DECISION THEORY AND SOCIAL ETHICS

Transcription

1 DECISION THEORY AND SOCIAL ETHICS

2 THEORY AND DECISION LIBRARY AN INTERNATIONAL SERIES IN THE PHILOSOPHY AND METHODOLOGY OF THE SOCIAL AND BEHAVIORAL SCIENCES Editors: GERALD EBERLEIN, University of Technology, Munich WERNER LEINFELLNER, University of Nebraska Editorial Advisory Board: K. BORCH, Norwegian School of Economics and Business Administration M. BUNGE, McGill University J. S. COLEMAN, University of Chicago W. KROEBER-RIEL, University of Saarland A. RApOPORT, University of Toronto F. SCHICK, Rutgers University A. SEN, University of London W. STEGMULLER, University of Munich K. SZANIAWSKI, University of Warsaw L. TONDL, Prague VOLUME 17

3 DECISION THEORY AND SOCIAL ETHICS Issues in Social Choice Edited by HANS W. GOTTINGER University of Bielefeld, Bielefeld, ER.G. and WERNER LEINFELLNER University of Nebraska, Lincoln, Nebraska, U.S.A. D. REIDEL PUBLISHING COMPANY DORDRECHT:HOLLAND/BOSTON :U.S.A. LONDON:ENGLAND

4 Library of Congress Cataloging in Pub6cation Data International Symposium on Decision Theory and Social Ethics, Schloss ReisensbUl:g, Decision theory and social ethics. (Theory and decision library ; v. 17) A selection of papers, with additional material, from the conference held June 24-30, under the sponsorship of the Bavarian Academy of Sciences Includes bibliographies and index. 1. Social choice-congresses. 2. Decision-making Congresses. 3. Social ethics-congresses. 4. Social justice Congresses. I. Gottinger, Hans-Werner. II. Leinfellner, Werner. III. Akademie der Wissenschaften, Munich. IV. Title. HB99.3.I ISBN-13: e-isbn-13: DOl: / Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada and Mexico by D. Reidel Publishing Company, Inc. Lincoln Building, 160 Old Derby Street, Hingham, Mass , U.S.A. All Rights Reserved Copyright 1978 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover 1st edition 1978 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any informational storage and retrieval system, without written permission from the copyright owner

5 T ABLE OF CONTENTS PREFACE LIST OF PARTICIPANTS Vll xxi PART 1/ PHILOSOPHY AND ETHICAL PRINCIPLES JOHN C. HARSANYI/ Rule Utilitarianism and Decision Theory 3 WERNER LEINFELLNER / Marx and the Utility Approach to the Ethical Foundation of Microeconomics 33 MENAHEM E. Y AARI / Endogenous Changes in Tastes: A Philosophical Discussion 59 PART 2/ SOCIAL AND COLLECTIVE CHOICE THEORY SALVADOR BARBERA / Nice Decision Schemes 101 JOHN A. FEREJOHN / The Distribution of Rights in Society 119 PETER C. FISHBURN / Acceptable Social Choice Lotteries 133 ALLAN GIBBARD / Social Decision, Strategic Behavior, and Best Outcomes 153 WULF GAERTNER and ACHIM HEINECKE / Cyclically Mixed Preferences-A Necessary and Sufficient Condition for Transitivity of the Social Preference Relation 169 LUCIAN KERN / Comparative Distributive Ethics: An Extension of Sen's Examination of the Pure Distribution Problem 187 CHARLES R. PLOTT/Rawls's Theory of Justice: An Impossibility Result 201 HEINZ J. SKALA/ Arrow's Impossibility Theorem: Some New Aspects 215 DA VID SCHMEIDLER and HUGO SONNENSCHEIN / Two Proofs of the Gibbard-Satterthwaite Theorem on the Possibility of a Strategy-Proof Social Choice Function 227 v

6 VI T ABLE OF CONTENTS PART 3/ SPECIAL TOPICS IN SOCIAL CHOICE KARL BORCH / Ethics, Institutions and Optimality 237 HANS W. GOTTINGER / Complexity and Social Decision Rules 251 DEEPAK K. MERCHANT / Discrete Optimization and Social Decision Methods 271 REINHARD SEL TEN / The Equity Principle in Economic Behavior 289 PATRICK SUPPES / The Distributive Justice of Income Inequality 303 INDEX OF NAMES 321 INDEX OF SUBJECTS 323

