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We provide the functional form for each of the classes we consider. This functional form is a characterization that explicitly describes how a social choice function of that particular class selects the collective choice corresponding to a profile. We provide a unified formulation of these characterizations using the new concept of \u201ccharacter\u201d. The choice of the character, depending on the class of social choice functions, gives the functional form of all social choice functions of the class.<\/jats:p>","DOI":"10.1007\/s00355-024-01546-x","type":"journal-article","created":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T15:02:49Z","timestamp":1725375769000},"page":"529-555","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The character of non-manipulable collective choices between two alternatives"],"prefix":"10.1007","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0264-7743","authenticated-orcid":false,"given":"Achille","family":"Basile","sequence":"first","affiliation":[]},{"given":"K. P. S. 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