Hidden Mathematical Structures of Voting

Donald G. Saari
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Donald G. Saari: University of California

A chapter in Mathematics and Democracy, 2006, pp 221-234 from Springer

Abstract: Abstract The complexities of voting theory are captured by Arrow’s Impossibility Theorem and McKelvey’s chaos result in spatial voting. A careful analysis of Arrow’s theorem, however, proves that not all of the supplied information is used by the decision rule. As such, not only does this seminal result admit a benign interpretation, but there are several ways to sidestep Arrow’s negative conclusion. McKelvey’s result is described in terms of more general voting rules. Then a new solution concept, called the ‘finesse point’, is introduced. This centrally located point generalizes the core and minimizes what it takes to respond to any proposal by another person.

Keywords: Arrow’s theorem; spatial voting; majority vote; chaos theorem; core; finesse point (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/3-540-35605-3_16

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