7 PREFACE Ethics, as one of the most respectable disciplines of philosophy, has undergone a drastic and revolutionary change in recent time. There are three main trends of this development. The first trend can be described as a tendency towards a rigorous formal and analytical language. This means simply that ethics has created beside its own formalized settheoretical language a variety of new formalized, logical and mathematical methods and concepts. Thus ethics has become a formalized metaor epidiscipline which is going to replace the traditional concepts, principles and ethical methods in the realm of social sciences. It is clear that a formalized form of ethics can be used more easily in social, economic and political theories if there are ethical conflicts to be solved. This first trend can be regarded as a conditio sine qua non for application in, and imposing ethical solutions on, social scientific theories. The second trend may be characterized as an association- or unification-tendency of a formalized and analytical ethics with decision theory. Decision theory as a new interdiscipline of social sciences is actually an assemblage of a variety of subtheories such as value-utility theory, game theory, collective decision theory, etc. Harsanyi has called this complex of subtheories a general theory of human behavior. Analytical or formal ethics is actually using this general theory of human behavior as a vehicle simply because this theory deals from the beginning with conflict solution, i.e. to find the optimal actions or decisions from a given set of open alternatives. Rational decision theories do not deal always with ethical conflicts. By an ethical conflict we understand, according to Harsanyi and Leinfellner, solely the conflict between individual (egotistical) interests and collective interests or collective welfare. If such a conflict appears, the theory of rational decision making needs ethical principles such as equality, freedom, non-dictatorship, justice, etc., as additional criteria to solve the ethical conflict. The startling origin of using or importing ethical principles into decision theory marked a new area in 'ethification' of decision theories. Arrow's famous result of imposing the principles or conditions (as he called it U & P & I & D) on a theory of collective Vll

8 viii PREFACE choice showed, at least according to Sen's interpretation, that the principles of U = unrestricted choice, P = Pareto optimality, 1= independence of irrelevant alternatives and D = non-dictatorship were too weak. Since then stronger and more detailed and elaborate principles borrowed from traditional ethics have been reformulated and used in this field. Sen's classical book describes this trend in a meticulous and dramatic way. Finally there is a third main trend, which goes beyond the scope of the analytic formalizing tendency as well as beyond the imposition of ethical principles on rational decision theory. It is clear that the conversion of decision theories in ethical ones-if there exists an ethical conflict-has to be done from a systematic point of view. Here at this moment the old systematic doctrines of traditional ethics have been introduced by the present adherents of these doctrines. Thus we are in a renaissance and critical reconstruction of utilitarian ethics (Sen, Harsanyi), of contractarian theory of society (Rawls), of libertarian ideas (Nozick) and finally of Marxian ethical foundations of economics as the basis of societal life (Leinfellner, Kern), just to mention a few of these systematic reconstructions and reformulations of historical ethical views. From June 24-30, 1976, an international conference on the topic 'Decision Theory and Social Ethics' took place at Schloss Reisensburg/Ulm, West Germany under the sponsorship of the Bavarian Academy of Sciences, Munich, West Germany. The papers published in this volume demonstrate very clearly the present status of social ethics. They testify that this discipline is not only capable of providing detailed and specialized analyses and solutions of ethical conflicting problems and of far-going cooperation with all social sciences but can contribute to outline new systematic approaches to solve the social problems of our present societies. At this conference thirtyfour invited papers were presented and discussed; the current volume includes fifteen of those, and the remaining two have been solicited from outside to achieve a reasonable balance of current trends in social ethics and decision theory with a view toward further integration. Furthermore, in this volume, an attempt is made to give potential newcomers to the field an authoritative guide to the multiple crosslinks between the two areas. In recent years there have been several attempts to treat problems of social ethics, in particular those relating to 'social justice', in a rigorous and analytical fashion. In this endeavor

