Collective Choice and Social Welfare

230 Pages·1970·9.41 MB·English

by  Amartya Sen

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,
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mecqanical, photo-copying, recordipg, or
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. from the publisher.
Copublished by
HOLDEN-DAY, INC.
500 Sansome Street
San Francisco, California
and OLIVER & BOYD LTD
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Printed in the United States of America
ISBN 0-8162-7765-6
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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