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The Core and the Stability of Group Choice in Spatial Voting Games

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  • Schofield, Norman
  • Grofman, Bernard
  • Feld, Scott L.

Abstract

The core of a voting game is the set of undominated outcomes, that is, those that once in place cannot be overturned. For spatial voting games, a core is structurally stable if it remains in existence even if there are small perturbations in the location of voter ideal points. While for simple majority rule a core will exist in games with more than one dimension only under extremely restrictive symmetry conditions, we show that, for certain supramajorities, a core must exist. We also provide conditions under which it is possible to construct a structurally stable core. If there are only a few dimensions, our results demonstrate the stability properties of such frequently used rules as two-thirds and three-fourths. We further explore the implications of our results for the nature of political stability by looking at outcomes in experimental spatial voting games and at Belgian cabinet formation in the late 1970s.

Suggested Citation

  • Schofield, Norman & Grofman, Bernard & Feld, Scott L., 1988. "The Core and the Stability of Group Choice in Spatial Voting Games," American Political Science Review, Cambridge University Press, vol. 82(1), pages 195-211, March.
    • Handle: RePEc:cup:apsrev:v:82:y:1988:i:01:p:195-211_08
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    Cited by:

    1. Mahajan, Aseem & Pongou, Roland & Tondji, Jean-Baptiste, 2023. "Supermajority politics: Equilibrium range, policy diversity, utilitarian welfare, and political compromise," European Journal of Operational Research, Elsevier, vol. 307(2), pages 963-974.
    2. Luigi Curini & Paolo Martelli, 2009. "Electoral Systems and Government Stability: A Simulation of 2006 Italian Policy Space," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 3(3), pages 305-322, October.
    3. Patrick J. Haney & Roberta Q. Herzberg & Rick K. Wilson, 1992. "Advice and Consent," Journal of Conflict Resolution, Peace Science Society (International), vol. 36(4), pages 603-633, December.
    4. A. J. McGann, 2004. "The Tyranny of the Supermajority," Journal of Theoretical Politics, , vol. 16(1), pages 53-77, January.
    5. Cesar Garcia Perez de Leon, 2012. "Does implicit voting matter? Coalitional bargaining in the EU legislative process," European Union Politics, , vol. 13(4), pages 513-534, December.
    6. Bernard Grofman & Thomas Brunell & Scott Feld, 2012. "Towards a theory of bicameralism: the neglected contributions of the calculus of consent," Public Choice, Springer, vol. 152(1), pages 147-161, July.
    7. Hee-Min Kim, 2000. "A Spatial Analysis of Policy Stability in Western Democracies, I: A Society-Centered Model with Applications to Spain and Sweden," International Area Studies Review, Center for International Area Studies, Hankuk University of Foreign Studies, vol. 3(1), pages 55-76, June.
    8. Thomas H. Hammond & Christopher K. Butler, 2003. "Some Complex Answers to the Simple Question ‘Do Institutions Matter?’," Journal of Theoretical Politics, , vol. 15(2), pages 145-200, April.
    9. Scott Feld & Bernard Grofman & Nicholas Miller, 1988. "Centripetal forces in spatial voting: On the size of the Yolk," Public Choice, Springer, vol. 59(1), pages 37-50, October.
    10. Reuben Kline, 2014. "Supermajority voting, social indifference and status quo constraints," Journal of Theoretical Politics, , vol. 26(2), pages 312-330, April.
    11. Gyung-Ho Jeong, 2017. "The supermajority core of the US Senate and the failure to join the League of Nations," Public Choice, Springer, vol. 173(3), pages 325-343, December.
    12. Michel Regenwetter & James Adams & Bernard Grofman, 2002. "On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity," Theory and Decision, Springer, vol. 53(2), pages 153-186, September.

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