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The Mathematics of Preference, Choice and Order

Essays in Honor of Peter C. Fishburn

  • Book
  • © 2009

Overview

Editors:
  1. Steven J. Brams

    1. Department of Politics, New York University, New York, USA

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  2. William V. Gehrlein

    1. Department of Business Administration, University of Delaware, Newark, USA

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  3. Fred S. Roberts

    1. DIMACS Rutgers University, Piscataway, USA

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  • Contains literature surveys to cover the mathematical aspects of various fields in social sciences
  • Presents the latest developments in research in the main subject areas
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Choice and Welfare (WELFARE)

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Utility, Preference, Individual Choice, Subjective Probability, and Measurement

    1. Utility Theory

      1. Entropy-Related Measures of the Utility of Gambling
        • R. Duncan Luce, Anthony J. Marley, Che Tat Ng
        Pages 5-25
      2. Altruistic Utility Functions for Joint Decisions
        • David E. Bell, Ralph L. Keeney
        Pages 27-38
      3. SSB Preferences: Nonseparable Utilities or Nonseparable Beliefs
        • Yutaka Nakamura
        Pages 39-55

    2. Decision Theory

      1. Decision Making Based on Risk-Value Tradeoffs
        • Jianmin Jia, James S. Dyer
        Pages 59-72
      2. Normally Distributed Admissible Choices are Optimal
        • James N. Bodurtha Jr, Qi Shen
        Pages 73-83
      3. A Conjoint Measurement Approach to the Discrete Sugeno Integral
        • Denis Bouyssou, Thierry Marchant, Marc Pirlot
        Pages 85-109

    3. Measurement Theory

      1. Additive Representability of Finite Measurement Structures
        • Arkadii Slinko
        Pages 113-133

  3. Social Choice, Voting, and Social Welfare

    1. Condorcet Domains and Probabilities

      1. Acyclic Domains of Linear Orders: A Survey
        • Bernard Monjardet
        Pages 139-160
      2. Condorcet Domains: A Geometric Perspective
        • Donald G. Saari
        Pages 161-182
      3. Condorcet's Paradox with Three Candidates
        • William V. Gehrlein
        Pages 183-196
      4. On the Probability to Act in the European Union
        • Marc R. Feix, Dominique Lepelley, Vincent Merlin, Jean-Louis Rouet
        Pages 197-211

    2. Voting Rules

      1. Voting Systems that Combine Approval and Preference
        • Steven J. Brams, M. Remzi Sanver
        Pages 215-237
      2. Anonymous Voting Rules with Abstention: Weighted Voting
        • William S. Zwicker
        Pages 239-258

    3. Social Choice

      1. Pareto, Anonymity or Neutrality, but Not IIA: Countably Many Alternatives
        • Donald E. Campbell, Jerry S. Kelly
        Pages 261-270

    4. Fair Division

      1. Bruhat Orders and the Sequential Selection of Indivisible Items
        • Brian Hopkins, Michael A. Jones
        Pages 273-285

  4. Posets, Graphs, Combinatorics, and Related Applied and Mathematical Topics

    1. Partial Orders and Interval Orders

      1. Fractional Weak Discrepancy of Posets and Certain Forbidden Configurations
        • Alan Shuchat, Randy Shull, Ann N. Trenk
        Pages 291-301
      2. Interval Order Representation via Shortest Paths
        • Garth Isaak
        Pages 303-311
      3. Probe Interval Orders
        • David E. Brown, Larry J. Langley
        Pages 313-322

    2. Graphs

      1. Mediatic Graphs
        • Jean-Claude Falmagne, Sergei Ovchinnikov
        Pages 325-343
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Keywords

About this book

Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn’s contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.

Editors and Affiliations

  • Department of Politics, New York University, New York, USA

    Steven J. Brams

  • Department of Business Administration, University of Delaware, Newark, USA

    William V. Gehrlein

  • DIMACS Rutgers University, Piscataway, USA

    Fred S. Roberts

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