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Uncovered Sets

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  • John Duggan

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

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    Abstract

    This paper covers the theory of the uncovered set used in the literatures on tournaments and spatial voting. I discern three main extant definitions, and I introduce two new concepts that bound exist- ing sets from above and below: the deep uncovered set and the shallow uncovered set. In a general topological setting, I provide relationships to other solutions and give results on existence and external stability for all of the covering concepts, and I establish continuity properties of the two new uncovered sets. Of note, I characterize each of the uncovered sets in terms of a decomposition into choices from externally stable sets; I define the minimal generalized covering solution, a nonempty refinement of the deep uncovered set that employs both of the new relations; and I define the acyclic Banks set, a nonempty generalization of the Banks set.

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    File URL: http://www.wallis.rochester.edu/WallisPapers/wallis_63.pdf
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    Bibliographic Info

    Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP63.

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    Length: 56 pages
    Date of creation: May 2011
    Date of revision:
    Handle: RePEc:roc:wallis:wp63

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    Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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    1. 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.
    2. Josep E. Peris & BegoÓa Subiza, 1999. "Condorcet choice correspondences for weak tournaments," Social Choice and Welfare, Springer, vol. 16(2), pages 217-231.
    3. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    4. B. Dutta & J-F. Laslier, 1998. "Comparison functions and choice correspondences," THEMA Working Papers 98-12, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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    Cited by:
    1. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2011. "Computing Tournament Solutions using Relation Algebra and REL VIEW," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639942, HAL.
    2. repec:hal:wpaper:hal-00756696 is not listed on IDEAS
    3. repec:hal:journl:halshs-00639942 is not listed on IDEAS
    4. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2013. "Computing tournament solutions using relation algebra and RelView," PSE - Labex "OSE-Ouvrir la Science Economique" hal-00756696, HAL.
    5. Duggan, John, 2011. "General conditions for the existence of maximal elements via the uncovered set," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 755-759.
    6. repec:hal:cesptp:hal-00756696 is not listed on IDEAS

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