The superdominance relation, the positional winner, and more missing links between Borda and Condorcet

Abstract

The field of social choice dates back to the eighteenth century, when Borda and Condorcet started a never-ending discussion about the use of either positional or pairwise information. Three centuries later, after countless axiomatic characterizations of voting rules, impossibility theorems and many other study subjects, researchers still debate whether positional information is really sensitive to manipulation or pairwise information disregards the transitivity of voters’ preferences. In a previous paper, we introduced the notions of supercovering relation and pairwise winner, which resulted in a meeting point for both points of view of the theory of social choice. In this paper, we continue this direction and propose the notions of superdominance relation and positional winner that will prove to be the alter egos of the supercovering relation and the pairwise winner when positional information (rather than pairwise information) is considered. Moreover, we analyse a new interesting choice set: the unsuperdominated set.