The Impossibility of a Neutral Hierarchy

Transcription

1 The Impossibiliy of a Neural Hierarchy THOMAS H. HAMMOND Michigan Sae Universiy PAUL A. THOMAS Washingon Universiy 1. INTRODUCTION I is commonplace for presidens, no long afer aking office, o develop a disrus of he informaion and advice sen o hem by he federal bureaucracy. All oo ofen, wha is sen appears biased. The informaion looks selecive, irrelevan, or misleading. The bureaucracy's inerpreaions of evens seem o reflec an insular bureaucraic culure. The bureaucras' advice appears self-serving and more suied o heir own needs and ineress han hose of presiden or counry. There are many reasons informaion and advice sen o he presiden migh be biased. Some sources of bias come from ouside he bureaucracy. Ineres groups and heir congressional allies, for example, can someimes force bureaucras o make one choice raher han anoher. Oher sources of bias sem from he views, ineress, and perspecives of he bureaucras hemselves. Air Force officers ofen seem o prefer flying manned airplanes o ending unmanned drones and supervising missiles in silos. Some Fores Service officials appear o prefer consumpive uses of he naional foreslands logging, mining, grazing o recreaional uses. Many The auhors hank Jane Fraser, Brian Humes, James Moore, Ed Packel, Ken Shepsle. Barry Weingas, he ediors and referees of his Journal, and paricipans in seminars a Purdue Universiy, Washingon Universiy, and SUNY-Sony Brook for heir percepive commens on earlier drafs of his paper. Suppor was provided by Purdue Universiy and he Purdue Research Foundaion, Michigan Sae Universiy, and he Naional Science Foundaion. We alone remain responsible for our inerpreaions and conclusions. Journal of Law, Economics, and Organizaion vol. 5, no. 1 Spring 1989 C 1989 by Yale Universiy. All righs reserved. ISSN

2 156 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 universiy professors prefer working on heir research o meeing wih undergraduaes. In each case, hese officials can be expeced o presen o heir superiors informaion and advice ha suppor heir own concerns and ineress. Sill anoher source of bias is he very fac ha policy-making in he execuive branch akes place inside a large hierarchical srucure. I has ofen been argued (see Tullock and Downs, for example) ha orders passed down a hierarchy and informaion and advice passed upward will end o be disored during ransmission. Wheher his disorion is deliberae or inadveren, wha he recipien hears may be quie differen from wha was originally sen. Thus hierarchy iself migh appear o be a cause of disorion. Whaever he source of bias, presidens have good reason o be concerned; as Noron Long once remarked abou he provision of informaion by bureaucracy: The enormous power ha subsanial conrol of he acceped version of he facs gives o any group mus be faced. Even wih he bes inenions, facs are rarely presened in a fashion ha is neural o all he paries a ineres. Indeed, if hey are o do any useful office in clarifying he real alernaives of public policy, hey mus foreclose some alernaives, and in doing so give umbrage o heir proponens. The danger ha he fac-gahering process will be corruped is always presen. (1954:28) To proec hemselves agains bureaucraic bias presidens have ried a wide variey of sraegies. One is for he presiden o consul personally wih lower- and middle-level expers in he bureaucracy, hereby avoiding biases in informaion and advice impared by upper-level officials. Presiden Kennedy's calls o mid-level officials (Halperin, 1974:170) serve as bu one example of his sraegy. This "do i yourself" approach has obvious coss. Consrains on he presiden's ime, energy, and cogniive capaciy make i difficul for him o mee wih each exper, comprehend wha each has o say, and ake heir recommendaions ino accoun. Presiden Carer's inclinaion o dive ino he deails of many issues suggess he limis of his sraegy. His eviden masery of deail came a he expense, or so i has been alleged, of a broad perspecive on he issues a hand. Anoher sraegy is o avoid reliance on he permanen bureaucracy by creaing a emporary advisory apparaus beholden only o he presiden. As he recen hisory of such boards and councils makes clear, his oo is an imperfec sraegy. The larger and more capable such an apparaus, he more i akes on he feaures of he insiuions i was designed o circumven: is officials develop ineress and views differen from hose of he presiden, and hey manifes he same concerns for saus and jurisdicional urf as heir brehren in he regular deparmens and bureaus. And his kind of advisory apparaus generally remains dependen on he regular agencies for raw informaion and for he capaciy o carry ou field operaions. A hird sraegy is o creae an incenive sysem o induce he bureaucras o do wha he presiden wans hem o do. Bu as presidens have invariably

