Preference-Approval Structures and Opportunity Sets

Abstract This paper first proposes the combination of preference-approval structures with ranking opportunity sets (i.e., collections of options), a relevant topic in welfare analysis. We suggest that various possibilities emerge, and we illustrate them with specific examples in finite contexts. Characterizations of three rankings of opportunity sets defined from preference-approval structures on the individual options are proven. Their representability by utilities is considered too. Various preference-approval structures on opportunity sets are defined from the information contained in a preference-approval structure on the options, that supplement these rankings of opportunity sets with appropriate collections of “approved” opportunity sets. Finally, preference-approval structures on opportunity sets are defined using the information derived from a ranking of the options. As a secondary contribution, we compute the number of preference-approval structures on a set with finite cardinality, thereby enriching the fundamental theory of this enhanced type of preferences.