Maximality with or without binariness: transfer-type characterizations J. C. R. Alcantud * Facultad de Econom´ ıa y Empresa, Universidad de Salamanca, Spain Abstract. We provide the first necessary and sufficient conditions in the literature for the ex- istence of maximal elements in a non-binary choice framework. As an application, the characterization of the existence of maximal elements for acyclic binary relations obtained in Rodr´ ıguez-Palmero and Garc´ ıa-Lapresta, 2002, Mathematical Social Sciences 43, 55-60, is deduced as a Corollary. Further characterizations in different settings given by Tian and Zhou, 1995, Journal of Mathematical Economics 24, 281-303, follow as well. Analogous characterization problems in the k-acyclic binary cases are solved too. Keywords: Maximization; non-binary choice functions; transfer continuity; k-acyclicity. JEL classification: D11. Address for correspondence: J.C.R. Alcantud, Facultad de Econom´ ıa y Empresa, Universidad de Salamanca, E 37008 Salamanca, Spain. Tel: +34-923-294500 ext. 3180; fax: +34-923-294686. Personal webpage http://web.usal.es/∼jcr * This work has been partially supported by FEDER and Ministerio de Ciencia y Tecnolog´ ıa under the Research Project BEC2002-02456, and by Junta de Castilla y Le´on under the Research Project SA061/02. 1