{"ID":23507352,"CreatedAt":"2026-09-18T02:21:44.056544415Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20579","arxiv_id":"2609.20579","title":"Faster Verification of PJR$^+$ via Mincuts","abstract":"PJR$^+$ is a polynomial-time verifiable proportionality axiom for approval-based committee elections, but its known polynomial-time verification procedure relies on general submodular-function minimisation. We show that its objective is a maximum-closure problem and give a direct mincut formulation of the problem on a bipartite graph. Using an almost-linear-time maximum-flow algorithm, this yields an $\\mathcal{O}(m(nk)^{1+o(1)})$-time verifier, where $n$, $m$, and $k$ are the numbers of voters, candidates, and committee members, respectively. The dependence of this bound on each parameter separately is almost linear: it is linear in $m$, and almost linear in $n$ and $k$. The verifier also returns an explicit group witnessing a violation and admits a slower but immediately implementable variant based on the preflow--push mincut algorithm. Finally, for the parameterised axiom $α$-PJR$^+$, where $α$ is used as a multiplier in the group size, we demonstrate how to compute the largest value of $α$ for which a committee still fails the axiom using this mincut formulation.","short_abstract":"PJR$^+$ is a polynomial-time verifiable proportionality axiom for approval-based committee elections, but its known polynomial-time verification procedure relies on general submodular-function minimisation. We show that its objective is a maximum-closure problem and give a direct mincut formulation of the problem on a...","url_abs":"https://arxiv.org/abs/2609.20579","url_pdf":"https://arxiv.org/pdf/2609.20579v1","authors":"[\"Drew Springham\"]","published":"2026-09-17T15:35:49Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}