Many recent works have investigated the problem of extending a preference over a set of alternatives to its power set, in an attempt to provide a formal representation of the notion of freedom of choice. In general, results are limited to the finite case, which excludes, for instance, the case...

Using a common framework, we consider the two existing extensions of the leximax criterion to infinite environments (Arlegi et al. (2005) and Ballester and De Miguel (2003)), and show that, though the respective definitions of the rules and their axiomatic characterizations appear to differ...