Social Choice and Welfare

, Volume 46, Issue 1, pp 81–91 | Cite as

A note on the McKelvey uncovered set and Pareto optimality

  • Felix Brandt
  • Christian Geist
  • Paul Harrenstein
Original Paper


We consider the notion of Pareto optimality under the assumption that only the pairwise majority relation is known and show that the set of necessarily Pareto optimal alternatives coincides with the McKelvey uncovered set. As a consequence, the McKelvey uncovered set constitutes the coarsest Pareto optimal majoritarian social choice function. Moreover, every majority relation is induced by a preference profile in which the uncovered alternatives precisely coincide with the Pareto optimal ones. We furthermore discuss the structure of the McKelvey covering relation and the McKelvey uncovered set.


Pareto Optimality Covering Relation Social Choice Function Condorcet Winner Preference Profile 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Felix Brandt
    • 1
  • Christian Geist
    • 1
  • Paul Harrenstein
    • 2
  1. 1.Technische Universität MünchenMunichGermany
  2. 2.University of OxfordOxfordUK

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