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Monotonic Norms and Orthogonal Issues in Multidimensional Voting

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  • Alex Gershkov

  • Benny Moldovanu

  • Xianwen Shi

Abstract

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 de ned 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 nite dimension, and show that they do not depend on p (unless p = 2).

Suggested Citation

  • Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2021. "Monotonic Norms and Orthogonal Issues in Multidimensional Voting," CRC TR 224 Discussion Paper Series crctr224_2021_290, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2021_290
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    Cited by:

    1. is not listed on IDEAS
    2. Gregorio Curello & Ludvig Sinander, 2020. "Agenda-manipulation in ranking," Papers 2001.11341, arXiv.org, revised Sep 2022.

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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