IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v57y2021i1d10.1007_s00355-021-01316-z.html
   My bibliography  Save this article

Dominance in spatial voting with imprecise ideals

Author

Listed:
  • Mathieu Martin

    (Cergy Paris Université)

  • Zéphirin Nganmeni

    (Paris 8 University)

  • Craig A. Tovey

    (Georgia Institute of Technology)

Abstract

We introduce a dominance relationship in spatial voting with Euclidean preferences, by treating voter ideal points as balls of radius $$\delta$$ δ . Values $$\delta >0$$ δ > 0 model imprecision or ambiguity as to voter preferences from the perspective of a social planner. The winning coalitions may be any consistent monotonic collection of voter subsets. We characterize the minimum value of $$\delta$$ δ for which the $$\delta$$ δ -core, the set of undominated points, is nonempty. In the case of simple majority voting, the core is the yolk center and $$\delta$$ δ is the yolk radius.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:57:y:2021:i:1:d:10.1007_s00355-021-01316-z
    DOI: 10.1007/s00355-021-01316-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-021-01316-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-021-01316-z?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. 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.
    2. Norman Schofield, 1983. "Generic Instability of Majority Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 695-705.
    3. Banks, Jeffrey S., 1995. "Singularity theory and core existence in the spatial model," Journal of Mathematical Economics, Elsevier, vol. 24(6), pages 523-536.
    4. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    5. 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.
    6. Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.
    7. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    8. 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.
    9. 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.
    10. 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.
    11. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    12. Ralph E. Steuer, 1976. "Multiple Objective Linear Programming with Interval Criterion Weights," Management Science, INFORMS, vol. 23(3), pages 305-316, November.
    13. 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.
    14. Katrin Borcherding & Thomas Eppel & Detlof von Winterfeldt, 1991. "Comparison of Weighting Judgments in Multiattribute Utility Measurement," Management Science, INFORMS, vol. 37(12), pages 1603-1619, December.
    15. Weber, Martin & Borcherding, Katrin, 1993. "Behavioral influences on weight judgments in multiattribute decision making," European Journal of Operational Research, Elsevier, vol. 67(1), pages 1-12, May.
    16. Jac C. Heckelman & Nicholas R. Miller (ed.), 2015. "Handbook of Social Choice and Voting," Books, Edward Elgar Publishing, number 15584.
    17. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    18. 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.
    19. Owen, Guillermo, 1990. "Stable outcomes in spatial voting games," Mathematical Social Sciences, Elsevier, vol. 19(3), pages 269-279, June.
    20. 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.
    21. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tasos Kalandrakis, 2022. "Generalized medians and a political center," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 301-319, February.
    2. Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐Baptiste Tondji, 2022. "Vaccine and inclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1101-1123, October.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐baptiste Tondji, 2022. "Vaccine and inclusion," Post-Print hal-04257703, HAL.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean-Baptiste Tondji, 2022. "Vaccine and Inclusion," Working Papers 2202E Classification-C62,, University of Ottawa, Department of Economics.
    3. Mathieu Martin & Zéphirin Nganmeni & Ashley Piggins & Élise F. Tchouante, 2022. "Pure-strategy Nash equilibrium in the spatial model with valence: existence and characterization," Public Choice, Springer, vol. 190(3), pages 301-316, March.

    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, 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.
    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. 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.
    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. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    6. 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.
    7. Mathieu Martin & Zéphirin Nganmeni & Ashley Piggins & Élise F. Tchouante, 2022. "Pure-strategy Nash equilibrium in the spatial model with valence: existence and characterization," Public Choice, Springer, vol. 190(3), pages 301-316, March.
    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. 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.
    10. Edward Wesep, 2012. "Defensive Politics," Public Choice, Springer, vol. 151(3), pages 425-444, June.
    11. 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.
    12. Tanner, Thomas Cole, 1994. "The spatial theory of elections: an analysis of voters' predictive dimensions and recovery of the underlying issue space," ISU General Staff Papers 1994010108000018174, Iowa State University, Department of Economics.
    13. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    14. Duggan, John & Fey, Mark, 2005. "Electoral competition with policy-motivated candidates," Games and Economic Behavior, Elsevier, vol. 51(2), pages 490-522, May.
    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. 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.
    17. Alesina, Alberto & Passarelli, Francesco, 2014. "Regulation versus taxation," Journal of Public Economics, Elsevier, vol. 110(C), pages 147-156.
    18. Nicholas R. Miller, 2015. "The spatial model of social choice and voting," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 10, pages 163-181, Edward Elgar Publishing.
    19. Mathieu Martin & Zéphirin Nganmeni, 2019. "The fi nagle point might not be within the Ɛ-core: a contradiction with Bräuninger's result," THEMA Working Papers 2019-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    20. Gerald H. Kramer, 1980. "Extension of a Dynamical Model of Political Equilibrium," Cowles Foundation Discussion Papers 556, Cowles Foundation for Research in Economics, Yale University.

    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:spr:sochwe:v:57:y:2021:i:1:d:10.1007_s00355-021-01316-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.