Ranking opportunity sets: An axiomatic approach (Q1332709)

The paper characterizes quasi-orderings on the power set of the alternatives; the subsets to be ranked are interpreted as opportunity sets available to an individual. The main criteria for ranking these opportunity sets are the individual preferences on the universal set of alternatives and the freedom of choice associated with each subset of the universal set. Given the individual's preferences for the alternatives, two basic ingredients of well-being of the individual are the achieved level of utility and the extent for freedom enjoyed are determined by the opportunity set. It is in this sense that the ranking of well being of an individual in different situations can be interpreted as the ranking of the opportunity sets in these situations. Four different rules for ranking opportunity sets in terms of well-being are axiomatically characterized: the leximax, under which if the best alternative in set \(A\) is better than best in another set \(B\), then \(A\) represents a higher level of well-being than \(B\). In the case of ties (indifference between distinct alternatives is ruled out), the common alternative is eliminated and the best alternatives in the reduced sets is compared and so on. If in the process, all alternatives of \(B\) get eliminated while alternatives in \(A\) remain, then \(A\) is ranked higher than \(B\). The remaining three rules are based on the indirect utility of an opportunity set (utility of the best alternative) and the cardinality of the opportunity set. The first of these is a lexicographic rule which gives priority to indirect utility over cardinality of the opportunity set; the second is also a lexicographic rule which gives priority to the cardinality of the opportunity set over indirect utility. The last one is a dominance rule based on the two criteria of indirect utility and cardinality.