Brams The Mathematics of Preference, Choice and Order

Essays in Honor of Peter C. Fishburn
1. Auflage 2009
ISBN: 978-3-540-79128-7
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 420 Seiten

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.

Autoren/Hrsg.

Brams, Steven

Inhaltsverzeichnis

1;Preface;6
2;Contents;12
3;Contributors;15
4;Utility, Preference, Individual Choice, Subjective Probability, and Measurement;19
4.1;Utility Theory;20
4.1.1;Entropy-Related Measures of the Utility of Gambling;21
4.1.2;Altruistic Utility Functions for Joint Decisions;42
4.1.3;SSB Preferences: Nonseparable Utilities or Nonseparable Beliefs;54
4.2;Decision Theory;71
4.2.1;Decision Making Based on Risk-Value Tradeoffs;72
4.2.2;Normally Distributed Admissible Choices are Optimal;86
4.2.3;A Conjoint Measurement Approach to the Discrete Sugeno Integral;97
4.3;Measurement Theory;122
4.3.1;Additive Representability of Finite Measurement Structures;123
4.3.2;Part II;144
5;Social Choice, Voting, and Social Welfare;144
5.1;Condorcet Domains and Probabilities;145
5.1.1;Acyclic Domains of Linear Orders: A Survey;146
5.1.2;Condorcet Domains: A Geometric Perspective;168
5.1.3;Condorcet’s Paradox with Three Candidates;190
5.1.4;On the Probability to Act in the European Union;204
5.2;Voting Rules;219
5.2.1;Voting Systems that Combine Approval and Preference;220
5.2.2;Anonymous Voting Rules with Abstention: Weighted Voting;243
5.3;Social Choice;263
5.3.1;Pareto, Anonymity or Neutrality, but Not IIA: Countably Many Alternatives;264
5.4;Fair Division;274
5.4.1;Bruhat Orders and the Sequential Selection of Indivisible Items;275
5.4.2;Part III;288
6;Posets, Graphs, Combinatorics, and Related Applied and Mathematical Topics;288
6.1;Partial Orders and Interval Orders;289
6.1.1;FractionalWeak Discrepancy of Posets and Certain Forbidden Configurations;290
6.1.2;Interval Order Representation via Shortest Paths;301
6.1.3;Probe Interval Orders;310
6.2;Graphs;320
6.2.1;Mediatic Graphs;321
6.2.2;An Application of Stahl’s Conjecture About the k-Tuple Chromatic Numbers of Kneser Graphs;340
6.3;Various Applied Mathematics Topics;348
6.3.1;Optimal Reservation Scheme Routing for Two-RateWide-Sense Nonblocking Three-Stage Clos Networks;349
6.3.2;Correlation Inequalities for Partially Ordered Algebras*;355
6.3.3;The Kruskal Count;364
6.3.4;Descending Dungeons and Iterated Base-Changing;385
6.3.5;Updating Hardy, Littlewood and Polya´ with Linear Programming;395