9 PREFACE IX various disciplines have been involved: philosophy, economics, sociology, political science, statistics and law. Much of the theory is still in flux, but already at this stage we observe that modem social ethics is deeply interconnected with rational decision making: on the one hand by the extensive use of decision criteria and the formalism of rational decision theories, on the other hand by superimposing on rational decision making ethical principles borrowed from traditional ethics. Of course, this is not too surprising in view of the historical origins of decision theory. On the other hand, decision theory over the past twenty years has generated its own dynamics, motivated by intrinsic (mathematical) problems of itself, thus creating highly sophisticated, technical subdisciplines (statistical decision theory, for instance, is fully integrated in mathematical statistics). However, in this development a potential danger is involved: some decision theorists may lose contact to problems in other areas requiring decision-theoretic tools. Conversely, those working in more applied fields may not follow up technical results in decision theory that could be of potential interest to them. If decision theory wants to keep its vitality it is contended that it should be open to substantial problems in more applied fields. Therefore, in this volume an attempt is made to discuss the status of decision theory (in view of most recent results) relevant to social ethics. It should also facilitate communication between more mathematically inclined decision theorists and those more interested in practical and philosophical aspects of the general area of social ethics (including voting theory, theory of democracy, theory of social and environmental indicators, collective and social choice theories). To give an example of how principles are used and how 'ethicizing' of social and economic theories is dependent on fundamental philosophical views, we want to discuss briefly three different approaches to solve ethical social conflicts. One could regard here the fundamental attitude of egalitarianism, of utilitarianism and of libertarianism as some kind of Kuhnian paradigm; as entrenched beliefs which have led in fact to revolutionary development of systematic theories by Rawls, Harsanyi and Nozick. It is perhaps good here to trace the major problem areas that characterize the substantive issues of social ethics and justice and that set up the interface between social ethics and decision theory. Without denying historical roots in the discussion of problems of justice, it is of interest here to point out that basically three problem areas of societal organization have received

10 x PREFACE renewed attraction in the modern discussion on ethical values: (1) Which principles form a just society and under which circumstances are social and economic inequalities justifiable? (2) Does there exist a catalogue of generic individual or collective rights on the basis of natural law which leads to incompatibilities between freedom and equality? (3) Which normative principles of social ethics generate statements on social or public policy embracing those on the allocation of collective and individual resources within society? For approaching these questions at least three fundamental procedures, rules or problem solving mechanisms, appear to be available: the libertarian, the egalitarian and the utilitarian approach. In the natural tension between freedom and equality, or between the libertarian and egalitarian view, we could discuss the controversial views of R. Nozick (State, Anarchy and Utopia, 1974) and John Rawls (A Theory of Justice, 1971). Rawls' theory of justice directly addresses to the problem of what is a just distribution in society, are inequalities justified and if so, what kinds and amounts of inequalities. According to Rawls only those inequalities are justified which work to the benefits of the most disadvantaged. The straight justification is that some inequalities of position or of resources may bring greater productivity and therefore greater benefit to all. Nozick's point of departure is different. He points out that inequalities are not created by some central authority, or 'accident by birth' but result from individuals innate or acquired differences in skills, capabilities and other resources. Rawls' principle seems to assume that these resources and products are collectively held, and that individuals have no rights (entitlements) to them. Nozick's theory is opposed to this assumption. Instead he assumes that each person has a set of natural rights which entitles the individual to the best (personal) use of his resources, and that the problem of justice must be applied to this criterion, thus it is irrelevant whether in particular situations equality or inequality prevails. Both philosophers set out from fundamental positions, in an axiomatic way, whereas the utilitaristic position (as represented by J. C. Harsanyi) is more pragmatic, economically oriented. According to the libertarian position, imposition of equality in benefits constitutes a significant loss of rights, not only for the 'haves' but also for the 'have-nots' (for after redistribution, they must be restrained from

11 PREFACE Xl market transactions that would destroy the pure equality and reinstate inequality). Rawls' position implies erasing all 'the accidents of birth' which give one person more opportunity than another. This necessitates removing the child from all influences of the family-and raising him as a ward of the state, subject to precisely the same conditions as any other child. Nozick's view implies, in contrast, no system of public education at all, since public education is redistributive, and by Nozick's 'entitlement' principle each child is entitled to the fullest untaxed benefit of his family's resources, in so far as it chooses to use these resources for his benefit. Obviously these are extreme positions: neither position can be a correct description of a just society. But these positions make clear what we gain or lose by moving in either direction. By moving in the direction of equality we lose individual liberty to a central authority which imposes equality, by moving in the direction of individual liberty, we lose equality to the accidents of birth reinforced by the markets. From the egalitarian point of view since the factors which make for success are simply luck, there is no ethical foundation for large disparities of income and status, and since one cannot equalize luck in order to create equal opportunity, one should seek to equalize results. But if equality of result is to be the main object of social policy it cannot succeed unless it is rooted in some universal ethical system that provides a philosophical foundation-a conception of fairness-for a communal society. Is Rawls' conception compatible with equality of opportunity or equality of result? The liberal principle accepts the elimination of social differences in order to assume an equal start, but it justifies unequal result on the basis of natural abilities and talents. For Rawls, however, natural advantages are as arbitrary or random as social ones. The only way inequality can be justified according to Rawls is on the basis of the so-called difference principle: an application of the maximin theorem of decision theory. It states that if some persons are to be better off the less advantaged are also to be better off. If one gains so must the others. (Rawls takes the metaphor of the family as a model for this principle. There are obvious links to the gift economy, representing altruistic behavior.) Rawls rejects the idea of meritocracy because it violates his conception of fairness, because equality of opportunity means an equal chance to leave the less fortunate behind in the personal quest for influence and social position, because it maintains

