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230 Pages·1970·9.41 MB·English
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COLLECTIVE CHOICE AND SOCIAL WELFARE AMARTYA K. SEN Delhi Schrol of Economics University of Delhi HOLDEN-DAY, INC. SAN FRANCISCO, CAMBRIDGE,. LONDON, AMSTERDAM OLIVER & BOYD EDINBURGH AND LONDON MATHEMATICAL ECONOMICS TEXTS Editors K. ARROW, Professor of Economics, Harvard University, U.S.A. F. HAHN, Professor of Economics, London School of Economics, U.K. J. JoHNSTON, Professor of Econometrics, University of Manchester, U.K. R. M. SoLOW, Professor of Economics, Massachusetts Institute of Technology, U.S.A. Students of mathematical economics and econometrics have.two unneces sary difficulties. One is that much of what t~ey have to read is spread over the journals, often written in different notations. The ~econd is that the theoretical and the empirical writings often make little reference to each other, and the student is left to relate them. The main object of this series is to overcome these difficulties. Most of the books are concerned with specific topics in economic theory, but they relate the theory to relevant empirical work. Others deal with the necess ary mathematical apparatus of economic theory and econometrics. They are designed for third-year undergraduates and postgraduate students. The editors are drawn from both sides of the Atlantic and are people w~o are known both for their contribution to economics and for the emphasis they place on clear exposition. Titles in the series l. -Dynamic Programming: D. J. WHITE 2. Uncertainty and Estimation in Economics-Volume I: D. G. CHAMPERNOWNE 3. Uncertainty and Estimation in Economics-Volume II: D. G. CHAMPERNOWNE 4. Uncertainty and Estimation in Economics-Volume III: D. G. CHAMPERNOWNE 5. Collective Choice and Social Welfare: A. K. SEN Other titles are in preparation H5 99 -3 54-7 Library of Congress Catalog Card No. 70-114684 First published 1970 ©Copyright 1970 by Holden-Day, Inc., · 500 Sansome Street, San Francisco, California. All rights reserved. · No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mecqanical, photo-copying, recordipg, or otherwise, without permission in writing . from the publisher. Copublished by HOLDEN-DAY, INC. 500 Sansome Street San Francisco, California and OLIVER & BOYD LTD Tweeddale Court Edinburgh 1 Printed in the United States of America ISBN 0-8162-7765-6 ' . > ~' .I ' ' .. ' To Nabaneeta PREFACE The theory of collective choice belongs to several disciplines. Economics is one of them but not the only one. . While this book a is part of series in "mathematical economics texts," no attemgt has been made to confine the treatment to economic pro]?lems exclusively. Indeed the approach of this book is based on the belief. that the problem cannot be satisfactorily discussed within the of economics. While collective choice is a crucial aspect confine~ of economics (notably of welfare economics, planning theory and public economics), the subject relates closely to politic;at·science, . in particular to the theory of the state and the theory of decision procedures. It also has important philosophical aspects, re.lated to ethics and especially to the theory of justice. The book is divided into starred chapters which contain formal analyses, and unstarred ones which are quite informaL They alter nate. A nontechnical reader can get an intuitive idea of the main arguments from the unstarred .. However, for precis·e chapt~rs statement of results as well as proofs, the starred chapters have to be reaq. The partitioning of the book into formal and informal chapters is a stylistic experiment. ·Many problems ·of collective choice re" quire. a rigorous and formal treatment for definiteness, and .iri- . formal arguments· can indeed be treacherous, but once the results are obtained, their meaning, significance and relevance p·an be dis cussed informally. In fact, a purely formal discussion of signifi" cance would be unnecessarily narrow. The book attempts to cater to two distinct groups of r.eaders, viz., those who are· primarily interested in the releVance of. the results rather than in their formal statement and ·technical derivation, and. those who are also concerned with the latter. Thus, the partitioning of the book into starred and unstarred chapters does have some rationale, aside from reflecting the author's incurable schizophrenia. The mathematics used in the book mainly involves the .logic of relations. The main of mathematical logic employed m re~ults vii PREFACE Vlll proving theorems on collective choice are stated, discussed and proved in Chapter 1 *. The book is in this sense self-contained. The field of collective choice is vast. It has not been possible to cover all the branches, and still less to discuss all of them equally thoroughly. While it is hoped that the book covers the major branches of the literature adequately, it must be recognized that the judgment of the relative importance of different branches repre sents the author's own bias. For facilities of typing and duplication of two versions of this manuscript I am grateful to the Delhi School of Economics and to the Harvard Institute of Economic Research. The actual typing of the two versions was done very efficiently