Weighted scoring rules for selecting a compatible committee

This paper addresses the challenge of incorporating a weighting system into the commit- tee selection process under scoring rules. Given a set of voters expressing their preferences on a set of candidates, the objective is to choose a fixed-size subset of candidates, called a committee, that optimally represents the voters' preferences. The main idea of the paper is that, beyond the voter's preferences, each committee of a given size may be associated with a weight vector based on a specific compatibility criterion such as communication, cooperation, connectivity, or diversity. This vector assigns weights to individual committee members, reflecting their ability to make the committee satisfactory with respect to the criterion under consideration. In order to integrate the weighting system into the committee selection process, we introduce the continuous weighted scoring function derived from any scoring function. This function is characterized by two crucial properties, namely linearity and independence of zero-weight members. We demonstrate how this continuous weighted scoring function facilitates a trade-off between the candidates' performance and their compatibility skills.