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Stability and Centrality of Legislative Choice in the Spatial Context

Author

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  • Grofman, Bernard
  • Owen, Guillermo
  • Noviello, Nicholas
  • Glazer, Amihai

Abstract

Majority-rule spatial voting games lacking a core still always present a “near-core” outcome, more commonly known as the Copeland winner. This is the alternative that defeats or ties the greatest number of alternatives in the space. Previous research has not tested the Copeland winner as a solution concept for spatial voting games without a core, lacking a way to calculate where the Copeland winner was with an infinite number of alternatives. We provide a straightforward algorithm to find the Copeland winner and show that it corresponds well to experimental outcomes in an important set of experimental legislative voting games. We also provide an intuitive motivation for why legislative outcomes in the spatial context may be expected to lie close to the Copeland winner. Finally, we show a connection between the Copeland winner and the Shapley value and provide a simple but powerful algorithm to calculate the Copeland scores of all points in the space in terms of the (modified) power values of each of the voters and their locations in the space.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:apsrev:v:81:y:1987:i:02:p:539-553_19
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    Citations

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    Cited by:

    1. Martin, Mathieu & Nganmeni, Zephirin & Tchantcho, Bertrand, 2017. "The Owen and Shapley spatial power indices: A comparison and a generalization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 10-19.
    2. Cheryl L. Eavey, 1991. "Patterns of Distribution in Spatial Games," Rationality and Society, , vol. 3(4), pages 450-474, October.
    3. 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.
    4. Scott Feld & Bernard Grofman, 1988. "The Borda count in n-dimensional issue space," Public Choice, Springer, vol. 59(2), pages 167-176, November.
    5. Karos, Dominik & Peters, Hans, 2018. "Effectivity and power," Games and Economic Behavior, Elsevier, vol. 108(C), pages 363-378.
    6. Thomas König & Thomas Bräuninger, 1996. "Power and Political Coordination in American and German Multi-Chamber Legislation," Journal of Theoretical Politics, , vol. 8(3), pages 331-360, July.
    7. Hun Chung & John Duggan, 2018. "Directional equilibria," Journal of Theoretical Politics, , vol. 30(3), pages 272-305, July.
    8. Hans Peters & José M. Zarzuelo, 2017. "An axiomatic characterization of the Owen–Shapley spatial power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 525-545, May.
    9. Guillermo Owen & Francesc Carreras, 2022. "Spatial games and endogenous coalition formation," Annals of Operations Research, Springer, vol. 318(2), pages 1095-1115, November.
    10. Scott L. Feld & Bernard Grofman, 1991. "Incumbency Advantage, Voter Loyalty and the Benefit of the Doubt," Journal of Theoretical Politics, , vol. 3(2), pages 115-137, April.
    11. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.
    12. Mark Fey, 2008. "Choosing from a large tournament," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 301-309, August.
    13. Barr, Jason & Passarelli, Francesco, 2009. "Who has the power in the EU?," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 339-366, May.
    14. Stefan Napel & Mika Widgren, 2004. "Power Measurement as Sensitivity Analysis," Journal of Theoretical Politics, , vol. 16(4), pages 517-538, October.
    15. Edward Wesep, 2012. "Defensive Politics," Public Choice, Springer, vol. 151(3), pages 425-444, June.

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