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Dominance in Spatial Voting with Imprecise Ideals: A New Characterization of the Yolk

Author

Listed:
  • Mathieu Martin
  • Zéphirin Nganmeni
  • Craig A. Tovey

    (Université de Cergy-Pontoise, THEMA)

Abstract

We introduce a dominance relationship in spatial voting with Euclidean preferences, by treating voter ideal points as balls of radius δ. Values δ > 0 model imprecision or ambiguity as to voter preferences, or caution on the part of a social planner. The winning coalitions may be any consistent monotonic collection of voter subsets. We characterize the minimum value of δ for which the δ-core, the set of undominated points, is nonempty. In the case of simple majority voting, the core is the yolk center and δ is the yolk radius. Thus the δ-core both generalizes and provides a new characterization of the yolk. We then study relationships between the δ-core and two other concepts: the Ɛ-core and the finagle point. We prove that every fi nagle point must be within 2.32472 yolk radii of every yolk center, in all dimensions m ≥ 2.

Suggested Citation

  • Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2019. "Dominance in Spatial Voting with Imprecise Ideals: A New Characterization of the Yolk," THEMA Working Papers 2019-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2019-02
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    References listed on IDEAS

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    1. Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.
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    4. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2016. "On the uniqueness of the yolk," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 511-518, October.
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    More about this item

    Keywords

    Spatial voting; dominance; core; yolk; fi nagle.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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