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., (AAAI-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 depends on the exact protocol for choosing the approved candidates.