12 xii PREFACE and perpetuates the power structure of the most successful without working to the advantage of the less successful. The difference principle has two implications for social policy: (1) Redress or compensation. Since inequalities of birth and natural endowment are undeserved, these inequalities are to be somehow compensated for (counteracting the natural or genetic lottery). (2) Personal resources are collectively held. Talent is a social asset, and its fruit should be available to all, especially to the less fortunate. The difference principle works in such a way that those who have been favored by nature may gain from the good fortune only on terms that improve the situation of those who have lost. There are certain difficulties with Rawls' position. (i) First, he denounces meritocracy, but always pretends that advancement in meritocracy is based on pure luck, rather than 'merit' or 'effort'. There is no discussion of how to compensate for effort, and if no effort should be rewarded how can effort be made to work for the advantage of the less qualified or successful. This raises the issue of incentives. (ii) A discussion is lacking of what 'disadvantaged' really means. A person usually accepts different roles in different situations, physically and naturally. A person may be black, a woman, and under thirty years of age. Should she get three votes? She may be disadvantaged according to one criterion, but advantaged according to another criterion. The scale between advantage and disadvantage is not one-dimensional. But unfortunately Rawls suggests a definition solely in terms of relative income and wealth with no reference to social position. Thus, all persons with less than half the median income and wealth may be taken as the least advantaged segment. It focuses attention on the 'social distance' between those who have the least and the average citizen. (iii) If Rawls' principle should have some practical implications, then in society Rawls' disadvantaged are identifiable largely in group terms, and the principle of equity is linked with quota representation. However, this raises the claim of group rights against individual rights and brings ambiguities into the conception of social justice, e.g. by the degree and extent of representation by groups, and by the potential dominance of group rights over individual rights. (iv) What if the 'disadvantaged' are there by their own choice? Do

13 PREFACE Xlll we have to teach them that they are disadvantaged? How do we distinguish the genuine disadvantaged from those who are not? One could very well imagine that the Rawlsian as well as the libertarian principle will lead to different, often controversial conclusions when applied to issues of social and public policy. Some of these issues will be briefly discussed as follows: (a) The most direct clash of the two principles of liberty and equality, pertaining to Nozick's and Rawls' positions respectively, has occurred over the imposition of compulsory busing within school districts in the United States. Compulsory busing means the assignment of children by a central authority to schools at some distance from their home to ensure that all schools have a similar racial composition. How is the issue of busing affected by the principles of Rawls and Nozick? With compulsory busing there are associated two ideas: first, that different children, because of different backgrounds, constitute resources for the learning of other children, and second that a central authority has the right to redistribute such resources 'equally' among all children. (There is an analogy here to the formation of 'Gesamtschulen', e.g. comprehensive education in primary and secondary schools, in the Federal Republic of Germany, where learning potentials are intended to be redistributed equally among all students.) Opposition to compulsory busing accepts the first idea, but rejects the second. If there is a redistribution, opponents of busing hold that it should be left up to individual parents who, through their choice of residence, decide where their children go to school. Advocates of compulsory busing subscribe to the premise underlying the arguments for equality: Resources or benefits are under the legitimate control of a central authority, not of individuals. Much can be said for and against both positions. Thus there are two policy options left reflecting these positions, and a third one which will be discussed. Rather than withdrawing rights from those who have the (economic) power to exercise them effectively, one could enlarge the rights of others. In the case of busing the libertarian alternative would be to provide any child in a metropolitan area the right to transfer to a school of his choice, so long as the receiving school has a smaller proportion of his race than the school he leaves. The school would be required to accept children from outside its attendance zone, up to its capacity. Thus the right to choose school by residence remains, but the right is added to choose a school

