The structure of strategy-proof social choice - Part I: General characterization and possibility results on median spaces

• 成果类型: Article; Proceedings Paper
• 署名作者: Nehring, Klaus; Puppe, Clemens
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; University of California System; University of California Davis
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2006.04.008
• 发表日期: 2007
• 页码: 269-305
• 关键词: Strategy-proofness; generalized single-peakedness; Median spaces; Intersection property

摘要

We define a general notion of single-peaked preferences based on abstract betweenness relations. Special cases are the classical example of single-peaked preferences on a line, the separable preferences on the hypercube. the multi-dimensionally single-peaked preferences on the product of lines, but also the unrestricted preference domain. Generalizing and unifying the existing literature, we show that a social choice function is strategy-proof on a sufficiently rich domain of generalized single-peaked preferences if and only if it takes the form of voting by issues (voting by committees) satisfying a simple condition called the Intersection Property. Based on the Intersection Property, we show that the class of preference domains associated with median spaces gives rise to the strongest possibility results; in particular, we show that the existence of strategy-proof social choice rules that are non-dictatorial and neutral requires an underlying median space. A space is a median space if, for every triple of elements, there is a fourth element that is between each pair of the triple; numerous examples are given (some well-known, some novel), and the structure of median spaces and the associated preference domains is analysed. (c) 2006 Elsevier Inc. All rights reserved.