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Szegedy and Xu, extending earlier work of Dokow and Holzman, extended this to predicates over arbitrary finite alphabets. Mossel extended Arrow\u2019s 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 and Holzman and of Szegedy and Xu to the setting of Mossel. As an application, we determine, for each symmetric predicate over [Formula: see text], all of its aggregators.<\/jats:p>","DOI":"10.1137\/25m1748901","type":"journal-article","created":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:54:31Z","timestamp":1777535671000},"page":"652-674","source":"Crossref","is-referenced-by-count":0,"title":["Aggregation of Evaluations without Unanimity"],"prefix":"10.1137","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1739-0872","authenticated-orcid":true,"given":"Yuval","family":"Filmus","sequence":"first","affiliation":[{"name":"Taub Faculty of Computer Science and Faculty of Mathematics, Technion\u2014Israel Institute of Technology, Haifa, Israel."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,4,30]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1086\/256963"},{"key":"ref2","volume-title":"Social Choice and Individual Values","author":"Arrow K. 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