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Necessary gradient restrictions at the core of a voting rule

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  • Duggan, John

Abstract

This paper generalizes known gradient restrictions for the core of a voting rule parameterized by an arbitrary quota. For the special case of majority rule with an even number of voters, the result implies that given any pointed, finitely generated, convex cone C, the difference between the number of voters with gradients in C and the number with gradients in −C cannot exceed the number of voters with zero gradient, plus a dimensional adjustment. When the cone has dimensionality less than three, the adjustment is zero. A difficulty in the proof of a result of Schofield (1983), which neglects the dimensional adjustment term, is identified, and a counterexample (in three dimensions) presented.

Suggested Citation

  • Duggan, John, 2018. "Necessary gradient restrictions at the core of a voting rule," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 1-9.
    • Handle: RePEc:eee:mateco:v:79:y:2018:i:c:p:1-9
    DOI: 10.1016/j.jmateco.2018.08.006
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    References listed on IDEAS

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    1. Norman Schofield, 1983. "Generic Instability of Majority Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 695-705.
    2. Banks, Jeffrey S., 1995. "Singularity theory and core existence in the spatial model," Journal of Mathematical Economics, Elsevier, vol. 24(6), pages 523-536.
    3. Donald G. Saari, 1997. "The generic existence of a core for q -rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 219-260.
    4. Hun Chung & John Duggan, 2018. "Directional equilibria," Journal of Theoretical Politics, , vol. 30(3), pages 272-305, July.
    5. McKelvey, Richard D & Schofield, Norman, 1987. "Generalized Symmetry Conditions at a Core Point," Econometrica, Econometric Society, vol. 55(4), pages 923-933, July.
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    Cited by:

    1. Hun Chung & John Duggan, 2018. "Directional equilibria," Journal of Theoretical Politics, , vol. 30(3), pages 272-305, July.
    2. Anindya Bhattacharya & Francesco Ciardiello, 2024. "How sensitive are the results in voting theory when just one other voter joins in? Some instances with spatial majority voting," Discussion Papers 24/03, Department of Economics, University of York.
    3. Knudson, Mathew, 2020. "Two candidate competition on differentiated policy sets," Games and Economic Behavior, Elsevier, vol. 121(C), pages 413-434.

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