Uncovered Sets

John Duggan ()
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John Duggan: W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158, http://www.johnduggan.net/

No WP63, Wallis Working Papers from University of Rochester - Wallis Institute of Political Economy

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.

Pages: 56 pages
Date: 2011-05
New Economics Papers: this item is included in nep-cdm and nep-gth
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Citations: View citations in EconPapers (8)

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