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General Conditions for Existence of Maximal Elements via the Uncovered Set

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  • John Duggan

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    (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158)

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    Abstract

    This paper disentangles the topological assumptions of classical results (e.g., Walker (1977)) on existence of maximal elements from rationality conditions. It is known from the social choice literature that under the standard topological conditions-with no other restrictions on preferences-there is an element such that the upper section of strict preference at that element is minimal in terms of set inclusion, i.e., the uncovered set is non-empty. Adding a condition that weakens known acyclicity and convexity assumptions, each such uncovered alternative is indeed maximal. A corollary is a result that weakens the semi-convexity condition of Yannelis and Prabhakar (1983).

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    Bibliographic Info

    Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 563.

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    Length: 9 pages
    Date of creation: Jul 2011
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    Handle: RePEc:roc:rocher:563

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    Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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    1. Alcantud, Jose C.R., 2006. "Maximality with or without binariness: Transfer-type characterizations," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 182-191, March.
    2. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    3. Donald J. Brown, 1973. "Acyclic Choice," Cowles Foundation Discussion Papers 360, Cowles Foundation for Research in Economics, Yale University.
    4. J.C. R. Alcantud, 2002. "Characterization of the existence of maximal elements of acyclic relations," Economic Theory, Springer, vol. 19(2), pages 407-416.
    5. Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
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