Old rockers

This paper discusses three classic social evaluation procedures in a very general scenario: the majority rule, the Borda count, and the Condorcet criterion. We do so assuming no structure on individual preferences and providing a very easy way of identifying and comparing those evaluation protocols. Our informational inputs are the individual pairwise comparisons of alternatives and the informational outputs can be social pairwise comparisons or social orderings. The majority rule is obtained as the only pairwise social evaluation that satisfies informational efficiency, anonymity, monotonicity, and symmetry (a variant of the classical result by May). Arrow’s impossibility theorem appears as a corollary of this result. Borda and Condorcet evaluation functions are obtained along the same lines when we require the evaluation to be a social ordering. Both social evaluation functions can be regarded as applying the same principle over different domains (individual pairwise comparisons or social pairwise comparisons).