Social Choice and Welfare

, Volume 28, Issue 3, pp 491–506 | Cite as

A systematic approach to the construction of non-empty choice sets

  • John Duggan
Original Paper


Suppose a strict preference relation fails to possess maximal elements, so that a choice is not clearly defined. I propose to delete particular instances of strict preferences until the resulting relation satisfies one of a number of known regularity properties (transitivity, acyclicity, or negative transitivity), and to unify the choices generated by different orders of deletion. Removal of strict preferences until the subrelation is transitive yields a new solution with close connections to the “uncovered set” from the political science literature and the literature on tournaments. Weakening transitivity to acyclicity yields a new solution nested between the strong and weak top cycle sets. When the original preference relation admits no indifferences, this solution coincides with the familiar top cycle set. The set of alternatives generated by the restriction of negative transitivity is equivalent to the weak top cycle set.


Maximal Element Strict Preference Mixed Strategy Equilibrium Political Science Literature Sophisticated Vote 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Political Science and Department of EconomicsUniversity of RochesterRochesterUSA
  2. 2.W. Allen Wallis Institute of Political EconomyUniversity of RochesterRochesterUSA

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