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Social Choice and Welfare

, Volume 41, Issue 3, pp 489–535 | Cite as

Uncovered sets

  • John Duggan
Original Paper

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 concepts that bound existing 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, and I define the minimal generalized covering solution, a nonempty refinement of the deep uncovered set that employs both of the new relations.

Keywords

Nonempty Intersection External Stability Mixed Strategy Equilibrium Deep Covering Shallow Covering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Political Science and Department of EconomicsUniversity of RochesterRochesterUSA

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