Unanimous and strategy-proof probabilistic rules for single-peaked preference profiles on graphs

Hans Peters, Souvik Roy, Soumyarup Sadhukhan

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Finitely many agents have single-peaked preferences on a finite set of alternatives structured by a connected graph. First, all unanimous and strategy-proof probabilistic rules are characterized when the graph is a tree. These rules are uniquely determined by their outcomes at those preference profiles where all peaks are on leafs of the tree, and thus extend the known case of a line graph. Second, it is shown that every unanimous
and strategy-proof probabilistic rule is random dictatorial if and only if the graph has no leafs. Finally, the two results are combined to obtain a general characterization for
every connected graph.
Original languageEnglish
JournalMathematics of Operations Research
Early online date11 Mar 2021
Publication statusE-pub ahead of print - 11 Mar 2021

JEL classifications

  • d71 - "Social Choice; Clubs; Committees; Associations"


  • Probabilistic rules
  • unanimity
  • Single-peaked preferences.
  • strategy-proofness
  • graphs

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