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Hidden Mathematical Structures of Voting

In: Mathematics and Democracy

Author

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  • Donald G. Saari

    (University of California)

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.

Suggested Citation

  • Donald G. Saari, 2006. "Hidden Mathematical Structures of Voting," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 221-234, Springer.
    • Handle: RePEc:spr:stcchp:978-3-540-35605-9_16
    DOI: 10.1007/3-540-35605-3_16
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    Cited by:

    1. McKelvey, Richard & Tovey, Craig A., 2010. "Approximation of the yolk by the LP yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 102-109, January.

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