14 XIV PREFACE in a different residence-according to one's like-and this right reduces inequality. By this alternative full equality is not realized, nor is full liberty of the economically advantaged to maintain homogeneous schools realized. (b) Equality of opportunity-as a program of the Kennedy and Johnson administration-emphasized compensatory education. But the Coleman Report showed that schooling has little effect in raising the achievement of disadvantaged groups in society. Although there was little difference between black and white schools as regarding physical facilities, formal curricula, teachers' qualifications etc. it found that a significant gap in achievement scores between black and white children was already present in the first grade-and the gap between the two groups widened by the end of elementary school. The only consistent variable explaining differences in scores within each racial group was the educational and economic backgrounds of the parents. But there was no consistent variable to explain the difference between racial groups-beyond the family background-which is why some persons have fallen back on genetic explanations. The logic of the argument has been pushed forward by Harvard psychologist R. Herrstein. He argues that 80 percent of a person's LO. is inherited while environmental factors accord for only 20 percent. The following chain of reasoning is employed: (1) if differences in mental abilities are inherited, (2) if success in society requires those abilities, (3) if the environment is 'equalized', then social standing will be based primarily on inherited differences. The dispute is first whether Western Society-because of social class privilege or culture advantage (biased LO. tests) actually provides genuine equality of opportunity, and second, whether a society, in which genuine equality of opportunity does prevail, and a new form of income and status inequality based on merit does result, would be desirable. According to the Rawlsian position, equality of opportunity is seen as leading to a new hierarchy and the current demand requires the reduction of all inequality-and this requires the creation of equality of result. The main sociological and philosophical objections to meritocracy pertain to (i) meritocracy is purely a selection by intelligence, but intelligence is based on inherited genetic differences. Therefore privilege is ob-

15 PREFACE xv tained on the basis of an arbitrary genetic lottery, the antithesis to social justice, (ii) there can never be a pure meritocracy because high status parents seek to pass privileges to their children, (iii) even in a society which proclaims to be meritocratic there are intangible or random factors that decide on economic success. Thus a situation of inequality exists which is justified on the basis of achievement, but is virtually due to other (random) factors such as luck or being in the right place, and degrees of inequality are not justified. This short discussion of some main positions in social ethics and especially the difficulties arising in Rawl's system show very clearly the urgent need for more precise and rigourous formulations, for systematic reconstructions of Rawls position as recently done by Sen et al. in the journal Theory and Decision. It demonstrates very clearly that the pending problems in this field can only be solved by intensifying the development of ethics by trying firstly to get better and more precise formal analytical ethics, secondly by working out the interrelation of traditional philosophizing with ethical principles and decision theory and finally by specifying in an exact sense the basic positions in ethics in such a way that they may be used to solve ethical conflicts in our society. But this is exactly the main theme of this volume and the goal of this collection of papers. The present collection of papers deal with some of the abovementioned theoretical and technical problems on the basis of three levels of organization: Part I: 'Philosophy and Ethical Principles', Part II: 'Social and Collective Choice Theory', Part III: 'Special Topics in Social Choice'. In Part I John C. Harsanyi analyzes and discusses various conceptions of utilitarianism, as a third avenue (besides those of Rawls and Nozick) to approach social justice. He makes a useful distinction between Act Utilitarianism (AU) and Rule Utilitarianism (RU), and shows that RU includes long-run considerations leading to quite different policy conclusions as compared to AD. In particular, he demonstrates that former 'proofs' on the equivalence between AU and RU are false, relying on former results of Gibbard (1965) and Ezorsky (1968); furthermore, some examples on social decision processes are provided to lend support to this thesis. Since RU seems to respect other people's basic rights and long-run considerations of beneficial