3 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 157 discovered, he incenives hey can manipulae are meager in scope and effeciveness. Sudies and commenaries by Heclo (1977a, 1977b), Allison (1982), Bower, Rapp and ohers have corroboraed his presidenial experience: he incenives available o public managers are rarely commensurae wih managerial goals. Execuives in he privae secor are no quie so helpless. Noneheless, he ineres hese execuives show in managerial echniques (for example, "change your corporae culure") no direcly relaed o radiional incenive sysems suggess ha even in privae firms hese incenive sysems have serious deficiencies. Of course, here are many oher sraegies; see discussions by Desler, George, Downs (1967, chap. 7), and Tullock (1965, chaps ), for example. Bu in one way or anoher hese sraegies also prove defecive; over ime, each presiden finds he has lile choice bu o rely, o a significan exen, on he informaion and advice produced by he permanen bureaucracy. Hence presidens also seek o proec hemselves by reorganizing he deparmens and bureaus so as o overcome heir apparen biases. The presidenial goal is o have informaion compiled and inerpreed, and advice proffered, wihou regard o personal, professional, or organizaional concerns. If anybody's concerns are o be refleced, hey should be he presiden's. Thus aemps are made o shif personnel from one office o anoher, o group he officials in differen sors of ways, o redefine heir responsibiliies, and o redraw lines of auhoriy connecing he officials o each oher and o he presiden. Presidens are no alone in his pracice: new chief execuives of business firms frequenly reorganize heir firms, and for similar reasons. This aricle focuses on he possibiliies and limis of his sraegy of reorganizaion. To ensure ha wha arrives a any chief execuive's desk is neural and unbiased is, in par, a problem of organizaional design. Tha adminisraive srucures could indeed be designed, a leas in principle, so as o have a neural impac on policy-making was implici in he radiional "poliics versus adminisraion" dichoomy of Wilson and Goodnow, as well as in he adminisraive heories of laer scholars and poliical reformers. Thus we find Kaufman discussing he progressive reformers' belief in he possibiliy of "neural compeence' in he bureaucracy, and March and Olsen (1983:283) observing ha classical adminisraive heory "sees adminisraion as he neural insrumen of public policies." These classical views sill reain heir hold, for as lae as he mid-1970s we see such sophisicaed scholars as Hugh Heclo discussing he crafing of he OMB's relaionship o he presidency in erms of "he problem of neural compeence," he subile of his widely read 1975 aricle. Even fify years ago, hough, some sudens of organizaion (see in paricular Gulick and Meriam) were beginning o sense ha organizaional design involves inescapably poliical dilemmas and choices (see Hammond,

4 158 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 Forhcoming). More recenly, in a sudy of federal execuive organizaion, Seidman observed ha "organizaional arrangemens are no neural. We do no organize in a vacuum. Organizaion is one way of expressing naional commimen, influencing program direcion, and ordering prioriies. Organizaional arrangemens end o give some ineress, some perspecives, more effecive access o hose wih decision-making auhoriy, wheher hey be in he Congress or in he execuive branch" (1970:14). Working in his general radiion, Hammond (1986) has skeched ou explici mehods for analyzing how organizaional srucures migh be expeced o influence oucomes. There is hus ample reason o hink ha any paricular organizaional srucure will bias policy-making oward some oucomes and away from ohers. Some of he sources of bias menioned above may be impossible o eliminae. For example, i is difficul o hink ha he influence of ineres groups and heir congressional allies can be compleely neuralized. Similarly, i is difficul o preven even he mos high-minded specialiss from developing personal ineress and concerns ha do no sem direcly from he subsance of heir experise. Ye wih regard o quesions of reorganizaion, here is no sudy, wheher in poliical science or economics, ha demonsraes ha aemping o creae a neural srucure for bureaucraic policy-making is necessarily an exercise in fuiliy. The poin is nowhere explicily addressed, much less formally demonsraed. Here, however, we confron he cenral problem: for a reasonably genera] se of circumsances, we formally prove ha i is impossible o design a hierarchy ha does no affec he choices made via he hierarchy. Our analysis and resuls conribue o an undersanding of neuraliy in hierarchical policy-making in several ways. Firs, our formal model makes clear he remarkably wide variey of organizaional feaures ha can conribue o organizaional bias. Even wihou furher analysis, mere consideraion of wha is required for a srucure o be neural we call hese "neuraliy properies" suggess how exraordinarily difficul a ask is he design of a "neural hierarchy," ha is, a hierarchy ha does no affec organizaional decisions. Asking a srucure o be uerly neural wih respec o oucomes urns ou o be a requiremen far more demanding han generally recognized. Second, by esablishing ha hese neuraliy properies are collecively incompaible we make i clear ha presidens and oher chief execuives should no wase heir ime pursuing wha urns ou o be an unachievable goal. Third, he incompaibiliy of he neuraliy properies forces he organizaional designer o consider rade-offs among he various kinds of biases ha are due o violaion of he various neuraliy properies. Alhough here is nohing in our formal model ha can ell he designer how o make hese rade-offs, our aricle begins he essenial process of clarifying wha hese various biases migh be and hus wha he rade-offs migh involve. Finally, and perhaps mos imporan, addressing he quesion of organi-

5 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 159 zaional neuraliy forces one o consider a variey of complex and suble issues abou he desirabiliy of neuraliy in policy-making. Belief in he desirabiliy of neuraliy is widespread. Bu asking ha a srucure be neural wih respec o oucomes requires organizaional feaures ha may be undesirable for oher reasons. If some feaure required for neuraliy is undesirable, one possible conclusion is ha neuraliy iself is less desirable han may have been hough. Ye we are relucan o asser ha a concern for organizaional neuraliy is misplaced, however impossible i may be o achieve. One prime reason is ha many large bureaucracies in governmen, ranging from he Bureau of Labor Saisics o he Cenral Inelligence Agency, have criical informaion gahering, processing, and assessing responsibiliies, and i seems reasonable o wish ha hese organizaions pursue heir asks in a neural and unbiased fashion. So we seem o have a problem of organizaional design in which every soluion is unsaisfacory in some respec. Indeed, his is a general characerisic of impossibiliy heorems: hey involve he discovery ha paricular kinds of conroversies canno, in principle, be resolved. Bu his does no mean ha such an analysis is no worhwhile. Once again, a succinc observaion by Long nicely summarizes he maer: "Once he fac is faced ha he bureaucracy is no, and canno be, a neural insrumen solely devoed o he unmoivaed presenaion of facs o, and he docile execuion of orders from, poliical superiors, a more realisic picure of is problems and poenial can be had" (1954:27). We hope our own essay conribues o his more realisic picure of he "problems and poenial" of bureaucracy. 2. DECISION MAKING IN "TREES" When he direcors of organizaions make decisions, hey are ofen dependen on he informaion and advice forwarded o hem by subordinaes. Our cenral concern here is wheher a srucure can be designed ha does no somehow affec he decisions, based on his informaion and advice, made by he direcor. Following he approach of he principal-agen heoriss (Levinhal), one could ask how he direcor should design an incenive sysem o elici advice from subordinaes ha will be "bes," in some sense, for him o adop. Bu as already noed, he incenives available o superiors are quie limied, and so models of organizaions ha downplay he role of incenives may have considerable relevance. In his aricle we se aside his imporan (and quie complex) incenive quesion and focus solely on he impac of he srucure hrough which he advice is rendered. Ulimaely, of course, a more general model of neural hierarchy will have o incorporae exensive hierarchical feaures as well as incenive sysems. (We make furher observaions abou incenive sysems and neuraliy in secion 5 below.) We will model he flow of informaion and advice from subordinaes o

