AbstractThis 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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Bibliographic InfoPaper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP63.
Length: 56 pages
Date of creation: May 2011
Date of revision:
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Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-29 (All new papers)
- NEP-CDM-2011-08-29 (Collective Decision-Making)
- NEP-GTH-2011-08-29 (Game Theory)
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- repec:hal:journl:halshs-00639942 is not listed on IDEAS
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