 . 20 190 . 50 1225 . \OGDQOWUln-DOJNO . . . A person has relationships not only with others individually and with groups, but groups are related to groups. As the number of possible groups increases, the complexity of group re— lationship increases in greater ratio.18 There is no question that Barnard's thinking was in- fluenced by that of Graicunas for he makes reference to Graicunas' "Relationship in Organization."19 Too, it does not seem likely that the number of relationships listed by Barnard coincidentally just happened to be half the number of relationships in the third set found by Graicunas and given in Table l. 18Chester I. Barnard, The Functions of the Exec— utive (Cambridge, Massachusetts: Harvard University Press, 1960), Pp. 106—109. 19Ibid., p. 109. 28 The final contributor to the development of the present principle of span of control is Ralph C. Davis who furtber amplified the Graicunas hypothesis by dis— tinguishing two qualitative levels of supervision. The first level is the unit of supervision which applies to the first—line supervisor and wherein the activities are mostly physical and mainly concerned with the con- trol Of current Operations. He then defines a span of executive control which he applies to all executives above the level of the first-line supervisor. Accord— ing to Davis, executives are more concerned with the planning and organizing of activities which he feels are more exacting types of work since they require working with intangibles and abstractions. Davis claims that, as a result, the executive cannot effectively supervise more than three to seven first—line super— visors Or subordinate executives. He indicates that the Optimum span of executive control is, in most cases, limited to not more than five people.20 The foregoing sketch essentially summarizes the theoretical development of the span of control principle as it is known today. It is suspected that there is no empirical evidence to support it for both its pro— tagonists and its adversaries are in agreement on this point. As Urwick stated: 20Ralph C. Davis, "The Influence of the Unit of Supervision and the Spancf Executive Control on the Economy of Line Organization Structure," Bureau of Re- search, Research Monggraph No. 26 (Columbus: The Ohio State University, 1941). 29 No—one has yet developed a satisfactory labora- tory technique to prove that A can conduct con— versations ("communicate with") five persons simultaneously with a reasonable hope of mutual comprehension, but that if the number is raised to eight or ten the prospect of success is less assured. Some practical men might even feel that such tests, even if they were practicable, were labouring the obvious. In any event they are not, within the limits of our present know- ledge, practicable.2l Of the practicability of determining more nearly pre— cisely how many conversations an individual can conduct simultaneously, Of pragmatic approaches that have been made toward develOping "proper" spans of control, and of the present status of the principle this study will have many comments to make in the chapters which follow. 21Lyndall Urwick, "The Span of Control——Some Facts About the Fables," Advanced Management, Vol. 22, No. 11 (November, 1956), p. 7. CHAPTER III A CRITICAL ANALYSIS OF SPAN OF CONTROL This chapter has three objectives. The first is to show that the Graicunas demonstration of span of control is not a rigorous proof. This is done by identifying and discussing some of its shortcomings. The second Objective is to show why the Graicunas— Urwick version of span of controlis unacceptable to both students and practitioners of administration. This is done by pointing to factors which the present principle overlooks and upon which some writers feel it depends, and by identifying and discussing other argu- ments, both theoretical and practical, that have been mustered against it. The third objective is to show that, in spite of their dissatisfaction with the prin— ciple, students of administration generally concede that something similar to it does actually affect super- visory situations. This is done by describing in de— tail the approaches that have been taken by large or- ganizations to determine "proper" spans Of control for their administrators. 30 31 A. Evaluation of Graicunas' Work From his article it can be seen that Graicunas intended to support the principle of span of control by revealing theoretical evidence of its validity and clarifying some matters concerning relationships among individuals and groups which he felt were not obvious.1 Whether or not he intended his work as a proof cannot be stated with certainty. However, as a proof it has a number of shortcomings of which this study has dis- covered three: (1) There is no evidence to show that a supervisor's ability is limited by his capacity for remembering simultaneously all of the relationships defined by Graicunas, (2) He failed to consider (or to explain away) all of the logically possible types of relationships that can be postulated to exist be— tween a supervisor and/or his subordinates or groups of subordinates, and (3) He failed to show that, be- cause an individual's memory span is generally limited to the immediate recall of about six digits, his capac- ity for supervising subordinates whose work "interlocks" is also limited to the same number. Examining the first of these shortcomings, Graicunas implied that there are two kinds of evidence, "theoretical" and practical. 