Aggregation theory and the relevance of some issues to others

• 成果类型: Article
• 署名作者: Dietrich, Franz
• 署名单位: Paris School of Economics; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2015.03.012
• 发表日期: 2015
• 页码: 463-493
• 关键词: Judgment aggregation; Generalized Arrow theorem; Generalized premise-based and sequential-priority rules; Priority graph; Aggregation of non-binary evaluations

摘要

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people's judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people's judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow's Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (C) 2015 Elsevier Inc. All rights reserved.