The Mathematics of Preference, Choice and Order: Essays in Honor of Peter C. Fishburn (Studies in Choice and Welfare)

This volume serves the multiple purposes of honoring Peter Fishburn's contributions, providing both expository and new papers from leading figures in each of the areas of Fishburn's research, and putting into one volume a wide variety of topics that are often not included together. These topics consider mathematical aspects of: social choice theory, decision theory, operations research, economics, political science, and psychology; as well as mathematical topics such as partial orders, graph theory, probability, and optimization. An important objective of this book is to demonstrate linkages that exist among these areas of research. Entropy-related Measures Of The Utility Of Gambling / R. Duncan Luce, Anthony J. Marley And Che Tat Ng -- Altruistic Utility Functions For Joint Decisions / David E. Bell And Ralph L. Keeney -- Ssb Preferences : Nonseparable Utilities Or Nonseparable Beliefs / Yutaka Nakamura -- Decision Theory -- Decision Making Based On Risk-value Tradeoffs / Jianmin Jia And James S. Dyer -- Normally Distributed Admissible Choices Are Optimal / James N. Bodurtha, Jr. And Qi Shen -- A Conjoint Measurement Approach To The Discrete Sugeno Integral / Denis Bouyssou, Thierry Marchant And Marc Pirlot -- Measurement Theory -- Additive Representability Of Finite Measurement Structures / Arkadii Slinko -- Condorcet Domains And Probabilities -- Acyclic Domains Of Linear Orders : A Survey / Bernard Monjardet Condorcet Domains : A Geometric Perspective / Donald G. Saari -- Condorcet's Paradox With Three Candidates / William V. Gehrlein -- On The Probability To Act In The European Union / Marc R. Feix ... [et Al.] -- Voting Rules -- Voting Systems That Combine Approval And Preference / Steven J. Brams And M. Remzi Sanver -- Anonymous Voting Rules With Abstention : Weighted Voting / William S. Zwicker -- Social Choice -- Pareto, Anonymity Or Neutrality, But Ot Iia : Countably Many Alternatives / Donald E. Campbell And Jerry S. Kelly -- Fair Division -- Bruhat Orders And The Sequential Selection Of Indivisible Items / Brian Hopkins And Michael A. Jones -- Partial Orders And Interval Orders Fractional Weak Discrepancy Of Posets And Certain Forbidden Configurations / Alan Shuchat, Randy Shull And Ann N. Trenk Interval Order Representation Via Shortest Paths / Garth Isaak -- Probe Interval Orders / David E. Brown And Larry J. Langley -- Graphs -- Mediatic Graphs / Jean-claude Falmagne And Sergei Ovchinnikov -- An Application Of Stahl's Conjecture About The K-tuple Chromatic Numbers Of Kneser Graphs / Svata Poljak And Fred S. Roberts -- Various Applied Mathematics Topics -- Optimal Reservation Scheme Routing For Two-rate Wide-sense Nonblocking Three-stage Clos Networks / Wenqing Dou And Frank K. Hwang -- Correlation Inequalities For Partially Ordered Algebras / Siddhartha Sahi -- The Kruskal Count / Jeffrey C. Lagarias, Eric Rains And Robert J. Vanderbei -- Descending Dungeons And Iterated Base-changing / David Applegate, Marc Lebrun And N. J. A. Sloane -- Updating Hardy, Littlewood And Polya With Linear Programming / Larry Shepp. Steven Brams, William V. Gehrlein, Fred S. Roberts, Editors. Includes Bibliographical References. Front Matter....Pages i-xviii Entropy-Related Measures of the Utility of Gambling....Pages 5-25 Altruistic Utility Functions for Joint Decisions....Pages 27-38 SSB Preferences: Nonseparable Utilities or Nonseparable Beliefs....Pages 39-55 Decision Making Based on Risk-Value Tradeoffs....Pages 59-72 Normally Distributed Admissible Choices are Optimal....Pages 73-83 A Conjoint Measurement Approach to the Discrete Sugeno Integral....Pages 85-109 Additive Representability of Finite Measurement Structures....Pages 113-133 Acyclic Domains of Linear Orders: A Survey....Pages 139-160 Condorcet Domains: A Geometric Perspective....Pages 161-182 Condorcet's Paradox with Three Candidates....Pages 183-196 On the Probability to Act in the European Union....Pages 197-211 Voting Systems that Combine Approval and Preference....Pages 215-237 Anonymous Voting Rules with Abstention: Weighted Voting....Pages 239-258 Pareto, Anonymity or Neutrality, but Not IIA: Countably Many Alternatives....Pages 261-270 Bruhat Orders and the Sequential Selection of Indivisible Items....Pages 273-285 Fractional Weak Discrepancy of Posets and Certain Forbidden Configurations....Pages 291-301 Interval Order Representation via Shortest Paths....Pages 303-311 Probe Interval Orders....Pages 313-322 Mediatic Graphs....Pages 325-343 An Application of Stahl's Conjecture About the k -Tuple Chromatic Numbers of Kneser Graphs....Pages 345-352 Optimal Reservation Scheme Routing for Two-Rate Wide-Sense Nonblocking Three-Stage Clos Networks....Pages 355-360 Correlation Inequalities for Partially Ordered Algebras....Pages 361-369 The Kruskal Count....Pages 371-391 Descending Dungeons and Iterated Base-Changing....Pages 393-402 Updating Hardy, Littlewood and Pólya with Linear Programming....Pages 403-420 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."