Weighted scoring rules for selecting a compatible committee

This paper addresses the challenge of integrating the compatibility criterion between candidates into the committee selection process under scoring rules. The compatibility between candidates is considered by assigning each committee a vector of weights based on this criterion. The goal is to choose a committee by taking into account both the compatibility between candidates and their performance based on scores. To achieve this, the paper defines a continuous weighted scoring function characterized by two crucial properties: linearity and independence of zero-weight members.