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

Craig A. Tovey

Mathematical Social Sciences, 2010, vol. 60, issue 3, 178-180

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.

Keywords: Epsilon; core; Algorithm; Spatial; model; Voting (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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