Set-rationalizable choice and self-stability

2009-10-19

Journal of Economics Theory

AI Summary

This paper addresses the failure of traditional binary preference rationalization in social choice when choices yield sets rather than single alternatives. Methodologically, it introduces the “set-rationalizability” framework, treating choice sets—not individual alternatives—as primitive units; it proposes two novel axioms—self-stability and weak expansiveness—and defines set-based coherence conditions $hat{alpha}$ and $hat{gamma}$, which are equivalent to set-rationalizability. Theoretically, it establishes necessary and sufficient conditions for set-rationalizability, proving its equivalence to the joint satisfaction of self-stability and weak expansiveness. This framework unifies the rational explanation of various non-standard choice behaviors—including multi-valued choice and cyclic dependencies—thereby substantially extending the scope and applicability of rational choice theory beyond classical single-outcome paradigms.

Problem

• Rationalizing choice functions via set preferences
• Introducing consistency conditions for set-rationalizability
• Exploring self-stability in social choice functions

Innovation

• Set-rationalizable choice via preference relations
• New consistency conditions hat_alpha and hat_gamma
• Self-stable social choice functions concept