1V. A. Graicunas, "Relationship in Organization," Bulletin of the International Management Institute. (Geneva: International Labour Office, 1933), as reprinted in Luther Gulick and Lyndall Urwick (eds.) Papers on the Science of Administration (New York: Institute of Public Administration, 1937), p. 184. 2Ibid. 32 By "theoretical" evidence he meant the abstract model of relationships which he defined and developed to help describe the supervisor's "burden of responsibility."3 However, such models exist only in the mind and do not necessarily bear any relationship to observable real— ity. For this reason, a theoretical model standing alone cannot be said to constitute evidence of any kind. To be sure,any model may be analogous to reality and it is true that, the closer and more nearly complete the analogy, the more nearly accurately it may be used to help describe, explain, and predict about the reality that it resembles. It is in this consideration that the seriousness of Graicunas' mistake lies for he built a model to explain span of control in tenms of certain kinds of relationships without ever establishing that these relationships really matter! Even if Graicunas had shown that his"relation- ships" could be used as a valid index for a supervisor's span of control, it may be shown that he either failed to consider all of the possible types of relationships that could be defined or at least to dispose of them satisfactorily. That he overlooked some types of re- lationships can be shown with a hypothetical situation. Let supervisor A be in charge of three co—equal 3Ibid. 33 subordinates, B, C and D. Following Graicunas, A must keep in mind all of the elements of three sets of re- lationships. Those in the first set he defined as the "direct single relationships between himself (the supervisor) and (each of) those he supervises."4 These can be counted and described symbolically, as follows: A * B (read "the relationship of A to B when B is alone with A"), A * C, and A * D. The second set of relationships was defined by Graicunas as "direct group relationships" but was actually thought of by him as direct single relationships between a supervisor and each of his subordinates in the presence of combinations of the other'subordinates.5 These are: A * B/C (read "the relationship of A to B in the presence of C"), B/D, C/B, C/D, D/B, D/C, B/CD (read "the relationship of A to B in the presence of C and D"), C/BD, and * D/BC. ** * * * * * fi>> >$>>’>3>> Finally, he recognized a third set of "cross relationships" which he took to mean what each subordinate thought of each other subordinate.6 Again, these may be counted and described as follows: 4Ibid. 51bid. 6Ibid. 34 (read "what B thinks of C"), and UCUWOW I I That these relationships have been described and counted correctly can be verified either by checking Table l for n = 3, or by calculating N in Equation (1) for n = 3. The first oversight that suggests itself is Graicunas' failure to consider the relationships between the supervisor and groups of his subordinates. Thus, in his own words, "If Tom supervises two persons, Dick and Harry, he can speak to each of them individually or he can speak to them as a pair" (underlining mine).7 This opens the door to an entire new set of relation- ships that may be set out in the following manner: A * (BC) (read "the relationship of A to the group composed of B and C when B and C are alone with A"), A * (BD), A * (CD),and A * (BCD). This set of relationships is analogous to the first of the three original sets defined by Graicunas. There is also an analogue to the second set: A * (BC)/D (read "the relationship of A to the group composed of B and C in the pres- ence of D"), A * (BD)/C, and A * (CD)/B. 7Ibid. 35 This thinking can even be extended to Graicunas' third set of relationships, to include: B -— (CD) (read "what B thinks of the group com— posed of C and D"), C —— (BD), and D —— (BC). The total number of relationships has now risen to twenty—eight, an increase of ten over those defined by Graicunas. It should be noted that the last six of these newly-found relationships could not have been discovered with thinking confined to only two subordinates. One wonders whether span of control would have been dif— ferent had not Graicunas chosen to do his thinking with Tom, Dick and Harry. A second and more interesting oversight becomes apparent when it is noted that, in going from direct to cross relationships, Graicunas shifted his attention from relationships to perceptions. That this is not merely a problem in semantics can be simply shown. To begin with, a relationship between two things is often expressed in two different sets of terms. Thus, in describing one of the relationships that exists between the numbers two and three, one may say either that three is greater than two or that two is less than three. Similarly, if A is superior to B, then B is subordinate to A and either statement will describe the one re- lationship equally well. On the other hand, as Graicunas himself observed, that which A thinks of B needs not be 36 the same as