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Directional equilibria

Author

Listed:
  • Hun Chung

    (School of Political Science and Economics, Waseda University, Tokyo, Japan)

  • John Duggan

    (Department of Political Science and Department of Economics, University of Rochester, Rochester, NY, USA)

Abstract

We propose the solution concept of directional equilibrium for the multidimensional model of voting with general spatial preferences. This concept isolates alternatives that are stable with respect to forces applied by all voters in the directions of their gradients, and it extends a known concept from statistics for Euclidean preferences. We establish connections to the majority core, Pareto optimality, and existence and closed graph, and we provide non-cooperative foundations in terms of a local contest game played by voters.

Suggested Citation

  • Hun Chung & John Duggan, 2018. "Directional equilibria," Journal of Theoretical Politics, , vol. 30(3), pages 272-305, July.
    • Handle: RePEc:sae:jothpo:v:30:y:2018:i:3:p:272-305
    DOI: 10.1177/0951629818775515
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    References listed on IDEAS

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    1. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
    2. Nina Baranchuk & Philip H. Dybvig, 2009. "Consensus in Diverse Corporate Boards," The Review of Financial Studies, Society for Financial Studies, vol. 22(2), pages 715-747, February.
    3. Norman Schofield, 1983. "Generic Instability of Majority Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 695-705.
    4. Daniel J. Benjamin & Ori Heffetz & Miles S. Kimball & Nichole Szembrot, 2013. "Aggregating Local Preferences to Guide Marginal Policy Adjustments," American Economic Review, American Economic Association, vol. 103(3), pages 605-610, May.
    5. Grofman, Bernard & Owen, Guillermo & Noviello, Nicholas & Glazer, Amihai, 1987. "Stability and Centrality of Legislative Choice in the Spatial Context," American Political Science Review, Cambridge University Press, vol. 81(2), pages 539-553, June.
    6. Brady, Richard L. & Chambers, Christopher P., 2015. "Spatial implementation," Games and Economic Behavior, Elsevier, vol. 94(C), pages 200-205.
    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. Duggan, John, 2018. "Necessary gradient restrictions at the core of a voting rule," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 1-9.
    9. Cervone, Davide P. & Dai, Ronghua & Gnoutcheff, Daniel & Lanterman, Grant & Mackenzie, Andrew & Morse, Ari & Srivastava, Nikhil & Zwicker, William S., 2012. "Voting with rubber bands, weights, and strings," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 11-27.
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    Cited by:

    1. Duggan, John, 2018. "Necessary gradient restrictions at the core of a voting rule," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 1-9.

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