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Generic Existence of Local Political Equilibrium

  • Norman Schofield

Abstract

The paper presents a model of multi-party, “spatial” competition under proportional rule with both electoral and coalitional risk. Each party consists of a set of delegates with heterogeneous policy preferences. These delegates choose one delegate as leader or agent. This agent announces the policy declaration (or manifesto) to the electorate prior to the election. The choice of the agent by each party elite is assumed to be a local Nash equilibrium to a game form \( \tilde g\). This game form encapsulates beliefs of the party elite about the nature of both electoral risk and the post-election coalition bargaining game. It is demonstrated, under the assumption that \( \tilde g\) is smooth, that, for almost all parameter values, a locally isolated, local Nash equilibrium exists.

Keywords

Nash Equilibrium Social Choice Vote Rule Game Form Coalition Structure 
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References

  1. 1.
    D. Austen-Smith and J. Banks, Elections, Coalitions and Legislative Outcomes, American Political Science Review, 82, 1988, 405–522.CrossRefGoogle Scholar
  2. 2.
    D. Austen-Smith and J. Banks (1998), Social Choice Theory, Game Theory, and Positive Political Theory, Annual Review of Political Science 1, 1998, 259–287.CrossRefGoogle Scholar
  3. 3.
    J. Banks, A Model of Electoral Competition with Incomplete Information, Journal of Economic Theory, 50, 1990, 309–325.CrossRefGoogle Scholar
  4. 4.
    J Banks, Singularity Theory and Core Existence in the Spatial Model, Journal of Mathematical Economics, 24, 1995, 523–536.CrossRefGoogle Scholar
  5. 5.
    J. Banks and J. Duggan, Stationary Equilibria in a Bargaining Model of Social Choice, Unpublished Typescript: University of Rochester, 1998.Google Scholar
  6. 6.
    J. Banks, J. Duggan and M. Le Breton, The Spatial Model of Elections with Arbitrary Distributions of Voters, Unpublished Typescript: University of Rochester, 1998.Google Scholar
  7. 7.
    J. Banks, J Duggan and M. Le Breton, Bounds for Mixed Strategy Equilibria and a Spatial Model of Elections, Typescript: University of Rochester 1998. Journal of Economic Theory (forthcoming).Google Scholar
  8. 8.
    R. Calvert, Robustness of the Multidimensional Voting Model: Candidates, Motivations, Uncertainty and Convergence, American Journal of Political Science 29, 1985, 69–85.CrossRefGoogle Scholar
  9. 9.
    S. Chib and E. Greenberg, Markov Chain Monte Carlo Simulation Methods in Econometrics, Econometric Theory 12, 1996, 409–431.CrossRefGoogle Scholar
  10. 10.
    G. Cox, An Expected-Utility Model of Electoral Competition, Quality and Quantity 18, 1984, 337–349.CrossRefGoogle Scholar
  11. 11.
    G. Cox, The Uncovered Set and the Core, American Journal of Political Science, 31, 1987, 408–22.CrossRefGoogle Scholar
  12. 12.
    G. Cox, Centripetal and Centrifugal Incentives in Electoral Systems, American Journal of Political Science, 34, 1990, 903–945.CrossRefGoogle Scholar
  13. 13.
    E. Dierker, Topological Methods in Walrasian Economics, Heidelberg, Springer, 1974.CrossRefGoogle Scholar
  14. 14.
    A. Downs, An Economic Theory of Democracy, New York, Harper and Row, 1957.Google Scholar
  15. 15.
    I. L. Glicksberg, A Further Generalization of the Kakutani Fixed Point Theorem with an Application to Nash Equilibrium Points, Proceedings of the American Mathematical Society, 38, 1952, 170–174.Google Scholar
  16. 16.