what B thinks of A since these two thoughts are distinct perceptions existing in two separate minds. Graicunas apparently switched from relationships to perceptions without noticing it. In defining direct single relationships, he spoke of the relationship of Tom to Dick and Tom to Harry but 22: of Dick to Tom nor of Harry to Tom. Yet, he did define a pair of in— direct cross "relationships" of Harry with Dick and of Dick with Harry.8 Had he been consistent throughout his discussion, his set of cross relationships would have included only half the number of elements that he found, that is, three, in the case of the hypothetical situa— tion established on page 31 of this study, as follows: OCDUJ C, * D, and * D. But now, having Opened Pandora's Box of perception—re- lationships, at least two more sets pagp_of relation— ships and perceptions can be defined. Of the relation— ships, the following indirect individual relationships may be defined: C/D, B B * D/C, and C * D/B. 8Ibid. 37 These are the additional direct group relationships: * (CD), B c * (BD), D * (ac). and The two additional sets of perceptions include: A -- B and B -- A, A —- C and C —- A, and A —- D and D —- A. Also: A -— (BC), A —— (CD), A —- (BD), and, finally, A —- (BCD). The total number of relationships and perceptions, including those defined by Graicunas, from eighteen to forty-seven. Table has been increased 2 shows how this new number N' of relationships and perceptions of all sets increases as the number n of subordinates increases: TABLE 2 VARIATIONS OF NUMBERS OF RELATIONSHIPS WITH THE NUMBER OF SUBORDINATES ' n N1 N2 N3 N 1 3 0 0 3 2 8 2 3 13 3 17 12 18 47 4 34 50 80 164 5 67 180 320 567 6 132 602 1,212 1,946 7 261 1,932 4,424 6,617 8 518 6,050 15,696 22,264 9 1,031 18,660 54,432 74,123 10 2,056 57,002 185,300 244,358 11 4,105 173,052 621,368 798,525 12 8,202 523,250 2,058,168 2689,620 38 There is no simple equation which would be similar to Equation (1) as defined by Graicunas. However, the following are true: N' = N1 + N2 + N3 where (2) N1 =2<2n-1) +n <3) —3 _ n—1 n-2 + C (2n “1) N2 — I’lcl(2 —l)+nC2 (2 I) n 3 +. . . + nCn-l’ and (4) N = 3 c + 2n [2”1 —n]+ c [2n‘2 - 1] 3 n 2 n 2 n—4 c (219‘3 — 1) + n—1C 3(2 ‘ l) + nEn—l 2 + . . . + n—lCn—2J. (5) In Equations (4) and (5) C = [h(n — 1) (n — 2) (n - 3) n r . . . (n — r + l] /[rfl which is the standard definition for enumerating the number of possible combinations of n things taken r at a time. The derivations of Equa- tions (2) through (5) are the subject of the Appendix, however, their accuracy may be verified by calculating N' for n = 3 and comparing the result with the total established by actual count. Also, the possible re- lationships and perceptions may be set out symbolically as was done on pages 33 through 37, for any n and their number may be compared to that derived for that n from Equations (2) through (5). These equations were used to construct Table 2. By comparing N' in Table 2 with N in Table 1 for any n, it can be seen that N' is always greater than N. Also, it increases at a 39 much more rapid rate as n increases. It is suggested that, had Graicunas found N' instead of N, span of control might be defined in a different way today. For example, had he noted the more rapid rate at which N' increases, he might have set the limit of super- vision (span of control) at three instead of four and Urwick might then have stated the span of control prin— ciple using four or five and not five or six subordin- ates. As another possible alternative, Graicunas might then have observed the rapid rate of increase of N' with an increase in n and have concluded that, perhaps, keeping track of all of those relationships and per— ceptions is not the crucial factor limiting span of control that he first thought it to be. In any case, Graicunas' oversight or failure to explain away some possibilities that could be derived from a logical extension of his thinking damages his rationale. It is recognized in this study that these additional relation- ships and perceptions can have no validity until empirical evidence in support of them is created. The last shortcoming of Graicunas' rationale to be discussed in this study was his failure to show that, because an individual's immediate memory span for digits is six, his capacity for the supervision of subordinates is limited to four. That is, he should have cited 40 evidence showing that, whereas an administrator's ability to supervise is judged to be adequate when there are no more than four subordinates with "interlocking" work, it rapidly becomes inadequate as the number of such subordinates is increased beyond four. Although Graicunas did state that the "span of attention" for digits is six,9 he did not show that the capacity for remembering relationships is related to immediate memory span for digits and he did not show why he could in- crease the capacity for remembering relationships to forty-four (the maximum number of relationships he as— sociated with four subordinates). Taken together, these shortcomings of Graicunas' demonstration suggest that it cannot stand as a proof of span of control. However, his work is valuable for a number of reasons. First, it probably channeled and encouraged Lyndall Urwick's thinking on the subject, without which it