6 160 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 he direcor as a boom-up kind of process. As former Secreary of Sae Acheson once remarked, "One fac... is clear o anyone wih experience in governmen: he springs of policy bubble up; hey do no rickle down" (1960:41). Our general sory does allow he direcor o ask his subordinaes, in a op-down fashion, o consider some paricular problem; a his poin alernaive soluions o he direcor's problem are generaed by boom-level field officials and forwarded o heir superiors. Whaever he background sory, policy-making in our model will be aken as saring wih he boomlevel field officials who make recommendaions o higher-level managers, wih he direcor making he ulimae decision. If a direcor's decisions are a funcion of he informaion and advice received from he subordinaes, hen changes in he informaion and advice he receives can be expeced o change his decisions. We will call a srucure neural if, given some iniial pieces of informaion or advice forwarded by he boom-level field officials, changes in he inervening srucure do no change choices made by he direcor. If a modificaion in he srucure changes wha he direcor chooses, assuming ha he field officials have no changed wha hey iniially repor, hen he srucure iself is affecing he direcor's decision. The srucure is hus nonneural wih respec o choices, and he srucure will be said o bias he choices. To show ha no neural hierarchy can exis, we firs esablish he properies of a neural hierarchy. We hen prove for wo classes of hierarchies ha no srucure of even modes complexiy can have all he required neuraliy properies. Srucures in he firs class have he simple pyramidal form shown in figure 1A, and a leas a minimal amoun of complexiy; we will call hese srucures "rees." Srucures in he second class have he form shown in figure IB and migh be called "marix hierarchies." The properies of rees will be considered in his secion and he nex; hose of marix hierarchies will be considered briefly in secion 4. Following Owen (1968:2), a ree can be formally defined in he following way: Definiion: A ree is a finie collecion of poins conneced by lines which form a conneced figure ha includes no closed curves. I follows ha here is a unique sequence of poins and lines joining any wo poins. Consider poins A, B, and C, and disinguish poin A from he ohers. The poin B is superior o C (C is subordinae o B) if he sequence of lines connecing A wih C passes hrough B. We say B is C's immediae superior (C is an immediae subordinae of B) if C is subordinae o B and here is a line connecing B o C. A poin is iniial if no poin is subordinae o i. All noniniial poins are decision-making. When applied o organizaions, he disinguished poin will be called he "direcor," each iniial poin is a "field official," and he oher decision-making poins are "managers." A se of poins wih a common immediae superior is a "policy group." Noe ha in radiional adminisraive language, a ree

7 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 161 Direcor Regional Headquarers Sae Headquarers Field Officials Figure 1A. "Tree" Direcor Regional Headquarers Sae Headquarers Field Officials Figure IB. "Marix Hierarchy" follows he "uniy of command": no subordinae has more han one immediae superior. We now inves a ree wih some organizaional feaures: Definiion: A hierarchy is a ree wih he following properies: HI: here exiss a se S which is he se of alernaives o be considered by he organizaion. H2: here exiss a se S,CS for each person i which is i's jurisdicional se. Each «may choose from among he elemens in S (. H3: here exiss a choice funcion f, for each field official i. The argumens of he choice funcion are hose exernal facors ha he field official is exposed o or is expeced o monior. The form of each /, depends upon unspecified parameers such as professional beliefs, personal ases, or poliical sraegies. Each f always produces an elemen of S, H4: here exiss an aggregaion funcion g, for each manager and he direcor i, which akes he vecor of all immediae subordinaes' choice funcion or aggregaion funcion values, called he advice vecor, and produces an elemen of S,. One noe abou HI: if S were o conain an opion ha everyone in he

