PREFERENCE EXTENSION RULES FOR RANKING SETS OF ALTERNATIVES WITH A FIXED CARDINALITY

This paper analyzes the problem of deriving a ranking of fixed-cardina lity subsets of a universal set from a given ranking of the elements o f this universal set. Only subsets with a given number of elements are being ranked, which is where the approach in this paper differs from the Literature on extension rules that establish preference relations on the power set of the universal set. Common examples for areas where such preferences on subsets with a fixed cardinality are needed are e lections of committees of a given size, many-to-one matchings, and dec ision problems under ignorance. The main result of the paper is a char acterization of a class of lexicographic rank-ordered rules by means o f two axioms, namely, a responsiveness condition used in the matching literature and a well-known neutrality requirement which ensures that the names of the alternatives are irrelevant for the ranking of the se ts.