Core-Stable Committees under Restricted Domains

We consider a model of committee elections, where the goal is to select a fixed-size subset of objects based on the preferences of a group of individuals. The objects and the individuals are typically referred to as the candidates and the voters, respectively, and we follow this convention in our paper. However, the candidates do not need to represent humans. For example, this model describes (1) the problem of locating public facilities--there the candidates correspond to possible physical locations where the facilities can be built [Farahani and Hekmatfar, 2009, Skowron et al., 2016], (2) the problem of presenting results by a search engine in response to a user query--there, the candidates are web-pages, and voters are potential users searching for a given query [Skowron et al., 2017], (3) the problem of selecting validators in the blockchain, where the candidates are the users of the protocol [Cevallos and Stewart, 2020, Burdges et al., 2020]. For more examples that fall into the category of committee elections we refer to the recent book chapter [Faliszewski et al., 2017] and to the recent survey [Lackner and Skowron, 2020]. In numerous applications that fit the model of committee elections it is critical to select a subset of candidates, hereinafter called a committee, in a fair and proportional manner. Proportionality is one of fundamental requirements of methods for selecting representative bodies, such as parliaments, faculty boards, etc.