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The almost surely shrinking yolk

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  • Tovey, Craig A.

Abstract

The yolk, defined by McKelvey as the smallest ball intersecting all median hyperplanes, is a key concept in the Euclidean spatial model of voting. Koehler conjectured that the yolk radius of a random sample from a uniform distribution on a square tends to zero. The following sharper and more general results are proved here: Let the population be a random sample from a probability measure [mu] on [real]m. Then the yolk of the sample does not necessarily converge to the yolk of [mu]. However, if [mu] is strictly centered, i.e. the yolk radius of [mu] is zero, then the radius of the sample yolk will converge to zero almost surely, and the center of the sample yolk will converge almost surely to the center of the yolk of [mu]. Moreover, if the yolk radius of [mu] is nonzero, the sample yolk radius will not converge to zero if [mu] contains three non-collinear mass points or if somewhere it has density bounded away from zero in some ball of positive volume. All results hold for both odd and even population sizes.

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  • Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.
    • Handle: RePEc:eee:matsoc:v:59:y:2010:i:1:p:74-87
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    1. Miller, Nicholas R., 2007. "In Search of the Uncovered Set," Political Analysis, Cambridge University Press, vol. 15(1), pages 21-45, January.
    2. 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.
    3. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
    4. Rapoport, Amnon & Golan, Esther, 1985. "Assessment of Political Power in the Israeli Knesset," American Political Science Review, Cambridge University Press, vol. 79(3), pages 673-692, September.
    5. 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.
    6. 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.
    7. 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.
    8. Sang Ahn & Colin Cooper & Gérard Cornuéjols & Alan Frieze, 1988. "Probabilistic Analysis of a Relaxation for the k -Median Problem," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 1-31, February.
    9. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401.
    10. Gordon Tullock, 1967. "The General Irrelevance of the General Impossibility Theorem," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 81(2), pages 256-270.
    11. Norman Schofield, 1978. "Instability of Simple Dynamic Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(3), pages 575-594.
    12. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    13. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    14. Scott Feld & Bernard Grofman & Nicholas Miller, 1988. "Centripetal forces in spatial voting: On the size of the Yolk," Public Choice, Springer, vol. 59(1), pages 37-50, October.
    15. 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.
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    1. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.

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