Group decisions from individual rankings: The Borda–Condorcet rule

Abstract

This paper presents an evaluation protocol that transforms a collection of rankings, defined over a set of alternatives, into a complete, transitive, and cardinal assessment. It combines the ideas of Borda and Condorcet by computing the support that each alternative receives on average when confronted with any other. The protocol evaluates those alternatives in terms of pairwise comparisons but weighs the outcomes differently depending on how each alternative fares with respect to the others. The evaluation appears as the stable distribution of an iterative process in which each alternative competes randomly with any other, and results in a vector of positive numbers that tells us the relative support of the different options. We show that this protocol does not require linear orderings and can also be applied in the presence of incomplete rankings and when dealing with several issues simultaneously.