The Mathematics of Preference, Choice and Order

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

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.

• Decision Theory
• Discrete Mathematics
• Mathematical Psychology
• Operations Research
• Preferences
• Social Choice
• Social Choice Theory
• combinatorics
• linear optimization
• optimization

• 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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