could easily have lapsed into obscurity. Then, it has served as the object of study, stimulating stu- dents of administration to theoretical and practical refinements of organization design. Last, it has dra— matized the complexity of the supervisory situation. As Koontz and O'Donnell so aptly put it: 9Ibid. 41 The Graicunas theory does serve to emphasize the dramatic complexity created by a manager's having more than a few subordinates, seeming to approve of the often accepted standard of three or four subordinates. But, most importantly, the formula serves as the key to the problemcf span of management. For any managerial action that will reduce the number and frequency of relationships requiring the manager's atten- tion will increase his span of management and thereby reduce the costs and inefficiencies of an undue number of departments. 10 B. Additional Factors Affecting Span of Control Students of administration are in disagreement over the validity of the span of control principle, on both theoretical and practical grounds. One reason for its unacceptability to some is its failure to recognize the Operation of factors other than "interlocking work" that would reasonably be expected to affect it. As Barnard points out: The size of the unit of supervision , there- fore, usually is determined by the limitations of effective leadership. These limitations de— pend upon (a) the complexity of purpose and technological conditions; (b) the difficulty of the communication process; (c) the extent to which communication is necessary; (d) the complexity of the personal relationships in— volved, that is, of the social conditions.1l lOHarold Koontz and Cyril O'Donnel, Principles of Management (New York: McGraw—Hill Book Company, ' Inc., 1959), p. 74. 11Chester I. Barnard, The Functions of the Executive (Cambridge, Massachusetts: Harvard University Press, 1960), p. 107. 42 Griffiths feels that "structure should be related to the decision—making process, not to the number of human relationships which a mathematician believes an adminis— 12 . . . trator can remember." Knezev1ch, c1t1ng Newman, feels that the factors which influence the numbers in- volved in an effective span of supervision are: 1. The time available for such supervision. It follows the longer period the executive is willing and able to devote to his job, the larger his span of supervision; The mental capacipy and the personal adapt- ability of the executive responsible for supervision. These differences help to ex— plain in part why the effective span of supervision will vary; The complexity of the situation being super- vised. A single situation with a number of workers doing fundamentally the same things will enable an executive to supervise a larger number of personnel than otherwise. On the other hand, if the executive is res— ponsible for many unrelated activities, he will be able to supervise effectively a far smaller span of positions; The other duties of the executive. If the executive is to be responsible for general planning and control of the institution as well as supervision of a number of other administrators, his effective span will be far smaller than that for an individual of similar ability and experience who does not have these added responsibilities. The stabilityiof Operations. The greater the turnover among the teaching or adminis— trative staff, the more difficult it be— comes to supervise effectively a large span of operations. 12 (New York: Daniel E. Griffiths, Administrative Theory Appleton—Century—Crofts, 1959), pp. 78—79. 43 The capability and experience of subordinates. The more capable, the better prepared pro— fessionally, and the greater the experience of principal and teacher the relatively easier it becomes to supervise larger num— bers. This would imply that as administrat— ors and teachers become more capable through greater professional preparation and exper— ience, the larger would be the effective span of supervision. l3 "It follows that there is no magic number such as 3,7, or 11 that represents the effective span of supervision for any and all executives."l4 In a pragmatic approach to a determination of a "proper" span of control the Lockheed Missiles & Space Company defined the follow— ing as the critical factors affecting the span: 1. Similarity of function: the degree to which functions performed by the various com- ponents are alike or different. Geographic contiguity: the physical loca— tion of the components and personnel re— porting to a principal. Complexity of functions: the nature of the duties being performed by the organization components or personnel. Takes into account the skills necessary to perform satisfactorily. Direction and control: the nature of the personnel reporting directly to a principal. Includes the degree of the principal's at— tention which they require for prOper super— vision of their actions. Coordination: the extent to which the prin— cipal must exert time and effort in keeping actions properly correlated and in keeping his activiQr keyed in with other activities of the company. 13William A. Newman, Administrative Action (Englewood Cliffs, New Jersey: Prentice—Hall, 1950), p. 161. 14 Stephen J. Knezevich, Administration of Public Education (New York: Harper & Brothers, 19627} pp. 67—68. 