Unanimous and Strategy-Proof Probabilistic Rules for Single-Peaked Preference Profiles on Graphs

Hans Peters, Souvik Roy () and Soumyarup Sadhukhan
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Souvik Roy: Economic Research Unit, Indian Statistical Institute, Kolkata, West Bengal 700108, India

Mathematics of Operations Research, 2021, vol. 46, issue 2, 811-833

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.

Keywords: Primary: 91B14, 91B03, 05C90, Primary: Facilities/equipment planning: stochastic location; games/group decisions: voting, probabilistic rules, unanimity, single-peaked preferences, strategy-proofness, graphs, block trees (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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