The Mathematics of Preference, Choice and Order

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.

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.

Utility, Preference, Individual Choice, Subjective Probability, and Measurement.- Entropy-Related Measures of the Utility of Gambling.- Altruistic Utility Functions for Joint Decisions.- SSB Preferences: Nonseparable Utilities or Nonseparable Beliefs.- Decision Making Based on Risk-Value Tradeoffs.- Normally Distributed Admissible Choices are Optimal.- A Conjoint Measurement Approach to the Discrete Sugeno Integral.- Additive Representability of Finite Measurement Structures.- Social Choice, Voting, and Social Welfare.- Acyclic Domains of Linear Orders: A Survey.- Condorcet Domains: A Geometric Perspective.- Condorcet's Paradox with Three Candidates.- On the Probability to Act in the European Union.- Voting Systems that Combine Approval and Preference.- Anonymous Voting Rules with Abstention: Weighted Voting.- Pareto, Anonymity or Neutrality, but Not IIA: Countably Many Alternatives.- Bruhat Orders and the Sequential Selection of Indivisible Items.- Posets, Graphs, Combinatorics, and Related Applied and Mathematical Topics.- Fractional Weak Discrepancy of Posets and Certain Forbidden Configurations.- Interval Order Representation via Shortest Paths.- Probe Interval Orders.- Mediatic Graphs.- An Application of Stahl's Conjecture About the k-Tuple Chromatic Numbers of Kneser Graphs.- Optimal Reservation Scheme Routing for Two-Rate Wide-Sense Nonblocking Three-Stage Clos Networks.- Correlation Inequalities for Partially Ordered Algebras.- The Kruskal Count.- Descending Dungeons and Iterated Base-Changing.- Updating Hardy, Littlewood and Pólya with Linear Programming.