Social Choice and Welfare

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

Uncovered sets

  • John Duggan
Original Paper


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.


Nonempty Intersection External Stability Mixed Strategy Equilibrium Deep Covering Shallow Covering 
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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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