How to choose a Compatible Committee?

TL;DR

This paper introduces a novel committee selection method that incorporates voter opinions on interdependencies among alternatives using cooperative game theory and the Shapley value, emphasizing compatibility.

Contribution

It proposes a new multi-winner voting rule based on cooperative game theory and the Shapley value, considering voters' opinions on alternative interdependencies.

Findings

The proposed rule effectively captures interdependencies among alternatives.

The properties of the Shapley value are suitable for committee selection.

The method emphasizes the importance of the compatibility principle.

Abstract

Electing a committee of size k from m alternatives (k < m) is an interesting problem under the multi-winner voting rules. However, very few committee selection rules found in the literature consider the coalitional possibilities among the alternatives that the voters believe that certain coalitions are more effective and can more efficiently deliver desired outputs. To include such possibilities, in this present study, we consider a committee selection problem (or multi-winner voting problem) where voters are able to express their opinion regarding interdependencies among alternatives. Using a dichotomous preference scale termed generalized approval evaluation we construct an $m$-person coalitional game which is more commonly called a cooperative game with transferable utilities. To identify each alternative's score we use the Shapley value (Shapley, 1953) of the cooperative game we construct for the purpose. Our approach to the committee selection problem emphasizes on an important issue called the compatibility principle. Further, we show that the properties of the Shapley value are well suited in the committee selection context too. We explore several properties of the proposed committee selection rule.