by Mr. C. G. Devarajan and Mrs. Helen Bigelow, respectively. I must express my indebtedness to people who have influenced this book. My inte.rest in the problem was first aroused by some stimulating discussions with Maurice Dobb when I was an under graduate at Trinity College, Cambridge, about a decade and a half ago, and I have had discussions with him intermittently ever since. My debt to Kenneth Arrow is immense, not merely his becau~e pioneering work has opened up several avenues of research in the field of collective choice, but, more personally, because he has gone through the entire manuscript and has suggested many important improvements. John Rawls read entirely the first version of the manuscript, which was prepared during 1966-1967, and· has put me right on several questions, especially on the philosophical side of the problem. During 1967-1968, Tapas Majumdar; James Mirr lees and Prasanta Pattanaik read the first draft of the manuscript and suggested numerous improvements both of substance and style, and the .final version of the book reflects the impact of their com ments. I have also benefited from the joint seminar on this subject that Arrow, Rawls and I conducted at Harvard University during 1968=1969, in particular from the participation of Franklin Fisher, A. Gibbard, Stephen Marglin, Howard Raiffa, Jerome Rothenberg, Ross Starr, David Starrett and Richard Zechhauser. I have also had useful discussions with, or helpful comments from, Dipak Banerji, Robert Cassen, J'artha Dasgupta, Peter Diamond, Jan Graaff, Frank Hahn, Bengt Hansson, John Harsanyi, Hans Herz berger, Ken-Ichi Inada, Tjalling Koopmans, Abba Lerner, Paul Samuelson, Thomas Schelling, and Subramanian Swamy. But I am, alas, reconciled to the fact that none of these gentlemen can PREFACE be held responsible for the errors and shortcomings of this work. A. K. S. Delhi School of Economics I st August, 1969 • •. CONTENTS PREFACE vii CHAPTER 1 INTRODUCTION 1 CHAPTER 1* PREFERENCE RELATIONS 7 CHAPTER 2 UNANIMITY 21 CHAPTER 2* COLLECTIVE CHOICE RULES AND PARETO COMPARISONS 28 CHAPTER 3 COLLECTIVE RATIONALITY 33 CHAPTER 3* SOCIAL WELFARE FUNCTIONS 4.1 CHAPTER 4 CHOICE VERSUS ORDERINGS 47 CHAPTER 4* SOCIAL DECISION FUNCTIONS 52 CHAPTER 5 . VALUES AND CHOICE 56 CHAPTER 5~ ANONYMITY, NEUTRALITY AND RESPONSIVENESS 71 CHAPTER 6 CONFLICTS AND DILEMMAS 78 CHAPTER 6* THE LIBERAL PARADOX 87 CHAPTER 7 INTERPERSONAL AGGREGATION AND COMPARABILITY 89 CHAPTER 7* AGGREGATION QUASI-ORDERINGS 105 I. t'·l (. xii CONTENTS CHAPTER 8 CARDINALITY WITH OR WITHOUT COMPARABILITY 118 CHAPTER 8* . BARGAINS AND SOCIAL WELFARE FUNCTIONS 126 . CHAPTER 9 EQUITY AND JUSTICE 131 CHAPTER 9* IMPERSONALITY AND COLLECTIVE QUASI-ORDERINGS 152 CHAPTER 10 MAJORITY CHOICE Al'fD RELATED SYSTEMS 161 CHAPTER 10* RESTRICTED PREFERENCES AND RATIONAL CHOICE 173 CHAPTER 11 THEORY AND PRACTICE 187 BIBLIOGRAPHY 201 INDEXES NAME INDEX 221 SUBJECT INDEX 223 Chapter 1 INTRODUCTION 1.1. Preliminary Remarks There is s.omething in common between singing romantic songs about an abstract motherland and doing optimization exer:cises with .an arbitrary objective function for a society. While both the activities are worthy, and certainly both are frequently per formed, this book, I fear, will not be concerned' with either. The · subject of our study is the. relation between the objectives of social policy and the preferences and of members of a society. a~pirations It is, of course, possible to take the view that a society is· an entity that is independent of the individuals in it, and that s-ocial preference need not be on the preference of the members of . bas~d the society. Or that there might be a dependence, but.one could abstract from it, and simply "assume'·' that society has a personality . and a preference of its own.1 Anyone who .finds his fulfillment in this assumption is entirely welcome to it, and this book must bore him. This study is concerned precisely with investigating the de pendence of judgments on social choice and of public. policy on the preferences of the members of the society. . Judgments on collective .choice, .while related to the needs and desires of the members of the community, can, however, take widely differenct·form. The calm economic technician who states that imposing a tax on commodity a will. be inoptiinal provides a judgement on collective ch0ice of one type. The angry crowd· whfch, ~m July 14, 1789, responded to De Launay, the governor of Bastille, by shouting, "Down with the second drawbridge!" 2 1 While this position is taken in some of the socialist literature, it was sharply rejected by Marx: "What is to be avoided above all is the re-establishing of 'Society' as an abstraction vis"a-vis the individual." (Marx (1844), p. 104.) G. Lefebvre, ·The Coming of the French· Revolution,. trans. by R. R. Palmer, 2 Vintage.Books, New York, 1957, p. 101. 1

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The theory of collective choice belongs to several disciplines. Economics is one of them but not the only one .. While this book is part of a series in "mathematical economics texts," no attempt has been made to confine the treatment to economic problems exclusively. Indeed the approach of this book
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