8 162 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 organizaion found unwise or undesirable, hen one migh no worry if policymaking is biased agains his undesirable opion. Hence we migh assume (hough his is no essenial o our formal resul) ha every opion in S is, a leas in principle, a "reasonable" or "desirable" choice. For example, S migh consis of he bureaucracy's enire reperoire of officially approved "sandard operaing procedures" (Allison, 1971, chaps. 3-4), and he bureau's problem would be o selec he proper SOP, given he bureau's curren siuaion. One would wan he curren siuaion o govern choice, and no he srucure, hence he desire for he srucure o be neural. Given definiions H1-H4, he following procedures describe how boomup policy-making works. Each field official selecs an elemen of S, via his choice funcion/. The advice vecor produced by he field officials in a policy group is processed by he policy group's immediae superior (is manager) who, using his aggregaion funcion g,, selecs some elemen of S,. This process coninues on up he hierarchy unil he direcor, using his aggregaion funcion g d, selecs some elemen of Sj, based on he advice vecor of he policy group immediaely beneah him. Our sudy concerns organizaions wih a leas a minimal amoun of complexiy, which we call nondegenerae hierarchies: Definiion: A nondegenerae hierarchy is a hierarchy wih he following properies: ND1: here are a leas wo elemens in S. ND2: here are a leas wo field officials REQUIRED NEUTRALITY PROPERTIES Wha properies mus a nondegenerae hierarchy have for i o be neural? Somewha surprisingly, almos no aenion seems o have been paid o his quesion in he lieraure of public adminisraion, organizaion heory, or he economics of organizaion. A he leas, we have been unable o find useful or illuminaing references. I urns ou ha each sep in he procedures described above, by which he field officials' repors are aggregaed ino a choice by he direcor, has he poenial o bias oucomes. Hence he working of each procedural sep mus be "neuralized" so ha he procedure will no affec policy-making. The eigh neuraliy properies lised below, labeled Nl hrough N8, all appear necessary for a srucure no o affec oucomes. Our argumen is ha if one wans a neural hierarchy, hen each of hese properies is essenial for neuraliy. If a real-world organizaion lacks one or more of hese properies, hen i is a risk of exhibiing some kind of bias in policy-making. We emphasize ha we are no arguing ha hese neuraliy properies are in some sense characerisic or descripive of real-world organizaions. In fac, some of hese properies may seem odd, unreasonable, or even undesirable for normal organizaional funcioning. In his sense, hen, our

9 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 163 analysis does no follow he more usual syle of impossibiliy proofs in social choice heory. Tha syle is o posi several principles, each of which is reasonable or desirable on is own erms and for is own reasons, and hen demonsrae ha hese principles conflic. For our purpose here, each of he properies we discuss is no necessarily desirable on is own erms; insead, each is required if here is o be neural policy-making in he hierarchy. So if any of our neuraliy properies seems unreasonable or undesirable, we sress ha his is no a flaw in our model's assumpions. Insead, i is a sign ha a deep conflic exiss beween neuraliy in organizaional policymaking and oher hings ha we legiimaely wan from organizaion. In fac, he surprise value of our analysis may lie as much in he recogniion of wha srucural properies are required for neuraliy as in our formal proof ha hese neuraliy properies can coexis only in a degenerae hierarchy. Nl: Neural choice rules: for each field official i, he image of/, is he enire se S,. This axiom requires ha each field official use a choice rule, / such ha he will choose any opion in S, under some circumsance. In effec, we are assuming ha no field official has such a bias agains some opion ha he will never recommend i under any circumsance. If some opion is always precluded by he choice rules, he consequence for he ulimae oucome would clearly be nonneural. While i may be impossible o eliminae individual bias, he assumpion of unbiased field officials is, for our purposes, a very imporan assumpion since we will prove ha a srucure necessarily biases oucomes even if each field official is compleely unbiased. This is a much more powerful and ineresing resul han a proof ha a srucure biases oucomes whenever he field officials hemselves are biased. Alhough we will assume ha he field officials will be he only individuals who can exercise rue choices, his is no essenial o our model. We could insead specify for each field official wha elemen of S mus be chosen for each "sae of he world" ha he field official observes. This would eliminae (by assumpion) any discreion for he field officials. Bu specifying he field officials' choices in his fashion would complicae he model wihou adding anyhing useful. Wha is of ineres for our model is wheher, given he iniial repors however generaed from he field officials, he hierarchy can process hem in a neural fashion. Hence we will simply assume ha he field officials are free o make choices, subjec o he key requiremen ha each field official i will choose each opion in S, under a leas some circumsances. N2: Neural aggregaion rules: for each i who is a manager or direcor, he image of g, is he enire se S,. Axiom N2 is similar o Nl: each manager and he direcor mus use an aggregaion rule, g,, such ha any opion in S, could conceivably be chosen, given some advice vecor from subordinaes. If he rule used o aggregae

10 164 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 he advice of subordinaes ino a decision never produces some paricular opion in S,, i has a permanen bias agains his opion. The aggregaion rule would hus be nonneural in is impac. N3: Neural jurisdicional assignmens: for all i, S, = S. This axiom specifies ha each person in he organizaion may choose (via his /, or g,) any alernaive from S, he enire se of alernaives which he organizaion is considering. This means here are no jurisdicional resricions ha limi he alernaives an individual may consider. (Nl, N2, and N3 ogeher play a role in our model which is analogous o he "universal domain" assumpion ofen made in social choice heory: every possible configuraion of choices by field officials and managers is allowable and mus be aken ino accoun by he decision rules.) We leave a complee discussion of his neuraliy requiremen o he end of his secion because i raises he mos complex and difficul issues in he enire lis of neuraliy properies. N4: Neural decision makers: a binary operaor, o, on S exiss such ha, for each decision maker each manager and he direcor any advice vecor (a,,..., a k ) which lies in he domain of g, has he image a, o (... (a _j o (a _, o a k ))) which lies in S. Thus he aggregaion rule g, in N2 is a binary operaor. Three aspecs of N4 bear discussion. Firs, a concern for neuraliy requires ha each decision maker use he same aggregaion rule: ha is, each decision maker mus make his aggregaion decisions exacly like every oher decision maker. This means ha he managers and direcor mus aggregae he field officials' repors according o fixed rules which are enirely impersonal in heir operaion. In oher words, decisions by he higher-level decision makers are compleely preprogrammed; he decision makers exercise no discreion whasoever. One migh hink of a manual or rulebook ha specifies in complee deail wha aggregaion decisions mus be made, given all possible combinaions of recommendaions from subordinaes. This resricion on he discreion of higher-level officials of course seems exreme. Ye if he same aggregaion rule were no used everywhere in he organizaion, wo managers receiving he same advice vecor from subordinaes migh respond differenly. Hence simple changes in he hierarchy could obviously affec he oucome: srucures placing hese wo managers in differen locaions (everyhing else held consan) should be expeced o produce differen oucomes. In figure 1A, for example, given some repors by he field officials, if managers A and B use differen aggregaion rules, he fac ha field officials 1 and 2 make heir repors o manager A and no o manager B could obviously be expeced o affec he ouicome. In oher words, a