44 6. Planning: the importance, complexity, and time required to review and establish future programs and objectives. 7. Organizational assistance: the help received by the principal from direct—line assistants, staff activities, and assistants—to. (In the case of first—line supervision, lead men would be included.) 15 It can be noted that, while some factors, such as com— plexity of function, are widely regarded to have a bear- ing on span of control, there is no general agreement on all of them. Regardless, the apparent over—simplifica- tion of Urwick's principle has rendered it unacceptable to many. The span of control principle has been challenged on both theoretical and practical grounds. Simon has questioned the validity of the principle in terms of its theoretical soundness. He writes: . . . A contradictory proverb of administra— tion can be stated which, though it is not so familiar as the principle of the span of con- trol, can be supported by arguments of equal plausibility. The proverb in question is the following: 'Administrative efficiency is enhanced by keeping at a minimum the number of organiza— tional levels through which a matter must pass before it is acted on.’ In many situations the results to which this principle leads are in direct contradiction to the requirements of the span of control. 16 15Harold Stieglitz, "Optimizing Span of Con— trol," Management Record, Vol. 24, No. 9, pp. 121— 129. Reprinted in Harold Koontz and Cyril O'Donnell (eds.) Management: A Bookof Readingp (New York: McGraw-Hill Book Company, 1964), p. 165. 16Herbert A. Simon, Administrative Behavior (New York: The Macmillan Co., 1947), pp. 26-28. 45 Simon's point is that, since no respectable theory of administration can be allowed to reflect internal in- consistency through the inclusion of two mutually con- tradictory propositions, then either span of control or the principle of fewest possible organizational levels must be rejected. The second criticism of span of control voiced by theoreticians is that it violates our democratic philosophy by encouraging centralization of authority and, thus, discouraging widespread participation in decision-making. The feeling is that such widespread participation is directly related to worker efficiency and morale. According to Gardner: There is good reason to believe that the gain in over—specialization and its twin brother, over—centralization of authority, has been lost in the debilitating and enervating effects they have had on employee morale and willingness to cooperate.17 Dale summarized the reasons for these challenges and the tendency toward a broader actual span of control: 1. The desire of executives to have access as high up as possible, as a means of advancement and a sign of status. 2. The need for keeping the chain of command as short as possible. The shorter the span of control, the more layers of super— vision there will be and the longer the lines of communication, with correspond— ing disadvantages. 17William H. Whyte, Jr. and the Editors of Fortune, Is Anybody Listenipg? (New York: Simon and Schuster, 1952), p. 129. 46 3. A natural tendency On the part of executives I to take a personal interest in as many as— ~pects of their job as possible, the lack of trust in the ability of subordinates, the fear of possible rivals, and the desire for power (as shown by the number of people re- porting). 4. The political argument that as many interests as possible should be represented. 5. The danger of overly—close supervision which may discourage initiative and self-reliance.l8 In real-life situations, span of control is gener- ally ignored. One needs only to look at the common class— room situation to find one teacher supervising the work of thirty or more pupils. Still in the educational setting, one building principal is often placed over fifteen or more teachers. In the Roman Catholic Church, some 750 line bishops and 1200 other persons report directly to the POpe.19 In 1955, although the Presi- dent of the General Motors Corporation had only six line Group Executives reporting to him directly, two of these Group Executives had eight General Managers reporting to him and one had thirteen!20 Many other industrial concerns have, with interesting results, rejected the span of control concept of Graicunas~Urwick. For example, in a twelve—year study of morale and efficiency conducted Sears, RoebuCk and Company, it was concluded that: 8Ernest Dale, Planningyand Developing the Com— pany Organization Structure (New York: American Manage- ment Association, 1955), pp. 52—53. 19Harold Koontz and Cyril O'Donnell, Principles of Management (New York: McGraw-Hill Book Co., 19643,p.229. 