The Mathematics of Preference, Choice and Order Essays in Honor of Peter C. Fishburn
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P. K. Pattanaik, K. Suzumura, Steven J. Brams, William V. Gehrlein, Fred S. Roberts.
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Steven Brams, William V. Gehrlein, Fred S. Roberts
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The Mathematics of Preference, Choice and Order Essays in Honor of Peter C. Fishburn
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Springer-Verlag
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9783540791287
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1
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CHF 142.40
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Mathematik
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English
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420
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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.
Preface
6
Contents
12
Contributors
15
Utility, Preference, Individual Choice, Subjective Probability, and Measurement
19
Utility Theory
20
Entropy-Related Measures of the Utility of Gambling
21
Altruistic Utility Functions for Joint Decisions
42
SSB Preferences: Nonseparable Utilities or Nonseparable Beliefs
54
Decision Theory
71
Decision Making Based on Risk-Value Tradeoffs
72
Normally Distributed Admissible Choices are Optimal
86
A Conjoint Measurement Approach to the Discrete Sugeno Integral
97
Measurement Theory
122
Additive Representability of Finite Measurement Structures
123
Part II
144
Social Choice, Voting, and Social Welfare
144
Condorcet Domains and Probabilities
145
Acyclic Domains of Linear Orders: A Survey
146
Condorcet Domains: A Geometric Perspective
168
Condorcet’s Paradox with Three Candidates
190
On the Probability to Act in the European Union
204
Voting Rules
219
Voting Systems that Combine Approval and Preference
220
Anonymous Voting Rules with Abstention: Weighted Voting
243
Social Choice
263
Pareto, Anonymity or Neutrality, but Not IIA: Countably Many Alternatives
264
Fair Division
274
Bruhat Orders and the Sequential Selection of Indivisible Items
275
Part III
288
Posets, Graphs, Combinatorics, and Related Applied and Mathematical Topics
288
Partial Orders and Interval Orders
289
FractionalWeak Discrepancy of Posets and Certain Forbidden Configurations
290
Interval Order Representation via Shortest Paths
301
Probe Interval Orders
310
Graphs
320
Mediatic Graphs
321
An Application of Stahl’s Conjecture About the k-Tuple Chromatic Numbers of Kneser Graphs
340
Various Applied Mathematics Topics
348
Optimal Reservation Scheme Routing for Two-RateWide-Sense Nonblocking Three-Stage Clos Networks
349
Correlation Inequalities for Partially Ordered Algebras*
355
The Kruskal Count
364
Descending Dungeons and Iterated Base-Changing
385
Updating Hardy, Littlewood and Polya´ with Linear Programming
395