11 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 165 change in srucure changing he locaions of A and B would no be neural wih respec o oucomes. Since he decision makers have no discreion and mus make decisions by fixed and impersonal aggregaion rules, one may even hink of he "managers" and "direcor" no as persons bu as "posiions" consising only of a rulebook (each posiion has he same rulebook) for making decisions. Each "posiion" in he srucure merely receives messages from subordinaes and repors he proper response from he rulebook. Noe here ha if we eliminae any role ha individual persons may play as managers and direcor and sill find ha he hierarchy is nonneural, we have a more general and powerful resul han if any policy-making biases can be ascribed in any sense o he acions (and biases) of he persons who are he managers or direcor. So alhough we will generally speak of managers and he direcor as persons, keep in mind ha for our purposes hey may as well be auomaons. The second aspec of N4 needing discussion is o poin ou ha he aggregaion rule mus produce decisions or oucomes ha lie in S; mahemaically speaking, he assumpion is ha he operaor saisfies closure. If a manager or direcor could selec an opion ha was no available (a leas in principle) o any subordinae, his would be equivalen o allowing he decision maker o make decisions ha compleely disregard he advice of subordinaes. Third, he assumpion ha he aggregaion rule used by each manager and he direcor is a binary operaor means ha he rule processes advice from subordinaes wo pieces a a ime. Unlike he oher aspecs of N4, he binary operaor assumpion does no sem from neuraliy concerns: a model of a neural hierarchy does no require a binary operaor. This assumpion is simply a paricularly useful one for conducing our formal analysis since i allows us o use a paricular kind of mahemaics o prove our resuls. Moreover, given our concern wih he boom-up aggregaion of informaion and advice in neural srucures, here does no seem o be an obvious alernaive. Noneheless, we can posi a clear behavioral raionale for he binary operaor assumpion. The raionale is he same as he raionale for why he direcor relies on a hierarchy o organize, summarize, and inerpre he field officials' advice in he firs place. The argumen is ha each manager and he d J recor is boundedly raional and, excep in he simples of hierarchies, could no possibly ake all he subordinaes' pieces of advice ino accoun simulaneously. Each would face an overwhelming compuaional problem if he ried. His decision problem mus be broken down and simplified in some fashion. One of he simples rules of humb he decision maker migh use here is o lisen o he firs wo pieces of advice in he advice vecor from subordinaes and aggregae hem ino a enaive decision. Then he nex piece of advice is considered'and a new enaive decision is made. This process

12 166 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l coninues unil he las elemen of he advice vecor has been considered. Many behavioral heories of decision making characerize individual decision makers as considering alernaives sequenially in his manner (see Simon, 1957; Cyer and March, 1963:86, 113; and Lindblom, 1959:81, for example). More recen models are also broadly consisen wih a sequenial iem-byiem or aspec-by-aspec view of decision making (see Tversky, 1972; Tversky and Saah, 1979; and Axelrod, 1973:1264, n. 116). This sequenial process can be represened by a binary operaor. This assumpion abou binary operaors may be he leas saisfacory of our assumpions. In secion 4 we prove ha no all aggregaion rules can be represened as binary operaors, and we also discuss alernaives o our binary operaor assumpion. N5: Neural grouping: he binary operaor, o, is associaive. This axiom requires ha he aggregaion rules he g/s used o process elemens of he advice vecor in sequence mus no depend on he way elemens are grouped and preprocessed before hey are considered. Tha is, if he hierarchy is o be neural, hese aggregaion rules mus work independenly of he manner in which field officials and managers are clusered in policy groups. If he binary operaor were no associaive, his would mean ha srucures wih differen ways of clusering subordinaes in policy groups would produce differen oucomes, and he srucures would no be neural. In figure 2, for insance, if he binary operaor were no associaive, hen srucure A, which clusers he middle and lef budge examiners in a policy group under he manager, migh yield a differen oucome from srucure B, which clusers he middle and righ budge examiners under he manager. (The full meaning of his figure 2 example will be discussed in secion 3.) In general, he associaive propery of he binary operaor forces he ulimae oucome from a paricular se of iniial choices by field officials o be independen of he shape of he ree. (This neural grouping assumpion is analogous o a requiremen ha he agenda used by a commiee or legislaure be "pah independen" ha is, ha he agenda chosen no affec he oucome. See Plo, 1973:1083, in which he speculaes ha "he mahemaical srucure underlying pah independence conceps such as hese appears o be... he associaive law.") Noe ha N5 presumes N4, bu N4 does no presume N5. N6: The possibiliy of neural choices and decisions: he se S possesses a righ neural elemen, e, such ha for all as, a o e = a. This axiom allows an individual in he organizaion o defer o he choice or decision of anoher person in his policy group. Thus in S here is always a "neural" alernaive for example, "I really don' have an opinion on his issue" which when aggregaed by a manager or direcor wih some oher recommendaion yields he oher recommendaion. In effec, an individual

