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The generic existence of a core for q -rules (*)

Author

Listed:
  • Donald G. Saari

    (Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA)

Abstract

A q-rule is where a winning coalition has q or more of the n voters. It is important to understand when, generically, core points exist; that is, when does the core exist in other than highly contrived settings? As known, the answer depends upon the dimension of issue space. McKelvey and Schofield found bounds on these dimensions, but Banks found a subtle, critical error in their proofs. The sharp dimensional values along with results about the structure of the core are derived here. It is interesting how these dimensional values correspond to the number of issues that are needed to lure previously supporting voters into a new coalition.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:9:y:1997:i:2:p:219-260
    Note: Received: November 3, 1995 revised version February 22, 1996
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    Cited by:

    1. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    2. 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.
    3. M. Puy, 2013. "Stable coalition governments: the case of three political parties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 65-87, January.
    4. A. J. McGann, 2004. "The Tyranny of the Supermajority," Journal of Theoretical Politics, , vol. 16(1), pages 53-77, January.
    5. Justin Fox, 2006. "Legislative Cooperation among Impatient Legislators," Journal of Theoretical Politics, , vol. 18(1), pages 68-97, January.
    6. Duggan, John, 2018. "Necessary gradient restrictions at the core of a voting rule," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 1-9.
    7. de Groot Ruiz, Adrian & Ramer, Roald & Schram, Arthur, 2016. "Formal versus informal legislative bargaining," Games and Economic Behavior, Elsevier, vol. 96(C), pages 1-17.
    8. 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.
    9. Juan Pablo Micozzi & Sebastián M Saiegh, 2016. "An empirical stochastic model of Argentina’s Impossible Game (1955–1966)," Journal of Theoretical Politics, , vol. 28(2), pages 266-287, April.
    10. Laurent Vidu, 2000. "The Minimal Quota for a Complete Majority Relation to be Transitive," Group Decision and Negotiation, Springer, vol. 9(6), pages 531-534, November.
    11. 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.
    12. 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.
    13. Hamilton, Timothy L. & Eynan, Amit, 2023. "Siting noxious facilities: Efficiency and majority rule decisions," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1344-1354.
    14. Gallego, Maria & Schofield, Norman, 2017. "Modeling the effect of campaign advertising on US presidential elections when differences across states matter," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 160-181.
    15. Reuben Kline, 2014. "Supermajority voting, social indifference and status quo constraints," Journal of Theoretical Politics, , vol. 26(2), pages 312-330, April.
    16. Muhammad Mahajne & Oscar Volij, 2019. "Condorcet winners and social acceptability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 641-653, December.
    17. Hannu Nurmi & Tommi Meskanen, 2000. "Voting Paradoxes and MCDM," Group Decision and Negotiation, Springer, vol. 9(4), pages 297-313, July.
    18. Maria Gallego & Norman Schofield & Kevin McAlister & Jee Jeon, 2014. "The variable choice set logit model applied to the 2004 Canadian election," Public Choice, Springer, vol. 158(3), pages 427-463, March.
    19. Sean Ingham, 2016. "Social choice and popular control," Journal of Theoretical Politics, , vol. 28(2), pages 331-349, April.
    20. Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.
    21. Richard F. Potthoff, 2022. "Radial Symmetry Does Not Preclude Condorcet Cycles If Different Voters Weight the Issues Differently," Economies, MDPI, vol. 10(7), pages 1-17, July.
    22. 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.

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