A critique of distributional analysis in the spatial model
Distributional analysis is widely used to study social choice in Euclidean models (, , , , , ,  and ,Â 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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Richard D. McKelvey & Richard E. Wendell, 1976. "Voting Equilibria in Multidimensional Choice Spaces," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 144-158, May.
- Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
- Norman Schofield, 1983. "Generic Instability of Majority Rule," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 695-705.
- Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.
- 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.
- Jeffrey S. Banks & John Duggan & Michel LeBreton, "undated". "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Wallis Working Papers WP14, University of Rochester - Wallis Institute of Political Economy.
- Demange, Gabrielle, 1982. "A limit theorem on the minmax set," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 145-164, January.
- Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
- 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.
- Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
- Gordon Tullock, 1981. "Why so much stability," Public Choice, Springer, vol. 37(2), pages 189-204, January.
- Gordon Tullock, 1967. "The General Irrelevance of the General Impossibility Theorem," The Quarterly Journal of Economics, Oxford University Press, vol. 81(2), pages 256-270.
- Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
- Norman Schofield, 1978. "Instability of Simple Dynamic Games," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 575-594.
- Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
- Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)