13 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 167 Srucure A Oucome: 0 Srucure B Oucome: OMB Direcor Manager Budge Examiners. Figure 2. can express nonineres in some policy area, or defer o he judgmens of ohers, and have no effec on he oucome. This propery is necessary because when an official has no opinion or feels he lacks experise on an issue, forcing him o ake a sand migh lead him o choose randomly. This could lead o oucomes ha are biased in unexpeced ways owing o he random componen. A any rae, no maer how demanding he rules abou expressing a leas some opinion, i seems likely ha an official could find a way o equivocae by missing a deadline for reporing a recommendaion, for example. Specificaion of a righ neural elemen merely refers o he side of he binary operaor on which he neural elemen lies, as in he equaion a e = a. Requiremen ha here is only a righ neural elemen is a slighly weaker and more general assumpion han an assumpion ha here are boh righ and lef neural elemens. Only he assumpion of a righ neural elemen is needed o drive our resuls. (In he presence of all he axioms excep unanimiy, i can be proved ha he righ neural elemen is also he lef neural elemen.) N7: The possibiliy of neuralizing choices and decisions: for every aes here is a leas one righ neuralizing elemen a*es such ha a o a* = e. This axiom requires ha for every policy recommendaion a (oher han e) by a field official or manager, here exiss in S a negaive recommendaion he inverse, a* which perfecly counerbalances he firs recommendaion. Thus whenever one field official says, "Do his," anoher field official has he opion of saying, "Don' do ha," and a manager or direcor receiving such counerbalancing recommendaions mus aggregae hem ino a "I have no official posiion on his maer" kind of decision. If his counerbalancing a* did no exis, any field official making an "asserive" recommendaion of a would have a naural advanage over someone who had conrary feelings on he maer. The hierarchy would consequenly no be neural in is decision making since one kind of recommendaion would always be favored over anoher.

14 168 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 Assumpion of a righ neuralizing elemen refers o he side of he binary operaor on which he neuralizing elemen lies, as in he equaion a o a* = e. I is slighly more general han assuming he exisence of boh righ and lef neuralizing elemens. (In he presence of all he axioms excep unanimiy, i can be proved ha a righ inverse is also a lef inverse.) Noe ha N7 presumes N6, bu N6 does no presume N7. N8: Decision neuraliy under unanimiy: if a policy group offers unanimous choices or decisions (ha is, here exiss as such ha /, = a or g, = a for every i in he policy group), hen he value of is immediae superior's aggregaion funcion equals whaever he policy group's recommendaion is; ha is, a o a = a. In oher words, whenever a manager or direcor receives a unanimous recommendaion from his immediae subordinaes, he mus agree o heir wishes. Aggregaing unanimous recommendaions so ha some oher opion is passed up he hierarchy would indicae a clear bias agains he unanimously recommended opion and hus i would clearly be a nonneural procedure. If he hierarchy is o provide a neural means of aggregaing field officials' choices, respec for unanimiy seems essenial. (This unanimiy assumpion is analogous in social choice heory o he Pareo principle, which assumes ha if everyone prefers x o y, y will no be he social choice if x is available.) This ends our lis of neuraliy axioms, bu o complee he presenaion we mus reurn o a jusificaion for N3, jurisdicional neuraliy. As already noed, his is he mos conroversial of our neuraliy axioms. We wish o emphasize ha we are no saing ha resricive jurisdicions are, in some general sense, useless or undesirable for organizaions. To he conrary, i is difficul o imagine a real-world bureaucracy wihou some degree of specializaion and division of labor wih accompanying jurisdicional resricions. Indeed, "bureaucracy" is usually defined parly in hese erms. Noneheless, our goal is o design a neural hierarchy, no o model how real organizaions work, and i is easy o demonsrae ha he presence of jurisdicional resricions can lead direcly o nonneuraliy. Consider figure 1A again. Assume field official 1 repors x and field official 2 repors y. Assume also ha he managers have resriced jurisdicions: manager A is no allowed o consider x and manager B is no allowed o consider y. If field officials 1 and 2 repor o manager A, y bu no x could be forwarded by he manager o his superior. If he wo field officials repor o manager B, x bu no y could be forwarded by he manager o his superior. Thus if he jurisdicions of managers A and B are differen, he fac ha field officials 1 and 2 repor heir recommendaions o A raher han B could easily make a difference in oucomes, even if A and B hemselves use exacly he same aggregaion funcion (as required by N4). In general, hen, jurisdicional resricions migh conceivably limi a field official's or manager's choices in such a way ha he hierarchy loses is neu-

15 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 169 raliy. Any resricions on he decisions of he managers and direcor should be a funcion of he recommendaions of heir subordinaes and no of jurisdicional rules placing some alernaives off-limis. Thus neuraliy requires ha here be no jurisdicional resricions; ha is, neuraliy requires ha S, = S. However, a seemingly plausible argumen can be made ha he absence of jurisdicional resricions can also lead o bias! The problem is ha if here are no jurisdicional resricions, people wihou any experise in he issue a hand can have an inpu ino policy-making. Allowing heir paricipaion could be expeced o impar a bias o oucomes. Several responses can be made o his argumen ha he S, = S assumpion, which is apparenly required for neuraliy, can noneheless lead o bias. Firs, if a field official wans o make no recommendaion because he does no believe his own judgmen should be rused, owing perhaps o his own lack of experise, he is free o repor e. Neuraliy requiremen N6 he exisence of he neural elemen e already allows an individual o express lack of an opinion. Second, if one is concerned ha ill-informed field officials will noneheless injec heir views ino he policy-making process, one could simply add ye anoher neuraliy requiremen ha specifies ha, if an individual does no have "sufficien" experise (by some sandard) abou he issue under consideraion, his views are o be disregarded by superiors. This new requiremen violaes neiher Nl, N2, nor N3. "Ignoran" field officials and managers can say whaever hey wan; heir recommendaions are simply ignored by superiors. Since he firs eigh neuraliy properies are incompaible, as we will soon show, adding a ninh does no improve maers. (We ignore he problem of how he superiors would ascerain wheher he subordinaes are eiher ignoran or knowledgeable. Even if subordinaes faihfully repor some it^ecs when hey are knowledgeable and e when hey are ignoran, his does no resore neuraliy o he srucure.) Third, even if jurisdicional resricions are imposed on he field officials (perhaps because of specializaion requiremens), here remains he problem of how he field officials' advice should be processed and aggregaed by he managers and direcor. If here are resricions on he jurisdicions of hese managers, hen changing he precise naure of hese resricions can be expeced o affec oucomes. Only if he managers have no jurisdicional resricions a all could he srucure be neural. (Even if jurisdicional neuraliy holds for he managers, nonneuraliy may be caused by jurisdicional specializaion of he field officials.). In his regard, for many complex issues considered by he federal bureaucracy issues like naional securiy, inernaional rade and compeiiveness, and naional energy supply i is no clear who should be considered an "exper" and who should no. There is cerainly no agreemen ha one paricular ype of "exper" should be given sole jurisdicion over policy-