    M. Golubitsky and V. Guillemin, Stable Mappings and their Singularities, Heidelberg, Springer, 1973.CrossRefGoogle Scholar
  17. 17.
    M. Hirsch, Differential Topology, Heidelberg, Springer, 1976.CrossRefGoogle Scholar
  18. 18.
    M. Laver, Models of Government Formation, Annual Review of Political Science, 1, 1998, 1–25.CrossRefGoogle Scholar
  19. 19.
    M. Laver and N. Schofield, Multiparty Governments, The Politics of Coalition in Europe, Oxford, Oxford University Press, 1990. Reprinted, Michigan University Press, 1998.Google Scholar
  20. 20.
    R. McKelvey, Covering, Dominance and Institution-Free Properties of Social Choice, American Journal of Political Science, 30, 1986, 283–314.CrossRefGoogle Scholar
  21. 21.
    E. Michael, Continuous Selections I, Annals of Mathematics, 63, 1956, 361–382.CrossRefGoogle Scholar
  22. 22.
    N. Miller, A New Solution Set for Tournaments and Majority Voting, Further Graph-theoretic Approaches to the Theory of Voting, American Journal of Political Science, 24, 1980, 68–96.CrossRefGoogle Scholar
  23. 23.
    J. Milnor, Morse Theory, Princeton, Princeton University Press, 1963.Google Scholar
  24. 24.
    K. R. Paxthasathy, Probability Measures on Metric Spaces, New York, Academic Press, 1967.Google Scholar
  25. 25.
    W. H. Riker, The Theory of Political Coalitions, New Haven, Yale University Press.Google Scholar
  26. 26.
    N. Schofield, Social Choice and Democracy, Heidelberg, Springer 1985.CrossRefGoogle Scholar
  27. 27.
    N. Schofield, Political Competition and Multiparty Coalition Governments, European Journal of Political Research, 23, 1993, 1–33.CrossRefGoogle Scholar
  28. 28.
    N. Schofield, Party Competition in a Spatial Model of Voting, in W. Barnett, M. Hinich and N. Schofield (eds.), Political Economy: Institutions, Competition and Prepresentation, Cambridge, Cambridge University Press 1993.Google Scholar
  29. 29.
    N. Schofield, in Existence of a Smooth Social Choice Functor, W. Barnett, H. Moulin, N. Schofield, and M. Salles (eds.), Social Choice, Welfare and Ethics, Cambridge, Cambridge University Press 1995.Google Scholar
  30. 30.
    N. Schofield, Coalition Politics: A Formal Model and Empirical Analysis, Journal of Theoretical Politics, 7, 1995, 245–281.CrossRefGoogle Scholar
  31. 31.
    N. Schofield, The C1-topology on the Space of Smooth Preference Profiles, Social Choice and Welfare, 16, 1999, 347–373.CrossRefGoogle Scholar
  32. 32.
    N. Schofield, A Smooth Social Choice Method of Preference Aggregation, in M. Wooders (ed.), New Directions in the Theory of Markets and Games, Toronto: Fields Institute for the American Mathematics Society, 1999.Google Scholar
  33. 33.
    N. Schofield, The Heart and the Uncovered Set, Journal of Economics, Zeitschift fur Nationaloconomie, Supplement 8, 1999, 79–113.Google Scholar
  34. 34.
    N. Schofield, A. Martin, K. Quinn and A. Whitford, Multiparty Electoral Competition in the Netherlands and Germany: A Model based on Multinomial Pro-bit, Public Choice, 97, 1998, 257–293.CrossRefGoogle Scholar
  35. 35.
    N. Schofield and A. Parks, Nash Equilibrium in a Spatial Model of Coalition Bargaining, Mathematical Social Sciences, 39, 2000, 133–174.CrossRefGoogle Scholar
  36. 36.
    I. Sened, A Model of Coalition Formation: Theory and Evidence, Journal of Politics 58, 1996, 350–372.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Norman Schofield
    • 1
  1. 1.Center in Political EconomyWashington UniversitySt. LouisUSA

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