New algorithm computes MMS voting rule without linear programming
Replaces linear programming with maximum flow for faster, error-free results.
Luis Sánchez-Fernández presents a new algorithm for computing the MMS (Maximin Support) voting rule, a method used in multi-winner elections to ensure proportional representation. Traditional implementations rely on linear programming (LP), which can be slow, opaque, and prone to numerical errors. The proposed algorithm replaces LP with a series of maximum flow problems, each solved efficiently using standard network flow techniques.
This shift brings three key benefits: efficiency (flow problems are typically faster than LP), traceability (each step is verifiable), and numerical stability (no floating-point rounding issues). The paper, now in its fourth version (July 2026), provides a concise 9-page description and is available on arXiv. While the work is theoretical, it has practical implications for any system using MMS—such as participatory budgeting or committee selection—by making the computation more reliable and accessible.
- Replaces linear programming with maximum flow problems for computing MMS voting rule
- Claims improved efficiency, traceability, and numerical error-free operation
- Paper updated to v4 on arXiv with 9 pages of technical detail
Why It Matters
Makes fair multi-winner elections computationally cheaper and more trustworthy for real-world applications.