16 170 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 making in each of hese issue areas. The consequence is ha allowing only "he expers" o ge involved may sill leave paricipaion open o a large number of individuals locaed in a number of differen bureaus. Resricion on paricipaion solves he problem of designing a neural hierarchy only if all bu wo field officials are eliminaed. Even if we limi ourselves o he problem of organizaional design for he aggregaion of exclusively exper advice, he same issue of hierarchical neuraliy remains. If jurisdicional resricions are imposed (criics would call his "muzzling" he officials), neuraliy will be direcly compromised. Finally, specialiss ofen injec heir own personal and professional biases ino heir work, and i is widely recognized ha "generaliss" consequenly have an imporan role o play in policy-making. I is cerainly he case ha individuals ofen have knowledge or wisdom exending beyond heir official jurisdicional areas. Ruling his knowledge or wisdom off-limis would be unwise and migh allow biased specialiss o dominae decision making. This complees our discussion of properies necessary for neural policymaking in a hierarchy. Our purpose was o elucidae wha properies are necessary for a srucure o be neural, however unreasonable or undesirable hey may be for oher organizaional purposes, or however unrepresenaive of real organizaions hey are. Noe ha we are no assering ha our eigh neuraliy properies are collecively sufficien o assure neuraliy. There may well be oher properies whose imporance we have no ye recognized; we suggesed a ninh in our discussion of N3 above and inroduce a enh in secion 4 below. Ye as we shall see in heorem 1 below, even he firs eigh properies cause insurmounable problems in he design of a neural hierarchy ha is nondegenerae NONEXISTENCE OF NONDEGENERATE NEUTRAL HIERARCHIES Thus far, our argumen is ha if any of he eigh axioms is violaed, hen oucomes may be biased in some fashion. Bu one can go furher: even if all eigh of he neuraliy properies hold, somehing else has o give, and wha gives in our proof below is he nondegeneracy requiremen ha S conain a leas wo opions. Our proof of his asserion urns on he fac ha four of he neuraliy assumpions in paricular N4, N5, N6, and N7 consiue wha is known as an algebraic group. Following Dean (1966:24), an algebraic group <S, o> is a nonempy se of elemens S and a binary operaor, o, which, when applied o paired elemens of he se, specifies some elemen of he se (ha is, saisfies closure) and which also saisfies: (1) associaiviy, for every riple {a,b,c) of elemens in S, (a o b) o c = a o (b o c). In oher words, he grouping of he elemens for applicaion of he operaor does no maer.

17 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 171 (2) exisence of a righ ideniy elemen: here is an elemen ees such ha a o e = a for all as. (3) exisence of a righ inxrse: for every as here exiss an elemen a*s such ha a o a* = e. An algebraic group may have addiional properies such as commuaiviy, ha is, a o b = b o a bu any heorems ha are rue of algebraic groups wih only hese iniial properies will also hold for groups wih any addiional properies (such as any of our oher four axioms). Since our assumpions consiue an algebraic group, his means ha we can use resuls from algebraic group heory o examine he workings of our supposedly neural srucure. Given our eigh neuraliy axioms, we pose he following: Definiion: A hierarchy is neural if i has properies Nl hrough N8. Using an elemenary resul from Dean (1966:30, Lemma 1) we can now prove: Theorem 1: No neural nondegenerae hierarchies wih hree or more field officials exis. Proof: <S, o> is an algebraic group by N4 (binary operaor saisfying closure), N5 (associaiviy), N6 (righ ideniy), and N7 (righ inverse). If he firs hree field officials choose x,, x 2, and x 3 in S respecively, and all oher field officials, if any, choose he neural elemen e (guaraneed o exis by N6), we will denoe he resuling vecor of choices by (x,,x z,x 3,S). Wihou loss of generaliy his will connoe (x,,x 2> x 3 ) if here are exacly hree field officials. By ND1, Nl, N3, N6, and N7, and he assumpion of a leas hree field officials, here exis wo disinc elemens x,ys such ha {x,x,x*,i), represened by i, and (y,y,y*,e) represened by y, may each be chosen by he field officials, where i* and y* are he righ inverses of i and y, respecively, as guaraneed by N7. By N2, N4, and N5 he direcor will make he decisions and g/i) = x o (x o (x* o (e o (... (e o e ))))) gay) = y o(yo(y* o(eo(... (e oe ))))). By N6 and N7, gj^i) reduces o i o (i o (i* o e) = x o (i o i*) = x o e = x. Bu by N5 he inermediae sep x o (x o i*) is also equivalen o (i o i) o i* which, by N8 and N7, reduces o x o x* = e. Thus x = e. In similar fashion, gjijj) reduces o y o (y o y*), wih he resul ha y = e. Thus x = e = y, which means ha here is only one elemen in S. Bu his conradics

