The Price of Justified Representation

In multiwinner approval voting, the goal is to select k-member committees based on voters' ballots. A well-studied concept of proportionality in this context justified representation (JR) axiom, which demands that no large cohesive group voters remains unrepresented. However, JR axiom may conflict with other desiderata, such as coverage (maximizing number who approve at least one committee member) or social welfare approvals obtained by members). work, we investigate impact imposing (as well more demanding EJR axiom) and coverage. Our approach threefold: derive worst-case bounds loss welfare/coverage caused JR, study computational complexity finding 'good' provide (obtaining a hardness result, an approximation algorithm, exact algorithm for one-dimensional preferences), examine setting empirically several synthetic datasets.