Ranking Opportunity Sets on the Basis of their Freedom of Choice and their Ability to Satisfy Preferences : A Difficulty

This paper examines Sen’s [21] suggestion that preference information be used to supplement the criterion of freedom of choice for ranking of the opportunity sets. This paper establishes, with some generality, that, in order for this supplementation to procedure a transitive ranking of the opportunity sets, it is necessary and sufficient to assume that the domain ranked is such that the individual preference ordering includes the criterion of freedom of choice as a subrelation. However, it is also shown that the quasi-transitivity of such a ranking can be obtained without further assumption. Hence, it seems difficult to construct a ranking of opportunity sets that attaches value to their freedom of choice while giving some weight to individual preferences. If freedom of choice is to have any value in the ranking, then in order for the ranking to be transitive, this value will have to be instrumental rather than intrinsic (using Sen’s [19] terminology).