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Monotonic Norms and Orthogonal Issues in Multidimensional Voting

Author

Listed:
  • Alex Gershkov
  • Benny Moldovanu
  • Xianwen Shi

Abstract

We study issue-by-issue voting and robust mechanism design in multidimensional frameworks where privately informed agents have preferences induced by general norms. 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).

Suggested Citation

  • Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2019. "Monotonic Norms and Orthogonal Issues in Multidimensional Voting," Working Papers tecipa-644, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-644
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    More about this item

    Keywords

    Multidimensional Voting; Dominant Strategy; Monotonic Norms; Orthogonality;

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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