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Approximation of the yolk by the LP yolk

Author

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  • McKelvey, Richard
  • Tovey, Craig A.

Abstract

If n points are sampled independently from an absolutely continuous distribution with support a convex subset of [real]2, then the center and radius of the ball determined by the bounding median lines (the LP yolk) converge with probability one to the center and radius of the yolk. The linear program of McKelvey (1986) is therefore an effective heuristic for computing the yolk in large samples. This result partially explains the results of numerical experiments in Koehler (1992), where the bounding median lines always produced a radius within 2% of the yolk radius.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matsoc:v:59:y:2010:i:1:p:102-109
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    References listed on IDEAS

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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. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    3. 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.
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    Cited by:

    1. Tovey, Craig A., 2010. "A finite exact algorithm for epsilon-core membership in two dimensions," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 178-180, November.

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