IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v90y2017icp145-149.html
   My bibliography  Save this article

Toward a 50%-majority equilibrium when voters are symmetrically distributed

Author

Listed:
  • Crès, Hervé
  • Utku Ünver, M.

Abstract

Consider a two-dimensional spatial voting model. A finite number m of voters are randomly drawn from a (weakly) symmetric distribution centered at O. We compute the exact probabilities of all possible Simpson–Kramer scores of O. The computations are independent of the shape of the distribution. The resulting expected score of O is an upper bound of the expected min–max score.

Suggested Citation

  • Crès, Hervé & Utku Ünver, M., 2017. "Toward a 50%-majority equilibrium when voters are symmetrically distributed," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 145-149.
    • Handle: RePEc:eee:matsoc:v:90:y:2017:i:c:p:145-149
    DOI: 10.1016/j.mathsocsci.2016.08.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489616300683
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2016.08.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Richard D. McKelvey & Richard E. Wendell, 1976. "Voting Equilibria in Multidimensional Choice Spaces," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 144-158, May.
    2. Kramer, Gerald H, 1973. "On a Class of Equilibrium Conditions for Majority Rule," Econometrica, Econometric Society, vol. 41(2), pages 285-297, March.
    3. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    4. Norman Schofield, 1983. "Generic Instability of Majority Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 695-705.
    5. Paul B. Simpson, 1969. "On Defining Areas of Voter Choice: Professor Tullock on Stable Voting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 83(3), pages 478-490.
    6. McKelvey, Richard D & Schofield, Norman, 1987. "Generalized Symmetry Conditions at a Core Point," Econometrica, Econometric Society, vol. 55(4), pages 923-933, July.
    7. Banks, Jeffrey S., 1995. "Singularity theory and core existence in the spatial model," Journal of Mathematical Economics, Elsevier, vol. 24(6), pages 523-536.
    8. 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.
    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. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    11. 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.
    12. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    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. 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.
    15. Schofield, N. & Tovey, C.A., 1992. "Probability and Convergence for Supramajority rule with Euclidean Preferences," Papers 163, Washington St. Louis - School of Business and Political Economy.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2021. "Dominance in spatial voting with imprecise ideals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 181-195, July.
    2. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    3. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    4. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    5. 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.
    6. Hervé Crès & Mich Tvede, 2001. "Proxy fights in incomplete markets: when majority voting and sidepayments are equivalent," Sciences Po publications 726/2001, Sciences Po.
    7. Norman Schofield, 2015. "Climate Change, Collapse and Social Choice Theory," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(1), pages 007-035, October.
    8. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    9. repec:hal:spmain:info:hdl:2441/10282 is not listed on IDEAS
    10. Pierre-Guillaume Méon, 2006. "Majority voting with stochastic preferences: The whims of a committee are smaller than the whims of its members," Constitutional Political Economy, Springer, vol. 17(3), pages 207-216, September.
    11. 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.
    12. Banks, Jeffrey S. & Duggan, John, 2008. "A Dynamic Model of Democratic Elections in Multidimensional Policy Spaces," Quarterly Journal of Political Science, now publishers, vol. 3(3), pages 269-299, October.
    13. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09iepsg269m is not listed on IDEAS
    14. Hervé Crès & M. Utku Ünver, 2010. "Ideology and Existence of 50%-Majority Equilibria in Multidimensional Spatial Voting Models," Journal of Theoretical Politics, , vol. 22(4), pages 431-444, October.
    15. Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.
    16. De Donder, Philippe & Gallego, Maria, 2017. "Electoral Competition and Party Positioning," TSE Working Papers 17-760, Toulouse School of Economics (TSE).
    17. B. D. Bernheim & S. N. Slavov, 2009. "A Solution Concept for Majority Rule in Dynamic Settings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 33-62.
    18. Duggan, John, 2018. "Necessary gradient restrictions at the core of a voting rule," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 1-9.
    19. repec:hal:spmain:info:hdl:2441/10277 is not listed on IDEAS
    20. 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.
    21. Itai Sened, 1995. "Equilibria in Weighted Voting Games with Sidepayments," Journal of Theoretical Politics, , vol. 7(3), pages 283-300, July.
    22. Edward Wesep, 2012. "Defensive Politics," Public Choice, Springer, vol. 151(3), pages 425-444, June.
    23. Itai Sened, 1991. "Contemporary Theory of Institutions in Perspective," Journal of Theoretical Politics, , vol. 3(4), pages 379-402, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:90:y:2017:i:c:p:145-149. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.