An Analysis of Approval-Based Committee Rules for 2D-Euclidean Elections

Abstract

We study approval-based committee elections for the case where the voters’ preferences come from a 2D-Euclidean model. We consider two main issues: First, we ask for the complexity of computing election results. Second, we evaluate election outcomes experimentally, following the visualization technique of Elkind et al. (2017). Regarding the first issue, we find that many NP-hard rules remain intractable for 2D-Euclidean elections. For the second one, we observe that the behavior and nature of many rules strongly depend on the exact protocol for choosing the approved candidates.