A characterization of proportionally representative committees

When voters elicit ranked preferences over candidates, one particular axiom for proportional representation is Proportionality of Solid Coalitions (PSC). This axiom was advocated by Dummett [4] and has been referred to as the most important requirement for proportional representation [15, 16, 18, 19]. PSC is the subject of many theoretical and empirical studies. Theoretical studies have focused on designing voting rules that satisfy PSC; these include single transferable vote (STV) [15], Quota Borda System (QBS) [4], Schulz-STV [14], and the Expanding Approvals Rule (EAR) [2].