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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- Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2013. "Computing tournament solutions using relation algebra and RelView," European Journal of Operational Research, Elsevier, vol. 226(3), pages 636-645.
- Rudolf Berghammer & Agnieszka Rusinowska & Harrie de Swart, 2011. "Computing Tournament Solutions using Relation Algebra and REL VIEW," Documents de travail du Centre d'Economie de la Sorbonne 11067, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- repec:hal:wpaper:hal-00756696 is not listed on IDEAS
- repec:hal:journl:halshs-00639942 is not listed on IDEAS
- 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.
- 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.
- repec:hal:cesptp:hal-00756696 is not listed on IDEAS
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