16 xvi PREFACE outcomes it therefore escapes undesirable implications of AU that violate elementary principles of justice. w. Leinfellner addresses himself to the problem of merging the utilitarian approach and the Marxist theory of destribution to a comprehensive, general value and welfare theory. He constructs an elaborate axiomatic system that includes the key features of different, partly contradictory ethical and value theories in use. Moreover he integrates the different ethical approaches of the traditional ethical systems and the present ones into an episystem of 'ethicizing' social, economic and political theories of today. M. E. Yaari uses a simple paradigm on the bargaining situation between the whisky-seller and the Indian demonstrating the phenomenon of 'commodity-dependence' (addicton) which sheds new light on the concept of 'consumer sovereignty' and 'rationality'. Under the hypothesis of 'endogeneous changes in preferences' one could explain very strange looking pricing strategies (from the seller's side) that initially set prices at relatively low levels but then suddenly jump to sharply higher levels and stay there for some time to come. The analysis of markets where these phenomena occur leads to considerations under which it seems justified to interfere into market interactions for reasons of consumer protection. The paper illustrates in a rather deep way under which particular set of assumptions market mechanisms may fail in providing morally sound results that are socially acceptable. Part II addresses special aspects of social and collective choice theories per se. S. Barbera makes a step toward constructing a truly stochastic social choice or decision scheme that given previous social choice configurations to be deterministic leaves the final choice subject to chance. He applies the construction to weighted voting schemes. J. Ferejohn points to some incompatibilities in proving the possibilities of democratic or liberal decision procedures, in particular, he is interested in weakening the consistency axiom and explores one type of consistency axiom which is shown to be in conflict with the strengthened Pareto axiom. P. C. Fishburn provides reasons for the acceptability of the use C?f social lotteries. He discusses and compares two important cases, for which social lotteries apply: the case of Condorcet alternatives which are preferred by the majority of non-indifferent agents (concerning

17 PREFACE XVII other alternatives) to every other alternative, and the case of Pareto lotteries where lotteries are not unanimously less preferred than other lotteries. Some examples on voting behavior for the two cases are given. A. Gibbard reports on technical results of a game-theoretic analysis to show that in particular social choice systems people may have an incentive to misrepresent their preferences because it makes them better off. In other words, he demonstrates that only a narrow class of uninteresting systems can make truthful revelation of preferences always a dominant strategy. This situation is quite important practically for voting behavior in the public policy domain. W. Gaertner and A. Heinecke present a new necessary and sufficient condition for transitivity of the social relation under a simple majority decision regime. Equivalent relationships are established between the condition of 'cyclically mixed preferences' and other known restrictions on the social welfare function. It is shown that this condition yields a Social Welfare Function of the Arrow type under the majority decision rule. L. Kern extends Sen's pure distribution problem for making allowance for a conservative rule as well as for a Marxian rule of distribution. He argues that the Rawlsian maximin criterion plays a mixed role between the conservative and the Marxian conception. C. Plott analyzes some difficulties in the Rawlsian system of justice which fully reformulated on a strictly axiomatic basis would lead to moral conclusions that almost anyone would reject. Difficulties of that sort have also been pointed out in the literature, e.g. by K. Arrow and J. C. Harsanyi. Furthermore, Plott discusses Rawls' theory in its possible impact to economics. H. J. Skala approaches social choice theory with Boolean valued models. He demonstrates convincingly and elegantly some kind of relativity in Arrow's theorem, for example that Arrows' results are dependent on the choice of the underlying logic. If one chooses a non-boolean, non-classical type of logic or even set theory the dictator would vanish. However, he discovers some logical difficulties in finding constructive proofs in the field of social choice theory. Another result of his paper is that the dictator appears and reappears depending on the number (cardinality) of the members of a society. D. Schmeidler and H. Sonnenschein provide a new proof of a particular version of Arrow's General Possibility Theorem, in this form

18 XVlll PREFACE essentially due to A. Gibbard and M. Satterthwaite, where the assumption of independence of irrelevant alternatives can be relaxed. Furthermore, the theorem is extended for permitting strongly ordered preferences (i.e. those which omit indifference relations). Under this qualification the concept of a Social Choice Function (instead of a Social Welfare Function) is used. Then the following general result is proved: if the social choice function is nonmanipulable and the set of social preference relations contains at least three elements then the Social Choice Function is dictatorial (this essentially is a corollary of Arrow's famous General Possibility Theorem). Part III is devoted to specific aspects of social choice theories of those which have not been treated in social choice theory per se but which are of interest for constructing the theory. K. Borch observes limiting factors in game situations given by institutional and ethical constraints or by tradition and customs, that create 'bounded rationality' of decision-makers. His considerations are exemplified in a simple model of insurance behavior where noncooperative behavior prevails. In a more general context H. W. Gottinger argues that many restrictive and partly paradoxical results in social choice theory are due to the implicit assumption of 'optimizing' for every decision-maker and that axioms of consistency or rationality often exceed the 'computational budget' of the decision-maker. A theory of complexity is needed to treat effectively computational limitations of the decision making process. A novel approach is suggested here by looking at decision rules in an automata-theoretic algebraic framework where there is a natural theory of complexity. Search and complexity appear to be intimately related-as we encounter choice problems with problem spaces as large as those of chess. D. K. Merchant is interested in dual aspects of the aggregation of individual preferences to social choice~, by finding procedures to induce a social ranking out of the given individual preference profiles. He uses methods of discrete optimization. R. Selten analyses the impact of a less-known principle, the equity principle on social or distributive justice which is also interesting in the light of not requiring too much 'computational power', and possibly coming closer to empirically observed human behavior. He shows that in particular market-game situations people tend to allocate rewards according to the equity principle although other allocation principles

