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

Hans Peters, Souvik Roy, Soumyarup Sadhukhan

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Abstract

Finitely many agents have preferences on a finite set of alternatives, single-peaked with respect to a connected graph with these alternatives as vertices. A probabilistic rule assigns to each preference profile a probability distribution over the alternatives. 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 at which all peaks are on leaves 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 leaves. Finally, the two results are combined to obtain a general characterization for every connected graph by using its block tree representation.

Original languageEnglish
Pages (from-to)811-833
Number of pages23
JournalMathematics of Operations Research
Volume46
Issue number2
Early online date11 Mar 2021
DOIs
Publication statusPublished - May 2021

JEL classifications

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

Keywords

  • Probabilistic rules
  • Single-peaked preferences.
  • graphs
  • strategy-proofness
  • unanimity
  • probabilistic rules
  • single-peaked preferences
  • block trees
  • SOCIAL CHOICE
  • SCHEMES

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