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

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.

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Informasi Detail

Judul Seri

MATHEMATICS OF OPERATIONS RESEARCH; Vol.46 No.2 May 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 811-833

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

GRAPHS
PROBABILISTIC RULES
UNANIMITY
SINGLE-PEAKED PREFERENCES
STRATEGY-PROOFNESS
BLOCK TREES

Info Detail Spesifik

-

Pernyataan Tanggungjawab

Hans Peters, Souvik Roy, Soumyarup Sadhukhan

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