Winner determination and manipulation in minisum and minimax committee elections

Abstract

In a committee election, a set of candidates has to be determined as winner of the election. Baumeister and Dennisen [2] proposed to extend the minisum and minimax approach, initially defined for approval votes, to other forms of votes. They define minisum and minimax committee election rules for trichotomous votes, incomplete linear orders and complete linear orders, by choosing a winning committee that minimizes the dissatisfaction of the voters. Minisum election rules minimize the voter dissatisfaction by choosing a winning committee with minimum sum of the disagreement values for all individual votes, whereas in a minimax winning committee the maximum disagreement value for an individual vote is minimized. In this paper, we investigate the computational complexity of winner determination in these voting rules. We show that winner determination is possible in polynomial time for all minisum rules we consider, whereas it is NP-complete for three of the minimax rules. Furthermore, we study different forms of manipulation for these committee election rules.