20Harlow H. Curtice, "General Motors Organization PhilOSOphy and Structure." "The DevelOpment and Growth 47 Detailed studies on the Span of control at Sears, Roebuck and Company very definitely showed the superiority in Operating efficiency of a large span of control, provided subordinates are of high competence and self—reliance. Sears' reg— ional vice—presidents now have full authority over everything in their territories, except purchasing, of course. These vice—presidents report to the president. As a result, Sears' president has now 13 executives directly under his supervision. These territorial vice presi— dents, in turn, have even more people reporting directly to them. In addition, other executives down the line have direct access to the presi— dent. 21 Military organizations, which first developed the notion of span of control and which are generally inclined to adhere to it closely in times of war, also modify existing spans of control by allowing large numbers of unsupervised subordinates to have the right of access to their chief. As Dale relates: General Eisenhower told me in an interview that in World War II he had at one time 150 battalion commanders reporting to him. This, he believed, resulted in cleaner understanding up and down the line, an opportunity for per- sonal inspiration, and a chance to voice com- plaints. Now it would be physically quite dif— ficult even to receive reports from 150 people or, to express it in organizational language, 'effectively supervise' so many people. What the General had in mind is that accessibility to the chief executive can make important con— tributions. The number of people he super- vised was small, while the number who had ac— cess to him was large. 22 of General Motors," a Statement before the Subcommittee on Anti—Trust and Monopoly of the United States Senate Committee on the Judiciary, Dec. 2, 1955, pp. 5—12. Reprinted in Harold Koontz and Cyril O'Donnell (eds.) Management: A Book of Readings (New York: McGraw-Hill Book Company, 1964), p. 196. :21Dale, Op. cit., p. 53. 22Ernest Dale, "Dynamics and Mechanics of Organiza- tion," in Organization Planning and Management Development (New York: Am. Management Association, 1951), pp. 7-8. 48 Although Urwick argues quite adroitly that the nominal ' rightcf access to a chief executive is quite different from the frequent use of that right,23 it goes without saying that even relatively infrequent use of such a right by each of a large number of peOple would signifi— cantly reduce a chief executive's amount of time for direct supervision and, with it, his effective span of control. A research study has made available information on the number of executives reporting to the president in one hundred companies having over 5,000 employees each. One of the major conclusions of this study was that the theoretical limits of the executive span of control are in practice more often violated than they are observed, as indicated in the following table. Table 3 indicates that the median number of executives reporting to the presidents of the organiza— tions surveyed was between eight and nine. It is in— teresting to compare the column headed "Number of Exec— utives" of Table 3 with the column headed "N" (the number of Graicunas—derived relationships) of Table 1. It is also interesting to note that, by Equation (1) that company president who has twenty—four executives 23Lyndall Urwick, "The Span of Control—~Some Facts About the Fables," Advanced Management, Vol. 22, No. 11 (November, 1956), p. 7. ’ 49 reporting to him had 201,327,144 such relationships to keep track of! It should also be noted that the presi- dents of twenty-four firms had thirteen or more subord- inates reporting to them directly. TABLE 3 NUMBER OF EXECUTIVES REPORTING To PRESIDENT IN 100 LARGE COMPANIES 24 Number of Number of Executives Companies 1 6 2 0 3 1 4 3 5 7 6 9 7 ll 8 8 9 8 10 6 ll 7 12 10 13 8 14 4 15 1 l6 5 17 0 18 1 l9 0 20 1 21 1 22 0 23 2 24 1 24Ernest Dale, Planning and Developing the Com— pany Organization Structure (New York: American Manage— ment Association, 1952, Research Report No. 20), p. 57. 50 C. Present Status of Span of Control Despite the reception that span of control has been accorded by administrators, there are at least two kinds of indicators of general agreement by them that something like it does affect supervisory situations. The first of these is the observation that, even though it is often not accepted, the Graicunas—Urwick conception is repeatedly found in new texts on administration.25 The other indication can be inferred from noting the repeated attempts that have been made to study it or to establish it for practical situations. The Sears, Roe— buck and Company study that has already been mentioned is one of these. Another is the study made by the Lock— heed Missiles and Space Company.26In the latter, wherein a "proper" span of control was pragmatically defined as one which was not improper, Lockheed first isolated‘ seven factors (see pp. 43—44 of this study) deemed to be the most significant to the span of management and then weighted six of them in order of their importance. The seventh factor, Organizational Assistance, was treated differently inasmuch as it was designed to lighten rather than increase the supervisory burden. So, in— stead of giving this factor a straight point value, Lockheed assigned percentage values to various types of 25The reader is requested to review the footnotes of this study. 26Harold Stieglitz, op.cit., pp. 164—169. 