The Mathematics of Preference, Choice and Order: Essays in Honor of Peter C. FishburnSteven Brams, William V. Gehrlein, Fred S. Roberts 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. |
Contents
| 5 | |
Graphs | 24 |
Altruistic Utility Functions for Joint Decisions 27 | 26 |
Nonseparable Utilities or Nonseparable Beliefs | 39 |
Decision Theory | 55 |
Normally Distributed Admissible Choices are Optimal | 73 |
A Conjoint Measurement Approach to the Discrete Sugeno Integral | 85 |
Additive Representability of Finite Measurement Structures | 113 |
Weighted Voting | 239 |
Social Choice | 257 |
Jerry S Kelly Department of Economics Syracuse University Syracuse | 260 |
Bruhat Orders and the Sequential Selection of Indivisible Items | 273 |
Fractional Weak Discrepancy of Posets and Certain Forbidden | 288 |
Probe Interval Orders 313 | 312 |
Mediatic Graphs | 325 |
An Application of Stahls Conjecture About the kTuple Chromatic | 344 |
A Survey 139 | 136 |
A Geometric Perspective | 161 |
Condorcets Paradox with Three Candidates | 183 |
On the Probability to Act in the European Union | 197 |
Voting Systems that Combine Approval and Preference 215 | 213 |
David E Brown Department of Mathematics and Statistics Utah State University | 355 |
Correlation Inequalities for Partially Ordered Algebras | 361 |
Descending Dungeons and Iterated BaseChanging | 393 |
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Common terms and phrases
2-graded acyclic domain algorithm alternatives altruistic utility function anonymous approval approval voting axiom binary relation Brams Bruhat order candidate Cartesian product Choice and Welfare comparative probability orders condition Condorcet Domain Condorcet winner Condorcet's Paradox CPPMRW decision defined Definition denote discrete Sugeno integral distribution distributive lattice elements equivalent example expected utility finite Fishburn forcing cycle gambles Gehrlein implies individual interval orders Journal lattice Lemma linear orders lottery majority majority-approved Mathematics maximal chain measure of risk Monjardet multiset n-tuple noncompensatory model outcomes pair partial order PAV and FV PAV winner permutations PMRW portfolio poset preferences probe interval graphs proof Proposition rankings risk averse risk-value models satisfies semiorders shortest path single-peaked Slinko social choice social choice theory stochastic dominance strategy subset Sugeno integral model Theorem triplet utility function voters weak order