Freedom of Optimal Choice

Abstract

In this paper we provide axiomatic characterizations of what we call the preference for the freedom of optimal choice, which ranks feasible sets according to the number of best elements it contains with respect to a given binary relation. In a final section of this paper, we provide an axiomatic characterization of the entire family of preferences for the freedom of choice which are defined so as to respect the property of responding favorably to an increase in the cardinality of the set of optimal choices when the cardinality of the set of available alternatives is held fixed and to a decrease in the cardinality of the set of alternatives when the cardinality of the set of optimal choices is held fixed. In the same section we also provide an axiomatic characterization of the measure of flexibility defined by evaluating the cardinality of the set of non-optimal alternatives.

Keywords: Logic, Applied Mathematics, Applied Math Other, Pure_mathematics/0109017