Justifiable preferences for freedom of choice

Abstract

In this paper we say that a preference for freedom of choice is justifiable if there exists a reflexive and complete binary relation on the set of alternatives, such that one oppurtunity is atleast as good as a second, if and only if the there is at least one alternative from the first set which is no worse than any alternative of the two sets combined together, with respect to the binary relation on the alternatives. In keeping with the revered tradition set by von Neumann and Morgenstern we call a reflexive and complete binary relation, an abstract game (note: strictly speaking von Neumann and Morgenstern refer to the asymmetric part of a reflexive and complete binary relation as an abstract game; hence our terminology though analytically equivalent, leads to a harmless corruption of the original meaning). It turns out that if a preference for freedom of choice is justifiable, then the base relation with respect to which it is justifiable, is simply the restriction of the preference for freedom of choice, to the set of all singletons. Our main result is about the justifiability of transitive preferences for freedom of choice. It says that such preferences are justifiable if and only if they satisfy Monotonicity and Concordance. Concordance says that if one opportunity set is at least as desirable as a second then it should also be the case that the first opportunity set is at least as desirable as the union of the two. Since, for the case of transitive preferences for freedom of choice, our notion of justifiability coincides with that of Arrow and Malishevsky, our axiomatic characterization can throw some light on properties of indirect utility functions.