18 172 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 ND1, he requiremen ha here be a leas wo elemens in S. Therefore he assumpions of neuraliy, nondegeneracy, and he exisence of hree or more field officials are muually inconsisen. QED. Since hierarchical neuraliy appears o require a large number of neuraliy properies, one migh wonder wheher his impossibiliy resul is paricularly surprising. Afer all, he general paern wih impossibiliy resuls in social choice heory is ha he greaer he number of axioms required, he more likely here will be an incompaibiliy among he axioms. However, he meaning of our heorem depars from his general paern. The reason is ha our axioms are all designed o eliminae any possibiliy of bias in hierarchical policy-making: he more axioms here are, he fewer any possible remaining sources of bias. Ye wih bias eliminaed from each sage of he policy-making process, our resul demonsraes ha he overall srucure sill canno be neural. In his sense, our heorem has considerable surprise value. 3. EXAMPLES OF NONNEUTRAL HIERARCHIES Theorem 1 demonsraes ha no hierarchy, of any complexiy a all, can saisfy all neuraliy condiions: in general, no neural hierarchy can exis. We now presen hree examples in which a hierarchy saisfies all of he neuraliy axioms save one. The organizaion in example 1 below violaes only neural grouping (N5). The organizaion in example 2 violaes only jurisdicional neuraliy (N3). The organizaion in example 3 violaes only he exisence of a righ neuralizing elemen (A/7) EXAMPLE 1 Suppose he Office of Managemen and Budge (OMB) is deciding wheher o increase, leave unchanged, or decrease budge requess from some agency. Recommendaions abou wha o do are iniially generaed by he OMB's "field officials" is budge examiners who are assigned responsibiliy for he agency. Assume he OMB assigns several budge examiners o he same agency bu requires ha hey funcion independenly of each oher. The OMB hereby allows for independenly generaed differences of opinion abou he meris of a budge reques from he agency. Assume ha each examiner's advice o modify a budge reques or leave i unchanged is aken ino accoun a higher levels in he OMB, bu ha he examiner's houghs on he magniude of any needed changes are no considered. (The amouns he OMB migh allocae depend on he meris of requess from oher agencies and on overall budge consrains.) Any decision by a middle-level OMB manager o recommend a change in he size of he budge, or o leave i as is, depends on he advice he receives from his budge examiners. The final decision by he OMB direcor abou wheher o

19 THE IMPOSSIBILITY OF A NEUTRAL HIERARCHY / 173 modify he overall budge likewise depends on he advice he receives from subordinaes. Thus S, he se of alernaives available o each official, has he elemens (+,0, -) whose respecive meanings are "increase," "leave unchanged," and "decrease" he size of he budge. For his siuaion, a reasonable binary operaor on S would be one ha saisfied +»+ = = = 0 +»o = = 0 _ o o = - + o _ = = - _ o _ = _ These operaions saisfy assumpions N4 (he exisence of he binary operaor and closure), N6 (0 is he righ neural elemen), N7 (+ has righ neuralizing elemen and vice versa, while 0 is is own righ neuralizing elemen), and N8 (+ o + = +, 0 o 0 = 0, - o - = -). Now consider he wo srucures in figure 2. If he srucures are neural, he oucome from srucure A mus be he same as he oucome from srucure B due o associaiviy. Bu if here are hree or more budge examiners and all he oher neuraliy axioms are saisfied, hen N5 (neural grouping) mus fail since he operaor canno be associaive. And in fac he oucome from srucure A is ( o ) o + = o + =0, while ha from srucure Bis-o(-o+)= -o0= -. Thus differen srucures lead o differen oucomes here. If one does no wish o forfei neural grouping (NS), some oher neuraliy propery will have o go. The nex example preserves neural grouping by sacrificing jurisdicional neuraliy (S3) EXAMPLE 2 A hierarchy may require is members o specialize by limiing he choices or decisions any paricular member may make. By violaing jurisdicional neuraliy he hierarchy can mee all he oher neuraliy condiions. Consider he hierarchies in figure 3, represening wo possible srucures for he nonmanufacuring division of a corporaion. In each srucure he hree field officials are expers in echnological developmen, marke research, and sales, respecively. In srucure A he firs wo expers are locaed in a research branch subordinae o a manager of research. In srucure B he second wo expers are locaed in a disribuion branch subordinae o a manager of disribuion. Suppose he division has fixed resources and mus decide how o allocae hese resources. The division could direc is resources oward f: echnological developmen, m: marke research, s: sales,

20 174 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION V:l, 1989 STRUCTURE A Direcor, Non-manufacuring Division S 5 = {,m,s,r,p,d,e} = S Research Branch S = {r..m.e} Technological Developmen S, = {.e} Marke Research S, = {m,e} STRUCTURE B Direcor, Non-manufacuring Division S 5 = {,m,s,r,p,d,e} = S Disribuion Branch S 4 = {d.m.s.e} Technological Developmen S, = {.e} S, = {m,e\ Figure 3. r: research consising of echnological developmen and marke research, p: produc improvemen consising of echnological developmen and sales, d: disribuion consising of marke research and sales, or e: he mainenance of is curren allocaion of resources. Assume each exper is allowed o reques more resources for himself (perhaps by documening poenial for increased profis) or o decline o make a reques (e), bu is no allowed o repor judgmens on he projecs of oher expers. Then he jurisdicional assignmens S, = (,e), S = (m,e), and S 3 = (s,e) are appropriae. Assume ha if an exper wishes o reques more resources, he can make a plausible case for an increase. Wha is possible for he direcor o give him, hough, depends on wha oher expers reques and on overall budge consrains.