Monotonic norms and orthogonal issues in multidimensional voting

• 成果类型: Article
• 署名作者: Gershkov, Alex; Moldovanu, Benny; Shi, Xianwen
• 署名单位: Hebrew University of Jerusalem; University of Surrey; University of Bonn; University of Toronto
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2020.105103
• 发表日期: 2020
• 关键词: Multidimensional voting; Dominant strategy incentive compatibility; Norm monotonicity

摘要

We study issue-by-issue voting by majority and incentive compatibility in multidimensional frameworks where privately informed agents have preferences induced by general norms and where dimensions are endogenously chosen. We uncover the deep connections between dominant strategy incentive compatibility (DIC) on the one hand, and several geometric/functional analytic concepts on the other. Our main results are: 1) Marginal medians are DIC if and only if they are calculated with respect to coordinates defined by a basis such that the norm is orthant-monotonic in the associated coordinate system. 2) Equivalently, marginal medians are DIC if and only if they are computed with respect to a basis such that, for any vector in the basis, any linear combination of the other vectors is Birkhoff-James orthogonal to it. 3) We show how semi-inner products and normality provide an analytic method that can be used to find all DIC marginal medians. 4) As an application, we derive all DIC marginal medians for l(p) spaces of any finite dimension, and show that they do not depend on p (unless p = 2). Crown Copyright (c) 2020 Published by Elsevier Inc. All rights reserved.