Deborah E. Berg, Serguei Norine, Francis Edward Su, Robin Thomas, Paul Wollan
Published 2008-11-20Version 1
When can a majority of voters find common ground, that is, a position they all agree upon? How does the shape of the political spectrum influence the outcome? When mathematical objects have a social interpretation, the associated theorems have social applications. In this article we give examples of situations where sets model preferences and develop extensions of classical theorems about convex sets, such as Helly's theorem, that can be used in the analysis of voting in "agreeable" societies.
Comments: 13 pages, 8 figures; to appear, Amer. Math. Monthly. Related work at http://www.math.hmc.edu/~su/papers.html
Journal: Amer. Math. Monthly 117 (2010), pp 27-39
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Intersection patterns of convex sets via simplicial complexes, a survey
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