02/02/2021

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

Michał T. Godziszewski, Paweł Batko, Piotr Skowron, Piotr Faliszewski

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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.

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