Optimization-Based Voting Rule Design: The Closer to Utopia the Better Piotr Faliszewski, Stanislaw Szufa, and Nimrod Talmon Abstract In certain situations, such as elections in a Euclidean domain, it is possible to specify clear requirements for the operation of a multiwinner voting rule, for it to provide committees that correspond to some desirable intuitive notions (such as individual excellence of committee members or their diversity). We formally describe several such requirements, which we refer to as “utopias”. Supplied with such utopias, we develop an optimization-based mechanism for constructing committee scoring rules that provide results as close to these utopias as possible; we test our mechanism on weakly separable and OWA-based rules. Using our method we acquire some interesting insights as well as recover some believed connections between known multiwinner voting rules and certain applications and get other interesting insights. 1 Introduction Multiwinner voting is a formalism for selecting a set of items to share (a committee), based on the preferences of a group of agents (the voters) (Kilgour 2010; Faliszewski et al. 2017; Faliszewski et al. 2017; Lackner and Skowron 2020). For example, a group of judges may need to select a set of finalists of a competition, a hiring committee may need to select a set of people to invite for on-site interviews, and an internet store may need to decide which items to present on its homepage, depending on how the preferences of its customers are perceived. In each of these examples, we need committees with different properties: the judges should select individually best P. Faliszewski (B ) AGH University, Krakow, Poland S. Szufa Jagiellonian University, Krakow, Poland N. Talmon Ben-Gurion University of the Negev, Be’er Sheva, Israel © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 T. Szapiro and J. Kacprzyk (eds.), Collective Decisions: Theory, Algorithms And Decision Support Systems, Studies in Systems, Decision and Control 392, https://doi.org/10.1007/978-3-030-84997-9_2 17