On some axioms for ranking sets of alternatives
Abstract The problem of extending an ordering on a finite set of alternatives to its power set is considered. It is shown that two fairly mild axioms imply the restrictive condition that every set is equivalent to the set consisting only of its least and greatest elements. A characterisation of all extensions of a linear ordering, which satisfy our two axioms, is made by means of a class of real valued functions defined on integer pairs. The induced orderings are interpreted in terms of choice under uncertainty and an application made to welfare economics.