## Abstract

In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked domain on a tree if and only if it is the pairwise majority rule (also known as the tree-median rule) and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even.

Original language | English |
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Pages (from-to) | 313-336 |

Number of pages | 24 |

Journal | Theory and Decision |

Volume | 91 |

Issue number | 3 |

Early online date | 26 Mar 2021 |

DOIs | |

Publication status | Published - Oct 2021 |

## Keywords

- Pairwise majority rule
- Single-peaked domains on trees
- Unanimity
- Anonymity
- Group strategy-proofness
- Strategy-proofness