An extension of Majority Judgment to non-uniform qualitative scales

Abstract

We consider the context of social choice in which individual evaluations of the alternatives are expressed over an ordered qualitative scale. We propose to extend the framework of Majority Judgment to the case of non-uniform ordered qualitative scales, described by an ordinal proximity measure. The central construct in our model is a weak order defined over multisets of ordinal proximity degrees. On the basis of this weak order, each alternative profile is represented by an ordinal mean which balances the multisets of ordinal proximity degrees associated with the upper and lower ordinal evaluations. The procedure for ranking the alternative profiles consists primarily in comparing means, plus a tie-breaking scheme in which the weak order plays once more an important role.