51 assistants. These point values were then set up as a supervisory index to "suggested spans." The higher the point value the greater the supervisory burden and the lower the suggested span. Relating of actual spans to point values was done by analyzing different super- visory situations and fitting a trend line to the re~ sults. From the analysis, it became apparent that two scales would be required——one for middle managers; another for first-line supervisors. In the latter case, the same index numbers provided for approximately twice the span. So far, Lockheed has used this program in only a few units of the company. In each case, the average span of control was extended from about a half person to slightly more than a person and the number of levels was reduced by about one. It was stated that reductions in managerial personnel and supervisory pay— roll were "substantial." It is to be quickly pointed out that, while Lockheed's organization analyst felt that their approach could be generally used throughout all other companies, its mere application did not bring about the reductions mentioned above. They felt that their approach was but a useful guide to be used along with and not as a substitute for astute judgments. In conclusion, it seems fair to say that span of control has evolved amid speculation, theorizing, 52 and practical experimentation, with few if any attempts to relate it empirically to observed reality. It is to this problem that the attention of this study is now focused. CHAPTER IV SOME NEW CONSIDERATIONS The objective of this chapter is to establish a basis in theory and research for a more—nearly ade— quate restatement of the principle of span of control. Consistent with the assumption that both supervision and control can be analyzed into communication and information—processing procedures, it was felt that the theoretical basis should describe the actual mechanisms of inter—personal communication and human information processing. To do so,each point in the theoretical model or models developed should cor— respond to a point in reality as evidenced by sup— porting research. In this chapter the two mechan— isms are modeled separately. Of the two the com— munication model is given first. It is the less difficult to develop because, while there are many such models to consider, these have been categorized and are capable of separate discussion and applica- tion. The model chosen as the basis for this study was taken from information theory because it was designed toaccommodate a measure of the amount of information in a communication. Such a measure is necessary if span of control is to be redefined 53 CHAPTER IV SOME NEW CONSIDERATIONS The objective of this chapter is to establish a basis in theory and research for a more—nearly ade— quate restatement of the principle of span of control. Consistent with the assumption that both supervision and control can be analyzed into communication and information-processing procedures, it was felt that the theoretical basis should describe the actual mechanisms of inter—personal communication and human information processing. To do so,each point in the theoretical model or models developed should cor— respond tO a point in reality as evidenced by sup— porting research. In this chapter the two mechan— isms are modeled separately. Of the two the com— munication model is given first. It is the less difficult to develop because, while there are many such models to consider, these have been categorized and are capable of separate discussion and applica- tion. The model chosen as the basis for this study was taken from information theory because it was designed toaccommodate a measure of the amount of information in a communication. Such a measure is necessary if span of control is to be redefined 53 54 in terms of Man's information receiving, processing and transmitting capabilities. On the other hand, if knowledge may be equated with consensus among researchers, then relatively little is known about human capacities for information processing. As a result the information processing model which is given second is the less comprehensive and the more tentative of the two. Nevertheless, some studies have been made in this field that are valuable both for their findings as well as their methods. From such studies a tentative description of some para- meters on human information processing has been modeled. Because relatively little is known about human information-processing mechanisms, it has been neces- sary to assume that there exist limitations on this capability that determine span of control. However, it is desirable to show that this assumption is both reasonable and useful so that researchers might be stimulated to efforts which will yield the findings needed before the principle can be established with satisfactory rigor. Since it is possible in this instance to demonstrate both reasonableness and util- ity, the third part of this chapter is devoted to this task. Reasonableness is established by showing how the factors that are held by administrators to be the 55 determiners of span of control may be translated into the terms of communication and information theory and treated in one cohesive theoretical structure. Util— ity is established by showing how the joint model may be used to explain the satisfactory operation of some particular supervisory situations having "broad" spans of control which apparently contradict the present concept. It is recognized that the utility of the concept would be enhanced by its ability to predict whether or not a prOposed supervisory situation is within the intended supervisor's span of control. How— ever, it is at this point that much patient study is needed to develop the concepts and to define the con- stants that will make the following body of ideas into an instrument that can be used successfully in organ- izational design. A. A Communication Model The communication model about to be developed is based upon that of Claude Shannon, the father of information theory.1 In Shannon's model, a source lClaude E. Shannon and Warren Weaver, The Mathematical Theory of Communication (Urbana, Ill— inois: The University of Illinois Press, 1964), p. 7. 