Set-rationalizable choice and self-stability

• 成果类型: Article
• 署名作者: Brandt, Felix; Harrenstein, Paul
• 署名单位: Technical University of Munich
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2011.03.006
• 发表日期: 2011
• 页码: 1721-1731
• 关键词: Choice theory; rationalizability; Consistency; Stable sets; Social choice theory

摘要

Rationalizability and similar notions of consistency have proved to be highly problematic in the context of social choice, as witnessed by a range of impossibility results, among which Arrow's is the most prominent. We propose to rationalize choice functions by preference relations over sets of alternatives (set-rationalizability) and introduce two consistency conditions, (alpha) over bar and (gamma)over bar>, which are defined in analogy to Sen's alpha and gamma. We find that a choice function satisfies (alpha) over bar and (gamma)over bar> if and only if it is set-rationalizable and that it satisfies (alpha) over bar and (gamma)over bar> if and only if it is self-stable, a new concept based on earlier work by Dutta. The class of self-stable social choice functions contains a number of appealing Condorcet extensions. (C) 2011 Elsevier Inc. All rights reserved.