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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.
    2. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    3. Shubik, Martin & Wooders, Myrna Holtz, 1983. "Approximate cores of replica games and economies. Part I: Replica games, externalities, and approximate cores," Mathematical Social Sciences, Elsevier, vol. 6(1), pages 27-48, October.
    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.
    5. Banks, Jeffrey S., 1995. "Singularity theory and core existence in the spatial model," Journal of Mathematical Economics, Elsevier, vol. 24(6), pages 523-536.
    6. McKelvey, Richard & Tovey, Craig A., 2010. "Approximation of the yolk by the LP yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 102-109, January.
    7. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
    8. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    9. Rubinstein, Ariel, 1979. "A Note about the "Nowhere Denseness" of Societies Having an Equilibrium under Majority Rule," Econometrica, Econometric Society, vol. 47(2), pages 511-514, March.
    10. Jac C. Heckelman & Nicholas R. Miller (ed.), 2015. "Handbook of Social Choice and Voting," Books, Edward Elgar Publishing, number 15584.
    11. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    12. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    13. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    14. Scott Feld & Bernard Grofman & Nicholas Miller, 1988. "Centripetal forces in spatial voting: On the size of the Yolk," Public Choice, Springer, vol. 59(1), pages 37-50, October.
    15. Craig Tovey, 2010. "The probability of majority rule instability in the 2D euclidean model with an even number of voters," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 705-708, October.
    16. Owen, Guillermo, 1990. "Stable outcomes in spatial voting games," Mathematical Social Sciences, Elsevier, vol. 19(3), pages 269-279, June.
    17. Shubik, Martin & Wooders, Myrna Holtz, 1983. "Approximate cores of replica games and economies : Part II: Set-up costs and firm formation in coalition production economies," Mathematical Social Sciences, Elsevier, vol. 6(3), pages 285-306, December.
    18. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-157, January.
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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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