Condorcet Consistency and the strong no show paradoxes

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We consider voting correspondences that are, besides
Condorcet Consistent, immune against the two strong no show
paradoxes. That is, it cannot happen that if an additional voter
ranks a winning alternative on top then that alternative becomes
loosing, and that if an additional voter ranks a loosing
alternative at bottom then that alternative becomes winning. This
immunity is called the Top Property in the first case and the
Bottom Property in the second case. We establish the voting
correspondence satisfying Condorcet Consistency and the Top
Property, which is maximal in the following strong sense: it is the union of all smaller voting correspondences with these two properties. The result remains true if we add the Bottom Property but not if we replace the Top Property by the Bottom Property. This voting correspondence contains the Minimax Rule but it is
strictly larger. In particular, voting functions (single-valued voting correspondences) that are Condorcet Consistent and immune against the two paradoxes must select from this maximal correspondence, and we demonstrate several ways in which this can or cannot be done.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
Publication statusPublished - 25 Jun 2017

Publication series

SeriesGSBE Research Memoranda

JEL classifications

  • d71 - "Social Choice; Clubs; Committees; Associations"
  • d72 - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior


  • Condorcet Consistency
  • strong no show paradoxes
  • Minimax Rule

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