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Monotonic norms and orthogonal issues in multidimensional voting

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  • Gershkov, Alex
  • Moldovanu, Benny
  • Shi, Xianwen

Abstract

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 lp spaces of any finite dimension, and show that they do not depend on p (unless p=2).

Suggested Citation

  • Gershkov, Alex & Moldovanu, Benny & Shi, Xianwen, 2020. "Monotonic norms and orthogonal issues in multidimensional voting," Journal of Economic Theory, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jetheo:v:189:y:2020:i:c:s002205312030096x
    DOI: 10.1016/j.jet.2020.105103
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    References listed on IDEAS

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    1. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 688-717.
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    Cited by:

    1. Gregorio Curello & Ludvig Sinander, 2020. "Agenda-manipulation in ranking," Papers 2001.11341, arXiv.org, revised Sep 2022.

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    More about this item

    Keywords

    Multidimensional voting; Dominant strategy incentive compatibility; Norm monotonicity;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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