56 generates a message that is sent by a transmitter as a coded signal through a noisy channel to a receiver that decodes the signal and sends the message along to a destination. Figure 1, below, shows the essential components of this model. NOISE SOURCE MESSAGE SIGNAL-—§ SIGNAL MESSAGE v I J L -' EMNHKE3__7 TRANSMITTER}Q _) RECEIVER _;]DESTINATION1 CHANNEL FIGURE 1 A DIAGRAM OF SHANNON'S COMMUNICATION MODEL A discussion of this model begins with a de— finition of terms. It is felt that knowledge is stored as potential energy. When it is desired to convey knowledge, the device in which the knowledge is stored, called the source,2 formulates a message which consists 2Definitions on pp.56 and 57 are taken from Ibid. pp. 7, 8, and 33, 34; also from Thomas H. Crowley, ep. ‘21. Modern Communications (New York: Columbia Univer— sity Press, 1962) Chapter I. 57 of a sequence of symbols. These symbols are then I transformed into an amount of kinetic energy called a signal, the forms of the symbols in the signal being called its 2292' For this discussion, the trans— formation of potential energy into kinetic energy is called encoding, the transformation of kinetic energy from one form into another is called re-coding and the transformation of kinetic energy into potential energy is called decoding. These three processes are car- ried out by arbitrary devices called transducers. A transducer is a transmitter if it emits output further from its source than it receives input and a receiver if it emits output nearer to its destination than it receives input. A pair of transducers is connected by a channel or papd which is the physical medium for prOpagating the signal energy. The channel is defined more nearly precisely by the kind of signal energy it carries, such as visual or auditory, while its ability to accept variations in code defines its band width. Within a given band may exist sub—bands. That is, within the visual band there are the literal and pictorial sub— bands and within the auditory band there are the cor— responding verbal and non—verbal (sound effects and music) sub—bands. Each of these sub—bands may carry signal energy in many different codes. 58 As a signal is carried along a channel, it is attenuated or weakened by resistance which is a char- acteristic of every channel. Every real channel also carries unwanted signal energy or noise which serves to confound the intended signal. The destination is the device for which the knowledge is intended and at which the signal is decoded and the message repro- duced. Because of attenuation and noise, it is not possible to reproduce a message faithfully. That is, every received message carries with it a degree of un— certainty or eguivocation. One goal of communication engineering is to build communication systems capable of reproducing messages as nearly faithfully as pos- sible. Such systems are commonly known as having high fidelity. The system illustrated in Figure 1 falls far short of describing typical two—way inter-personal communication. To increase its usefulness for this purpose it needs further development. First of all, let it be noted that, in such communication,source and destination are frequently interchanged as mes- sages are sent back and forth. Also, more than one channel segment is usually found between a source and a destination. That is, there may be any number of channel segments and transducers connected in series if some qualifications may be specified: (1) the 59 transducer must be able to accept the signal from one segment and recode it so that it can be accepted by the other segment, (2) attenuation must not reduce the signal strength below that needed for satisfactory reception, and (3) the amount of noise introduced must not garble the message beyond recognition. Fin— ally, it is to be observed that inter-personal com- munication is frequently multi—modal; that is, a "mes— sage" is frequently if not usually derived from the synthesis of several messages, simultaneously received along two or more modalities. For example, in a face— to—face conversation between two individuals, an ob— jective message received in the auditory verbal mod- ality is modified by the speaker's tone of voice (auditory non—verbal modality), by gestures he makes (visual pictorial modality) and, perhaps, by others as well. By means of these accompanying modalities the affective dimension of personal interaction may be achieved. Taken together, such "messages" must be conveyed by sets of channel segments and transducers that are connected in parallel between two source- destination combinations. The system illustrated in Figure 2 incorporates these additional features. ZOHHKNUHZDZZOU 1Hemomm. momDOm _ one _ _ Iemomm mmobnmz