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A critique of distributional analysis in the spatial model

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  • Tovey, Craig A.
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    Abstract

    Distributional analysis is widely used to study social choice in Euclidean models ([35], [36], [1], [5], [11], [19], [7] and [4], e.g). This method assumes a continuum of voters distributed according to a probability measure. Since infinite populations do not exist, the goal of distributional analysis is to give an insight into the behavior of large finite populations. However, the properties of finite populations do not necessarily converge to the properties of infinite populations. Thus the method of distributional analysis is flawed. In some cases (Arrow, 1969) it will predict that a point is in the core with probability 1, while the true probability converges to 0. In other cases it can be combined with probabilistic analysis to make accurate predictions about the asymptotic behavior of large populations, as in Caplin and Nalebuff (1988). Uniform convergence of empirical measures (Pollard, 1984) is employed here to yield a simpler, more general proof of [alpha]-majority convergence, a short proof of yolk shrinkage, and suggests a rule of thumb to determine the accuracy of distribution-based predictions. The results also help clarify the mathematical underpinnings of statistical analysis of empirical voting data.

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    Bibliographic Info

    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 59 (2010)
    Issue (Month): 1 (January)
    Pages: 88-101

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    Handle: RePEc:eee:matsoc:v:59:y:2010:i:1:p:88-101

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    Web page: http://www.elsevier.com/locate/inca/505565

    Related research

    Keywords: Probability Euclidean preference Voting Minimax Convergence Yolk;

    References

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    1. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    2. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    3. Gordon Tullock, 1981. "Why so much stability," Public Choice, Springer, vol. 37(2), pages 189-204, January.
    4. Schofield, Norman, 1978. "Instability of Simple Dynamic Games," Review of Economic Studies, Wiley Blackwell, vol. 45(3), pages 575-94, October.
    5. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    6. Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003. "Social Choice and Electoral Competition in the General Spatial Model," IDEI Working Papers 188, Institut d'Économie Industrielle (IDEI), Toulouse.
    7. Schofield, Norman, 1983. "Generic Instability of Majority Rule," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 695-705, October.
    8. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
    9. Demange, Gabrielle, 1982. "A limit theorem on the minmax set," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 145-164, January.
    10. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-57, January.
    11. 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.
    12. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May.
    13. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    14. 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.
    15. Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.
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    Cited by:
    1. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    2. McKelvey, Richard & Tovey, Craig A., 2010. "Approximation of the yolk by the LP yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 102-109, January.
    3. Sadiraj, Vjollca & Tuinstra, Jan & van Winden, Frans, 2010. "Identification of voters with interest groups improves the electoral chances of the challenger," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 210-216, November.
    4. Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.

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