Using Borda Scores for Ranking Sets of Objects

VCLA and WPI hosted a talk by Christian Klamler

ABSTRACT

Ranking sets of objects based on a ranking over the single objects has been widely discussed in the literature.But does it make sense to use the Borda score to make such comparisons? Recently various papers, in particular in the literature on fair division, applied the Borda score to such comparisons.The Borda-sum ranking would of course provide a complete ranking of sets of objects and therefore is an alternative to comparisons of sets based on best and/or worst objects. However, we show that the use of Borda scores in such a framework has - in general - severe problems. For restricted settings, i.e., fixed sets of objects and sets of equal cardinality, we provide a characterization of the whole family of Borda-sum rankings based on different Borda scores.In addition, for unequal cardinalities we determine the properties of the Borda-sum ranking based on the most commonly used Borda scores.