The Arrow Impossibility Theorem

The Arrow Impossibility Theorem

ERIC MASKIN
AMARTYA SEN
KENNETH J. ARROW
PARTHA DASGUPTA
PRASANTA K. PATTANAIK
JOSEPH E. STIGLITZ
Copyright Date: 2014
Pages: 168
https://www.jstor.org/stable/10.7312/mask15328
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  • Book Info
    The Arrow Impossibility Theorem
    Book Description:

    Kenneth J. Arrow's pathbreaking "impossibility theorem" was a watershed in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, nondictatorship, and independence. In this book, Amartya Sen and Eric Maskin explore the implications of Arrow's theorem. Sen considers its ongoing utility, exploring the theorem's value and limitations in relation to recent research on social reasoning, while Maskin discusses how to design a voting rule that gets us closer to the ideal -- given that achieving the ideal is impossible. The volume also contains a contextual introduction by social choice scholar Prasanta K. Pattanaik and commentaries from Joseph E. Stiglitz and Kenneth Arrow himself, as well as essays by Sen and Maskin outlining the mathematical proof and framework behind their assertions.

    eISBN: 978-0-231-52686-9
    Subjects: Economics, Mathematics, Political Science

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. ACKNOWLEDGMENTS
    (pp. vii-x)
    Joseph E. Stiglitz
  4. INTRODUCTION
    (pp. 1-22)
    PRASANTA K. PATTANAIK

    Since its publication more than six decades ago, Kenneth J. Arrow’s (1950, 1951) impossibility theorem has profoundly influenced the thinking of all who are interested in issues relating to social choice and welfare, and the contributions of Eric Maskin and Amartya Sen to the vast literature, which followed Arrow’s theorem, have been of fundamental importance. It is a great pleasure for me to write an introduction to this volume based on Eric Maskin’s and Amartya Sen’s lectures at Columbia University on Arrow’s impossibility theorem, especially since, as a graduate student, I was first introduced to Arrow’s impossibility theorem (and much...

  5. PART I: THE LECTURES

    • OPENING REMARKS
      (pp. 25-28)
      JOSEPH E. STIGLITZ

      The Kenneth J. Arrow lectures are given in honor of Kenneth Arrow, who was one of Columbia’s most distinguished graduates. The topic of the second annual Arrow lecture, on which this book is based, was Ken’s thesisSocial Choice and Individual Values. For anyone doing a PhD, it would be no bad thing to aspire to the standards this work has set.

      The fact that Ken’s PhD thesis remains an icon more than a half century after its writing shows just how much it changed the way we think about the whole problem of social choice. That someone could even...

    • ARROW AND THE IMPOSSIBILITY THEOREM
      (pp. 29-42)
      AMARTYA SEN

      It was wonderful for me to have the opportunity to pay tribute to Kenneth Arrow, who is not only one of the greatest economists of our time but also one of the finest thinkers of our era. That itself made the occasion of the second annual Arrow lecture very special for me, but on top of that, it was marvelous to have the company of Eric Maskin, with whom I used to teach a most enjoyable joint course on social choice theory at Harvard, until he deserted us for the Institute for Advanced Study at Princeton.² And it was very...

    • THE ARROW IMPOSSIBILITY THEOREM: WHERE DO WE GO FROM HERE?
      (pp. 43-56)
      ERIC MASKIN

      Giving a lecture in honor of Kenneth Arrow would be a high point for any economist, but, in my case, there were two additional reasons why the occasion of the second annual Arrow lecture was such a special pleasure.

      First, Ken Arrow was my teacher and PhD advisor, and most likely I would not have become an economist at all had it not been for him. I was a math major in college and intended to continue in that direction until I happened to take a course of Ken’s—not on social choice theory but on “information economics.” The course...

    • COMMENTARY
      (pp. 57-64)
      KENNETH J. ARROW

      I am very grateful to the two lecturers; it was indeed an honor to have Eric Maskin and Amartya Sen speak about my now quite old impossibility theorem. I cannot imagine two better discussants. Let me first turn to Eric’s presentation. He presented an extraordinarily interesting theorem about the situations in which the impossibility theorem fails. In other words, he imposes restrictions on the sets of individual preferences and finds that under his conditions majority voting will work. Of course he added the condition of anonymity to the ones I impose in order to achieve that result. It is an...

  6. PART II: SUPPLEMENTAL MATERIALS

    • THE INFORMATIONAL BASIS OF SOCIAL CHOICE
      (pp. 67-100)
      AMARTYA SEN

      Social choice theory addresses a wide range of decisional and judgmental problems, dealing with a variety of procedures—from voting to making normative social assessments. It encompasses theories of elections and balloting on one side, to welfare economics on the other, as well as theories of normative measurement, such as the evaluation of national incomes, measurement of inequality and poverty, and appraisal of social welfare. These distinct problems often demand quite dissimilar approaches, and there is little hope of getting some uniform approach that would work equally satisfactorily for all the different exercises.² Nevertheless, all the social choice problems have...

    • ON THE ROBUSTNESS OF MAJORITY RULE
      (pp. 101-142)
      PARTHA DASGUPTA and ERIC MASKIN

      How should a society select a president? How should a legislature decide which version of a bill to enact?

      The casual response to these questions is probably to recommend that a vote be taken. But there are many possible voting rules—majority rule, plurality rule, rank-order voting, unanimity rule, runoff voting, and a host of others (avoting rule, in general, is any method for choosing a winner from a set of candidates on the basis of voters’ reported preferences for those candidates¹)—and so this response, by itself, does not resolve the question. Accordingly, the theory of voting typically...

    • THE ORIGINS OF THE IMPOSSIBILITY THEOREM
      (pp. 143-148)
      KENNETH J. ARROW

      As requested, this is a personal account of the steps by which I came to state and prove the so-called impossibility theorem for social choices. It will be worthwhile to restate the theorem in abbreviated form in order to understand better its genesis.

      We consider a society which must make a choice binding on all its members. On any given occasion, there is a set of alternatives,S, among which the social choice must be made. It will be assumed that both the society and any set of alternatives considered are finite. Theith individual in the society has a...

  7. NOTES ON CONTRIBUTORS
    (pp. 149-152)