Veto Players and Non-Cooperative Foundations of Power in Legislative Bargaining



In legislative bargaining of the Baron-Ferejohn type, veto players either hold all of the overall power of 1 and share proportional to their recognition probabilities, or hold no power at all. Hence, in this setting, it is impossible to provide non-cooperative support for power indices that do not assign all or no power to veto players. This highlights problems in the interpretation of results of Valenciano (2008a, b) which are taken as support for the Shapley-Shubik index and other normalized semi-values.



I am grateful for financial support from the Academy of Finland, and also want to thank Manfred J. Holler, Stefan Napel, Maria Montero as well as two anonymous referees for very valuable comments.


  1. Banzhaf, J. (1965). Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review, 19, 317–343.Google Scholar
  2. Baron, D., & Ferejohn, J. (1989). Bargaining in legislatures. American Political Science Review, 83, 1181–1206.Google Scholar
  3. Deegan, J., & Packel, E. (1978). A new index of power for simple n-person games. International Journal of Game Theory, 7, 113–123.Google Scholar
  4. Eraslan, H. (2002). Uniqueness of stationary equilibrium payoffs in the Baron-Ferejohn model. Journal of Economic Theory, 103, 11–30.Google Scholar
  5. Eraslan, H., & McLennan, A. (2011). Uniqueness of stationary equilibrium payoffs in coalitional bargaining. Working paper.Google Scholar
  6. Gul, F. (1989). Bargaining foundations of Shapley value. Econometrica, 57(1), 81–95.Google Scholar
  7. Hart, S., & Mas-Colell, A. (1996). Bargaining and value. Econometrica, 64(2), 357–380.Google Scholar
  8. Holler, M. (1982). Forming coalitions and measuring voting power. Political Studies, 30, 262–271.CrossRefGoogle Scholar
  9. Laruelle, A., & Valenciano, F. (2008a). Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index. Games and Economic Behavior, 63, 341–353.Google Scholar
  10. Laruelle, A., & Valenciano, F. (2008b). Voting and collective decision making: Bargaining and power. Cambridge: Cambridge University Press.Google Scholar
  11. Montero, M. (2006). Noncooperative foundations of the nucleolus in majority games. Games and Economic Behavior, 54, 380–397.CrossRefGoogle Scholar
  12. Pérez-Castrillo, D., & Wettstein, D. (2001). Bidding for the surplus: A non-cooperative approach to the Shapley value. Journal of Economic Theory, 100, 274–294.CrossRefGoogle Scholar
  13. Schmeidler, D. (1969). The nucleolus of a characteristic function game. SIAM Journal on Applied Mathematics, 17(6), 1163–1170.CrossRefGoogle Scholar
  14. Shapley, L. (1953). A value for \(n\)-person games. In H. Kuhn & A. Tucker (Eds.), Contributions to the theory of games, II. Vol. 28 of Annals of Mathematical Studies (pp. 307–317). Princeton: Princeton University Press.Google Scholar
  15. Shapley, L., & Shubik, M. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review, 48, 787–792.CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Public Choice Research CentreUniversity of TurkuTurkuFinland
  2. 2.Institute of Socio EconomicsUniversity of HamburgHamburgGermany

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