Consistency, Choice, and Rationality

In __Consistency, Choice, and Rationality__, economic theorists **Walter Bossert** and **Kotaro Suzumura** present a thorough mathematical treatment of Suzumura consistency, an alternative to established coherence properties such as transitivity, quasi-transitivity, or acyclicity. Applications in individual and social choice theory, fields important not only to economics but also to philosophy and political science, are discussed. Specifically, the authors explore topics such as rational choice and revealed preference theory, and collective decision making in an atemporal framework as well as in an intergenerational setting. Contents ......Page 6 Preface ......Page 10 I. Foundations ......Page 14 1.1 Suzumura Consistency ......Page 16 1.2 Rational Choice as Purposive Behavior ......Page 19 1.3 Samuelson's Weak Axiom ......Page 20 1.4 Houthakker's Axiom ......Page 25 1.5 General Choice Functions ......Page 28 1.6 Rational Choice: An Outlook ......Page 33 1.7 Reference-Dependent Choice ......Page 34 1.8 External Norms ......Page 36 1.9 Welfare Economics and Social Choice Theory ......Page 39 1.10 Beyond Finite-Population Social Choice ......Page 42 2.1 Binary Relations ......Page 45 2.2 Greatest and Maximal Elements ......Page 54 2.3 Extensions of Relations ......Page 55 2.4 Filters and Ultrafilters ......Page 65 II. Rationalizability on General Domains ......Page 68 3.1 Preliminaries ......Page 70 3.2 Greatest-Element Rationalizability ......Page 74 3.3 Maximal-Element Rationalizability ......Page 85 3.4 A Synthesis ......Page 88 4.1 A Preliminary Result ......Page 90 4.2 Three Special Cases ......Page 91 4.3 A Unifed Approach ......Page 94 4.4 Summary ......Page 122 III. Rationalizability on Specific Domains ......Page 126 5.1 Additional Choice Coherence Axioms ......Page 128 5.2 Logical Relationships ......Page 132 5.3 Closedness under Intersection ......Page 134 5.4 Closedness under Union ......Page 135 6.2 Logical Relationships on Base Domains ......Page 141 6.3 Characterizations on Base Domains ......Page 143 6.4 Base Domains and Closedness under Union ......Page 147 IV. Alternative Notions of Rationalizability ......Page 150 7.1 Individual Non-deteriorating Choice ......Page 152 7.2 Characterization of ND-Rationalizability ......Page 157 7.3 The Multi-agent Case ......Page 159 7.4 Characterizing Efficient and Non-deteriorating Choice ......Page 166 8.1 Internal Coherence of Choice ......Page 175 8.2 Norm-Conditional Choice ......Page 176 8.3 Norm-Conditional Rationalizability ......Page 177 8.4 Characterization Results ......Page 178 V. Topics in Social Choice Theory ......Page 184 9.1 Weakening Social Coherence Properties ......Page 186 9.2 Earlier Results ......Page 190 9.3 Generalizations of the Pareto Rule ......Page 191 9.4 A Characterization ......Page 193 10.1 Decisive Coalitions, Filters, and Ultrafilters ......Page 198 10.2 Decisiveness without Social Richness Assumptions ......Page 200 10.3 Intergenerational Social Choice ......Page 206 10.4 Multi-profile Stationarity ......Page 211 References ......Page 218 Index ......Page 228 "The authors present a thorough mathematical treatment of Suzumura consistency, an alternative to established coherence properties such as transitivity, quasi-transitivity, or acyclicity. Applications in individual and social choice theory, fields important not only to economics but also to philosophy and political science, are discussed. Specifically, the authors explore topics such as rational choice and revealed preference theory, and collective decision making in an atemporal framework as well as in an intergenerational setting."--Publisher An impressive and magisterial work from the top contributors in the world on choice-demand theory.