A finite exact algorithm for epsilon-core membership in two dimensions
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.
Year of publication: |
2010
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Authors: | Tovey, Craig A. |
Published in: |
Mathematical Social Sciences. - Elsevier, ISSN 0165-4896. - Vol. 60.2010, 3, p. 178-180
|
Publisher: |
Elsevier |
Keywords: | Epsilon core Algorithm Spatial model Voting |
Saved in:
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