Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Moreover, we compare these choice functions with those that already exist in the literature.Thanks are due to José Alcalde, J.V. Llinares and M.C. Sánchez, for helpful comments. The comments and suggestions of a referee’s report have improved the work; we are most grateful to her/him. Financial support from the Spanish DGICYT, under project BEC2001-0781, Fundación Séneca (PI74/00826/FS/01) and from the IVIE is acknowledged.
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