How to choose a compatible committee?

Electing a committee of size k from m candidates (\(k < m\)) is an interesting problem under multi-winner voting situations. In this paper, we propose a new committee selection rule based on cooperative game theoretic tools, where voters can approve both individuals and groups of candidates simultaneously. This flexibility of approving groups of candidates allows the voters to assess the candidates’ compatibility to work in a group. In many situations, the k-elected candidates have no particular status as a group and voters in such multi-winner elections are presumably concerned about the personal qualities of the candidates. However, many committees function in unison and therefore, their productivity also depends on the compatibility of the members to accomplish a task together. We assume that the voters have prior beliefs about this compatibility. The profile of summed approval votes constitutes the characteristic function of a cooperative game. The Shapley value of this game is calculated to measure the candidates’ expected marginal contributions in accomplishing the group task as perceived by the voters. The top k-ranked candidates prescribed by the Shapley value are selected to form the desired committee. The Shapley value as a committee selection rule is characterized by a set of intuitive axioms. We explore several properties of the committee selection rule.