## Abstract

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.

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 language | English |
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Journal | Mathematics of Operations Research |

Early online date | 11 Mar 2021 |

DOIs | |

Publication status | E-pub ahead of print - 11 Mar 2021 |

## JEL classifications

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

## Keywords

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