Random mechanism design on multidimensional domains

• 成果类型: Article
• 署名作者: Chatterji, Shurojit; Zeng, Huaxia
• 署名单位: Singapore Management University; Shanghai University of Finance & Economics
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2019.04.003
• 发表日期: 2019
• 页码: 25-105
• 关键词: Generalized random dictatorships; Top-separability; separability; Multidimensional single-peakedness; Connected(+) domains; voting under constraints

摘要

We study random mechanism design in an environment where the set of alternatives has a Cartesian product structure. We first show that all generalized random dictatorships are sd-strategy-proof on a minimally rich domain if and only if all preferences are top-separable. We call a domain satisfying top-separability a multidimensional domain, and furthermore generalize the notion of connectedness (Monjardet, 2009) to a broad class of multidimensional domains: connected(+) domains. We show that in the class of minimally rich and connected' domains, the multidimensional single-peakedness restriction is necessary and sufficient for the design of a flexible random social choice function that is unanimous and sd-strategy-proof. Such a flexible random social choice function allows for a systematic notion of compromise. We prove an analogous result for deterministic social choice functions satisfying anonymity. Our characterization remains valid for a problem of voting under constraints where not all alternatives are feasible (Barbera et al., 1997). (C) 2019 Elsevier Inc. All rights reserved.