The Mathematics of Preference, Choice and Order

by Brams, Steven J.; Gehrlein, William V.; Roberts, Fred S.

• ISBN13: 9783540791270
• ISBN10: 3540791272
• Format: Hardcover
• Copyright: 2008-11-03
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Utility, Preference, Individual Choice, Subjective Probability, and Measurement
Utility Theory
Entropy-Related Measures of the Utility of Gambling	p. 5
Altruistic Utility Functions for Joint Decisions	p. 27
SSB Preferences: Nonseparable Utilities or Nonseparable Beliefs	p. 39
Decision Theory
Decision Making Based on Risk-Value Tradeoffs	p. 59
Normally Distributed Admissible Choices are Optimal	p. 73
A Conjoint Measurement Approach to the Discrete Sugeno Integral	p. 85
Measurement Theory
Additive Representability of Finite Measurement Structures	p. 113
Social Choice, Voting, and Social Welfare
Condorcet Domains and Probabilities
Acyclic Domains of Linear Orders: A Survey	p. 139
Condorcet Domains: A Geometric Perspective	p. 161
Condorcet's Paradox with Three Candidates	p. 183
On the Probability to Act in the European Union	p. 197
Voting Rules
Voting Systems that Combine Approval and Preference	p. 215
Anonymous Voting Rules with Abstention: Weighted Voting	p. 239
Social Choice
Pareto, Anonymity or Neutrality, but Not IIA: Countably Many Alternatives	p. 261
Fair Division
Bruhat Orders and the Sequential Selection of Indivisible Items	p. 273
Posets, Graphs, Combinatorics, and Related Applied and Mathematical Topics
Partial Orders and Interval Orders
Fractional Weak Discrepancy of Posets and Certain Forbidden Configurations	p. 291
Interval Order Representation via Shortest Paths	p. 303
Probe Interval Orders	p. 313
Graphs
Mediatic Graphs	p. 325
An Application of Stahl's Conjecture About the k-Tuple Chromatic Numbers of Kneser Graphs	p. 345
Various Applied Mathematics Topics
Optimal Reservation Scheme Routing for Two-Rate Wide-Sense Nonblocking Three-Stage Clos Networks	p. 355
Correlation Inequalities for Partially Ordered Algebras	p. 361
The Kruskal Count	p. 371
Descending Dungeons and Iterated Base-Changing	p. 393
Updating Hardy, Littlewood and Pólya with Linear Programming	p. 403
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