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The “probability of a fit choice”

  • Norman Schofield

    ()

This paper attempts to model elections by incorporating voter judgments about candidate and leader competence. The proposed model can be linked to Madison’s understanding of the nature of the choice of Chief Magistrate (Madison, James Madison: writings. The Library of America, New York, 1999 [1787]) and Condorcet’s work on the so-called “Jury Theorem” (Condorcet 1994 [1785]). Electoral models use the notion of a Nash Equilibrium. This notion generally depends on a fixed point argument. For deterministic electoral models, there will typically be no equilibrium. Instead we introduce the idea of a preference field, $$H,$$ for the society. A condition called half-openess of $$H$$ is sufficient to guarantee existence of a local direction gradient, $$d,$$ Even when $$d$$ is not well-defined we can use the idea of the heart for the society. This is an attractor of the set of social moves that can occur. As an application, a stochastic model of elections is considered, and applied to the 2008 presidential election in the United States. In such a stochastic model the electoral origin will satisfy the first order condition for a local Nash equilibrium. We then show how to compute the Hessian of each candidate’s vote share function, and obtain necessary and sufficient conditions for convergence to the electoral origin, suggesting that there will be a social direction gradient. The origin maximizes aggregrate voter utility and can be interpreted as a fit choice for the polity. Copyright Springer-Verlag Berlin Heidelberg 2013

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Article provided by Springer in its journal Review of Economic Design.

Volume (Year): 17 (2013)
Issue (Month): 2 (June)
Pages: 129-150

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Handle: RePEc:spr:reecde:v:17:y:2013:i:2:p:129-150
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  2. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
  3. Smale, S., 1974. "Global analysis and economics IIA : Extension of a theorem of Debreu," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 1-14, March.
  4. Schofield, Norman, 1984. "Social equilibrium and cycles on compact sets," Journal of Economic Theory, Elsevier, vol. 33(1), pages 59-71, June.
  5. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
  6. Chichilnisky, G., 1993. "Intersecting Families of Sets and the Topology of Cones in Economics," Papers 93-17, Columbia - Graduate School of Business.
  7. Schofield, Norman, 1978. "Instability of Simple Dynamic Games," Review of Economic Studies, Wiley Blackwell, vol. 45(3), pages 575-94, October.
  8. Schofield, Norman., . "Classification Theorem for Smooth Social Choice," Working Papers 514, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. Aliprantis, Charalambos D. & Brown, D. J., 1982. "Equilibrium in Markets with a Riesz Space of Commodities," Working Papers 427, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  11. Norman Schofield & Christopher Claassen & Ugur Ozdemir & Alexei Zakharov, 2011. "Estimating the effects of activists in two-party and multi-party systems: comparing the United States and Israel," Social Choice and Welfare, Springer, vol. 36(3), pages 483-518, April.
  12. Norman Schofield, 2007. "The Mean Voter Theorem: Necessary and Sufficient Conditions for Convergent Equilibrium," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 965-980.
  13. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
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  17. Norman Schofield, 2010. "Social orders," Social Choice and Welfare, Springer, vol. 34(3), pages 503-536, March.
  18. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
  19. Schofield, Norman, 1983. "Generic Instability of Majority Rule," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 695-705, October.
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  21. Borglin, Anders & Keiding, Hans, 1976. "Existence of equilibrium actions and of equilibrium : A note on the `new' existence theorems," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 313-316, December.
  22. Graciela Chichilnisky, 1996. "Markets And Games: A Simple Equivalence Among The Core, Equilibrium And Limited Arbitrage," Metroeconomica, Wiley Blackwell, vol. 47(3), pages 266-280, October.
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  24. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
  25. McKelvey, Richard D. & Schofield, Norman., 1985. "Generalized Symmetry Conditions at a Core Point," Working Papers 552, California Institute of Technology, Division of the Humanities and Social Sciences.
  26. Patty, John W. & Snyder, James M. & Ting, Michael M., 2009. "Two's Company, Three's an Equilibrium: Strategic Voting and Multicandidate Elections," Quarterly Journal of Political Science, now publishers, vol. 4(3), pages 251-278, October.
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  28. Arrow, Kenneth J, 1986. "Rationality of Self and Others in an Economic System," The Journal of Business, University of Chicago Press, vol. 59(4), pages S385-99, October.
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  30. Schofield, N. & Tovey, C.A., 1992. "Probability and Convergence for Supramajority rule with Euclidean Preferences," Papers 163, Washington St. Louis - School of Business and Political Economy.
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