Distortion of Multi-winner Elections on the Line Metric: The Polar Comparison Rule

Negar Babashah, Hasti Karimi, Masoud Seddighin, Golnoosh Shahkarami

Abstract: We study the problem of deterministically selecting a committee of size k from a set of m alternatives, based solely on the ordinal preferences of voters. Both voters and alternatives lie on the line metric, and the goal is to minimize a social cost function based on metric distances. While the distances to committee members fully determine the social cost, voting rules only have access to the ordinal preference list of each voter. The distortion of a voting rule is the worst-case ratio between the cost of the selected committee and the cost of the optimal one, over all consistent distance metrics. Extending distortion to multi-winner elections requires defining how a voter’s cost is aggregated over the committee. Caragiannis et al. [9] studied q-cost, where the cost is defined as the distance to the voter’s qth closest committee member. In this work, we focus on the additive cost, where a voter’s cost is the sum of their distances to all committee members. The overall social cost is either utilitarian (sum of individual costs) or egalitarian (maximum individual cost).

External IDs:dblp:conf/sagt/BabashahKSS25