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Uncovered Sets

  • John Duggan


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

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

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    1. Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1997. "Condorcet choice correspondences for weak tournaments," Working Papers. Serie AD 1997-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    2. 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.
    3. 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.
    4. 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.
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