# A Polynomial-Time Rule Satisfying Full Justified Representation

arXiv: https://arxiv.org/abs/2608.05397 · HTML: https://mlsanity.com/paper/2608.05397/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2026.

## Built on by (most cited first, 1 of 1)

- [Strengthening Full Justified Representation: Efficient Verification and Computation](https://mlsanity.com/paper/2608.11500/) (2026)

## Abstract (arXiv)

In approval-based multiwinner voting, voters submit an approval ballot on which basis a committee of fixed size k has to be selected. Compared to single-winner voting this makes it possible to represent minorities in the selection of the committee as well. Thus, one of the most desirable goals of multiwinner voting is to satisfy proportional representation. In this paper we propose a variant of the Greedy Justified Candidate rule that satisfy the notion of Full Justified Representation (FJR). This variant can be computed in polynomial time answering the open question of whether an FJR committee can always be computed efficiently. Additionally, we answer an open question whether committees returned by MES can always be extended in a way to satisfy FJR negatively.