Committees providing EJR can be computed efficiently

TL;DR

This paper introduces a family of approval-based multi-winner voting rules satisfying proportional justified representation, including a polynomial-time computable subfamily that guarantees extended justified representation, with one rule computable in $O(n m k)$ time.

Contribution

It identifies a family of PJR-satisfying voting rules, including a polynomial-time subfamily that guarantees EJR, advancing computational efficiency in approval voting.

Findings

Family of approval-based voting rules satisfying PJR

Subfamily satisfying EJR can be computed in polynomial time

One rule computed in $O(n m k)$ time

Abstract

We identify a whole family of approval-based multi-winner voting rules that satisfy PJR. Moreover, we identify a subfamily of voting rules within this family that satisfy EJR. All these voting rules can be computed in polynomial time as long as the subalgorithms that characterize each rule within the family are polynomial. One of the voting rules that satisfy EJR can be computed in $O(n m k)$.