Consistency, Choice, and Rationality

Preface
I. Foundations
- 1. Historical Background
  - 1.1 Suzumura Consistency
  - 1.2 Rational Choice as Purposive Behavior
  - 1.3 Samuelson’s Weak Axiom
  - 1.4 Houthakker’s Axiom
  - 1.5 General Choice Functions
  - 1.6 Rational Choice: An Outlook
  - 1.7 Reference-Dependent Choice
  - 1.8 External Norms
  - 1.9 Welfare Economics and Social Choice Theory
  - 1.10 Beyond Finite-Population Social Choice
- 2. Mathematical Background
  - 2.1 Binary Relations
  - 2.2 Greatest and Maximal Elements
  - 2.3 Extensions of Relations
  - 2.4 Filters and Ultrafilters
II. Rationalizability on General Domains
- 3. Definitions of Rationalizability
  - 3.1 Preliminaries
  - 3.2 Greatest-Element Rationalizability
  - 3.3 Maximal-Element Rationalizability
  - 3.4 A Synthesis
- 4. Characterizations
  - 4.1 A Preliminary Result
  - 4.2 Three Special Cases
  - 4.3 A Unified Approach
  - 4.4 Summary
III. Rationalizability on Specific Domains
- 5. Domain Closedness Properties
  - 5.1 Additional Choice Coherence Axioms
  - 5.2 Logical Relationships
  - 5.3 Closedness under Intersection
  - 5.4 Closedness under Union
- 6. Cardinality-Complete Domains
  - 6.1 Base Domains
  - 6.2 Logical Relationships on Base Domains
  - 6.3 Characterizations on Base Domains
  - 6.4 Base Domains and Closedness under Union
IV. Alternative Notions of Rationalizability
- 7. Non-deteriorating Choice
  - 7.1 Individual Non-deteriorating Choice
  - 7.2 Characterizations of ND-Rationalizability
  - 7.3 The Multi-agent Case
  - 7.4 Characterizing Efficient and Non-deteriorating Choice
- 8. External Norms and Rational Choice
  - 8.1 Internal Coherence of Choice
  - 8.2 Norm-Conditional Choice
  - 8.3 Norm-Conditional Rationalizability
  - 8.4 Characterization Results
V. Topics in Social Choice Theory
- 9. Collective Choice Rules
  - 9.1 Weakening Social Coherence Properties
  - 9.2 Earlier Results
  - 9.3 Generalizations of the Pareto Rule
  - 9.4 A Characterization
- 10. Decisiveness and Infinite Populations
  - 10.1 Decisive Coalitions, Filters, and Ultrafilters
  - 10.2 Decisiveness without Social Richness Assumptions
  - 10.3 Intergenerational Social Choice
  - 10.4 Multi-profile Stationarity
References
Index

Walter Bossert

Kotaro Suzumura

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