Aggregation of evaluations without unanimity

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Detalles Bibliográficos
Autor principal:	Filmus, Yuval
Formato:	Preprint
Publicado:	2025
Materias:	Combinatorics Discrete Mathematics Logic
Acceso en línea:	Acceder al recurso
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author	Filmus, Yuval
author_facet	Filmus, Yuval
contents	Dokow and Holzman determined which predicates over $\{0, 1\}$ satisfy an analog of Arrow's theorem: all unanimous aggregators are dictatorial. Szegedy and Xu, extending earlier work of Dokow and Holzman, extended this to predicates over arbitrary finite alphabets. Mossel extended Arrow's theorem in an orthogonal direction, determining all aggregators without the assumption of unanimity. We bring together both threads of research by extending the results of Dokow-Holzman and Szegedy-Xu to the setting of Mossel. As an application, we determine, for each symmetric predicate over $\{0,1\}$, all of its aggregators.
format	Preprint
id	arxiv_https___arxiv_org_abs_2502_20428
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Aggregation of evaluations without unanimity Filmus, Yuval Combinatorics Discrete Mathematics Logic Dokow and Holzman determined which predicates over $\{0, 1\}$ satisfy an analog of Arrow's theorem: all unanimous aggregators are dictatorial. Szegedy and Xu, extending earlier work of Dokow and Holzman, extended this to predicates over arbitrary finite alphabets. Mossel extended Arrow's theorem in an orthogonal direction, determining all aggregators without the assumption of unanimity. We bring together both threads of research by extending the results of Dokow-Holzman and Szegedy-Xu to the setting of Mossel. As an application, we determine, for each symmetric predicate over $\{0,1\}$, all of its aggregators.
title	Aggregation of evaluations without unanimity
topic	Combinatorics Discrete Mathematics Logic
url	https://arxiv.org/abs/2502.20428

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