19 PREFACE xix are available and some seem even more reasonable to apply in this situation. P. Suppes deals with the problem of justification of hierarchical societies such as meritocracies, he looks at different 'ideal-type' societies in which inequality is an intrinsic feature and compares the degree of inequality with empirical measurements for various developed and developing nations. His approach is based on a qualitative theory of relations between class intervals, relations indicating the degree of inequality, which has been proven useful for purposes of measurement theory. Numerical representation of inequality relations leads to an alternative measure of inequality. Surpes' arguments against first-principle-egalitarianism are a convincing approach to a formal reconstruction of meritocracy as a social system. Finally we want to thank all authors who contributed to this volume and D. Reidel for friendly cooperation. We also like to thank Mrs U. Schlomann and Mrs R. Goergel, Bielefeld, for secretarial assistance and Dr Hal Berghel, Lincoln. WERNER LEINFELLNER University of Nebraska, U.S.A. H. W. GOTIINGER Universitiit Bielefeld, Germany

20 LIST OF PARTICIPANTS BARBERA, SALVADOR-Universidad Autonoma de Madrid, Departamento de Teoria Economica, Facultad de Ciencias Economicas Madrid, Spanien. BaRcH, KARL-The Norwegian School of Economics and Business Administration, Institute of Insurance, Helleveien 30, 5000 Bergen, Norway. FEREJOHN, JOHN ARTHUR-Division of Humanities and Social Sciences, California Institute of Technology, Pasadena, CA , U.S.A. FISHBURN, PETER C.-The Pennsylvania State University, Business Administration Bldg., University Park, PA , U.S.A. GIBBARD, ALLAN-University of Pittsburgh, Faculty of Arts and Sciences, Dept. of Philosophy, Pittsburgh, PA , U.S.A. GAERlNER, WULF-Universitat Bielefeld, Fakultat fur Wirtschaftswissenschaften, 4800 Bielefeld 1, B.RD. GOTTINGER, HANS W.-Universitat Bielefeld, Fakultat fur Soziologie, 4800 Bielefeld 1, B.RD. HARSANYI, JOHN C.-University of California, School of Business Administration, 350 Barrows Hall, Berkeley, CA , U.S.A. KERN, LucIAN-Universitat Bielefeld, Fakultat fur Soziologie, 4800 Bielefeld 1, B.RD. LEINFELLNER, WERNER-University of Nebraska, Lincoln, NE , U.S.A. MERCHANT, DEEPAK, K.-The Graduate School of Management, The University of Rochester, Rochester, New York 14627, U.S.A. PLOTI', CHARLES R-California Institute of Technology, Division of the Humanities and Social Sciences, Pasadena, CA , U.S.A. SELTEN, REINHARD-Universitat Bielefeld, Institut fur Mathematische Wirtschaftsforschung, Postfach 8640, 4800 Bielefeld 1, B.RD. SKALA, HEINZ J.-Gesamthochschule Paderborn, 4790 Paderborn, B.RD. SCHMEIDLER, DAVID-Tel-Aviv University, Dept. of Economics, Tel Aviv, Israel. xxi

21 XXlI LIST OF PARTICIPANTS SONNENSCHEIN, HUGo-Department of Economics, Princeton University, Princeton, N.J , U.S.A. STEGMiJLLER, WOLFGANG-Universitat Munchen, B.R.D. SUPPES, PATRICK-Institute for Mathematical Studies in the Social Sciences, Ventura Hall, Stanford University, Stanford, CA , U.S.A. Y AARI, MENAHEM E.-The Hebrew University Jerusalem, Department of Economics, Jerusalem, Israel.