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Abstention Causes Bifurcations in Two-Party Voting Dynamics

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  • Bärbel M. R. Stadler

Abstract

In a recent dynamical systems model of platform adaptation in spatial voting models, Miller and Stadler showed that, assuming concave voter utility functions and complete participation, there is a globally stable equilibrium located at the mean voter position. Here we show that abstention depending on the distances between voters and platforms may lead to bifurcations rendering the mean voter equilibrium unstable. We find up to seven equilibria, up to four of which are local attractors for the platform dynamics.

Suggested Citation

  • Bärbel M. R. Stadler, 1998. "Abstention Causes Bifurcations in Two-Party Voting Dynamics," Working Papers 98-08-072, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:98-08-072
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    References listed on IDEAS

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    1. A. Smithies, 1941. "Optimum Location in Spatial Competition," Journal of Political Economy, University of Chicago Press, vol. 49(3), pages 423-423.
    2. Kollman, Ken & Miller, John H. & Page, Scott E., 1998. "Political Parties and Electoral Landscapes," British Journal of Political Science, Cambridge University Press, vol. 28(1), pages 139-158, January.
    3. Larry Samuelson, 1984. "Electoral equilibria with restricted strategies," Public Choice, Springer, vol. 43(3), pages 307-327, January.
    4. McKelvey, Richard D. & Ordeshook, Peter C., 1976. "Symmetric Spatial Games Without Majority Rule Equilibria," American Political Science Review, Cambridge University Press, vol. 70(4), pages 1172-1184, December.
    5. Kollman, Ken & Miller, John H. & Page, Scott E., 1992. "Adaptive Parties in Spatial Elections," American Political Science Review, Cambridge University Press, vol. 86(4), pages 929-937, December.
    6. Kramer, Gerald H, 1973. "On a Class of Equilibrium Conditions for Majority Rule," Econometrica, Econometric Society, vol. 41(2), pages 285-297, March.
    7. Axelrod, Robert & Bennett, D. Scott, 1993. "A Landscape Theory of Aggregation," British Journal of Political Science, Cambridge University Press, vol. 23(2), pages 211-233, April.
    8. Kollman, Ken & Miller, John H. & Page, Scott E., 1997. "Landscape formation in a spatial voting model," Economics Letters, Elsevier, vol. 55(1), pages 121-130, August.
    9. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-157, January.
    10. Axelrod, Robert, 1986. "An Evolutionary Approach to Norms," American Political Science Review, Cambridge University Press, vol. 80(4), pages 1095-1111, December.
    11. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    12. Miller, J. H. & Stadler, P. F., 1998. "The dynamics of locally adaptive parties under spatial voting," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 171-189, September.
    13. Enelow,James M. & Hinich,Melvin J., 1984. "The Spatial Theory of Voting," Cambridge Books, Cambridge University Press, number 9780521275156, January.
    14. John S. Irons, 1997. "Voter Turnout, Ideological Candidates, and Platforms Setting with Non-Quadratic Preferences," Research in Economics 97-06-053e, Santa Fe Institute.
    15. Coughlin, Peter & Nitzan, Shmuel, 1981. "Directional and local electoral equilibria with probabilistic voting," Journal of Economic Theory, Elsevier, vol. 24(2), pages 226-239, April.
    16. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
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