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Condorcet Domains: A Geometric Perspective

In: The Mathematics of Preference, Choice and Order

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  • Donald G. Saari

    (University of California)

Abstract

One of the several topics in which Fishburn (1997, 2002) has made basic contributions involves finding maximal Condorcet Domains. In this current paper, I introduce a geometric approach that identifies all such domains and, at least for four and five alternatives, captures Fishburn's clever alternating scheme (described below), which has advanced our understanding of the area. To explain “Condorcet Domains” and why they are of interest, start with the fact that when making decisions by comparing pairs of alternatives with majority votes, the hope is to have decisive outcomes where one candidate always is victorious when compared with any other candidate. Such a candidate is called the Condorcet winner. The attractiveness of this notion, where someone beats everyone else in head-to-head comparisons, is why the Condorcet winner remains a central concept in voting theory. For a comprehensive, modern description of the Condorcet solution concept, see Gehrlein's recent book (2006).

Suggested Citation

  • Donald G. Saari, 2009. "Condorcet Domains: A Geometric Perspective," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 161-182, Springer.
    • Handle: RePEc:spr:stcchp:978-3-540-79128-7_9
    DOI: 10.1007/978-3-540-79128-7_9
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    Cited by:

    1. Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.

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