A note on the method of equal shares

The Method of Equal Shares (ES) is a popular approval-based multi-winner voting rule, which was originally proposed by Peters and Skowron. It satisfies several well-known representation axioms, like extended justified representation (EJR) and priceability, and it can be computed in polynomial time. Further, it has already been employed in several real participatory budgeting elections. In this note, we prove that ES is an instance of the EJR-Exact family of voting rules that also satisfy EJR and were proposed by Aziz et al. 2018 before the work of Peters and Skowron. • EJR-Exact is a broad family of approval-based multi-winner voting rules. • All the voting rules in the EJR-Exact family satisfy EJR and EJR+. • Many rules in the EJR-Exact family can be computed in polynomial time. • We prove that the popular Method of Equal Shares is a particular instance of this family.