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Monotonic Norms and Orthogonal Issues in Multidimensional Voting

Gershkov, Alex, Moldovanu, Benny and Shi, Xianwen (2020) Monotonic Norms and Orthogonal Issues in Multidimensional Voting Journal of Economic Theory.

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We study issue-by-issue voting by majority and incentive compatibility in multi-dimensional 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 coor- dinates 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 Birkho¤-James orthogonal to it. 3) We show how semi-inner products and normality provide an analytic method that can be used to �nd all DIC marginal medians. 4) As an application, we derive all DIC marginal medians for lp spaces of any finite dimension, and show that they do not depend on p (unless p = 2).

Item Type: Article
Divisions : Faculty of Arts and Social Sciences > School of Economics
Authors :
Moldovanu, Benny
Shi, Xianwen
Date : 2 August 2020
Additional Information : Embargo OK Metadata Pending
Depositing User : James Marshall
Date Deposited : 12 Aug 2020 10:25
Last Modified : 12 Aug 2020 10:25

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