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A finite exact algorithm for epsilon-core membership in two dimensions

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  • Tovey, Craig A.

Abstract

Given a set V of voter ideal points in the plane, a point x is in the epsilon core if for any other point y, x is within epsilon of being as close as y is to at least half the voters in V. The idea is that under majority rule x cannot be dislodged by any other point y if x is given an advantage of epsilon. This paper provides a finite algorithm, given V,x, and epsilon, to determine whether x is in the epsilon core. By bisection search, this yields a convergent algorithm, given V and x, to compute the least epsilon for which x is in the epsilon core. We prove by example that the epsilon core is in general not connected because the least epsilon function has multiple local minima.

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  • 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.
    • Handle: RePEc:eee:matsoc:v:60:y:2010:i:3:p:178-180
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    Cited by:

    1. Robi Ragan, 2015. "Computational social choice," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 5, pages 67-80, Edward Elgar Publishing.
    2. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2016. "On the uniqueness of the yolk," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 511-518, October.

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