THE ARROW IMPOSSIBILITY THEOREM KENNETH J. ARROW LECTURE SERIES KENNETH J. ARROW LECTURE SERIES Kenneth J. Arrow’s work has shaped the course of economics for the past sixty years so deeply that, in a sense, every modern economist is his student. His ideas, style of research, and breadth of vision have been a model for generations of the boldest, most creative, and most innovative economists. His work has yielded such seminal theorems as general equilibrium, social choice, and endogenous growth, proving that simple ideas have profound effects. The Kenneth J. Arrow Lecture Series highlights econo- mists, from Nobel laureates to groundbreaking younger scholars, whose work builds on Arrow’s scholarship as well as his innovative spirit. The books in the series are an expansion of the lectures that are held in Arrow's honor at Columbia University. Creating a Learning Society: A New Approach to Growth, Development, and Social Progress Joseph E. Stiglitz and Bruce C. Greenwald. THE ARROW IMPOSSIBILITY THEOREM ERIC MASKIN | AMARTYA SEN WITH KENNETH J. ARROW PARTHA DASGUPTA PRASANTA K. PATTANAIK JOSEPH E. STIGLITZ COLUMBIA UNIVERSITY PRESS | NEW YORK Columbia University Press Publishers Since 1893 New York Chichester, West Sussex cup.columbia.edu Copyright © 2014 Columbia University Press All rights reserved Library of Congress Cataloging-in-Publication Data Maskin, Eric. The Arrow impossibility theorem / Eric Maskin and Amartya Sen with Kenneth J. Arrow, Partha Dasgupta, Prasanta K. Pattanaik, and Joseph E. Stiglitz. pages cm. — (Kenneth J. Arrow lecture series) Includes bibliographical references and index. ISBN 978-0-231-15328-7 (cloth: alk. paper) — ISBN 978-0-231-52686-9 (ebook) 1. Voting. 2. Social choice. 3. Probabilities. 4. Voting— Mathematical models. 5. Social choice—Mathematical models. 6. Probabilities—Mathematical models. I. Sen, Amartya, 1933- II. Arrow, Kenneth Joseph, 1921- III. Title. JF1001.M275 2014 324.6'5—dc23 2014007031 Columbia University Press books are printed on permanent and durable acid-free paper. This book is printed on paper with recycled content. Printed in the United States of America c 10 9 8 7 6 5 4 3 2 1 Cover design: Noah Arlow References to websites (URLs) were accurate at the time of writing. Neither the author nor Columbia University Press is responsible for URLs that may have expired or changed since the manuscript was prepared. CONTENTS Acknowledgments vii INTRODUCTION 1 PRASANTA K. PATTANAIK PART I: THE LECTURES 23 OPENING REMARKS 25 JOSEPH E. STIGLITZ ARROW AND THE IMPOSSIBILITY THEOREM 29 AMARTYA SEN THE ARROW IMPOSSIBILITY THEOREM: WHERE DO WE GO FROM HERE? 43 ERIC MASKIN COMMENTARY 57 KENNETH J. ARROW PART II: SUPPLEMENTAL MATERIALS 65 THE INFORMATIONAL BASIS OF SOCIAL CHOICE 67 AMARTYA SEN CONTENTS ON THE ROBUSTNESS OF MAJORITY RULE 101 PARTHA DASGUPTA AND ERIC MASKIN THE ORIGINS OF THE IMPOSSIBILITY THEOREM 143 KENNETH J. ARROW Notes on Contributors 149 vi (cid:81) (cid:81) ACKNOWLEDGMENTS T he Kenneth J. Arrow Lecture Series has been made possible through the efforts of Columbia Univer- sity’s Committee on Global Thought (which I chaired when this series was inaugurated and which is now co- chaired by Saskia Sassen) and by the Program in Economic Research of the Department of Economics at Columbia University (chaired by Michael Woodford at the time of this lecture) with the support and encouragement of Columbia University Press. We are especially indebted to Robin Stephenson and Sasha de Vogel of the Committee on Global Thought and Myles Thompson and Bridget Flannery-McCoy for guiding this series to publication. Joseph E. Stiglitz THE ARROW IMPOSSIBILITY THEOREM