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

Article Type

Research Article

Publication Title

Mathematics of Operations Research

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.

First Page

811

Last Page

833

DOI

10.1287/moor.2020.1089

Publication Date

5-1-2021

Comments

Open Access, Green

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