{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T14:20:30Z","timestamp":1768486830294,"version":"3.49.0"},"reference-count":16,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T00:00:00Z","timestamp":1733702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>Recently, it has been shown that the characterizations of different classes of non-manipulable social choice functions with binary range can be reduced to a common functional form. In the present paper, we investigate the reasons why this happens. We show that all the classes considered share a common mathematical property. We name this property, which is lattice theoretical in nature, isotonicity.<\/jats:p>","DOI":"10.3390\/g15060043","type":"journal-article","created":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T10:11:47Z","timestamp":1733739107000},"page":"43","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Isotone Classes of Social Choice Functions with Binary Range"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0264-7743","authenticated-orcid":false,"given":"Achille","family":"Basile","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze Economiche e Statistiche, Universit\u00e0 Federico II di Napoli, 80126 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K. P. S.","family":"Bhaskara Rao","sequence":"additional","affiliation":[{"name":"Computer Information Systems Department, Indiana University Northwest, Gary, IN 46408, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9665-2032","authenticated-orcid":false,"given":"Anna","family":"De Simone","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Applicazioni R. 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