# The Schulze Method of Voting

arXiv: https://arxiv.org/abs/1804.02973 · HTML: https://mlsanity.com/paper/1804.02973/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

## Built on by (most cited first, 7 of 7)

- [RobustSpring: Benchmarking Robustness to Image Corruptions for Optical Flow, Scene Flow and Stereo](https://mlsanity.com/paper/2505.09368/) (2025)
- [Evaluating State of the Art, Forecasting Ensembles- and Meta-learning Strategies for Model Fusion](https://mlsanity.com/paper/2203.03279/) (2022)
- [Dynamic Normativity: Necessary and Sufficient Conditions for Value Alignment](https://mlsanity.com/paper/2406.11039/) (2024)
- [MANI-Rank: Multiple Attribute and Intersectional Group Fairness for Consensus Ranking](https://mlsanity.com/paper/2207.10020/) (2022)
- [Fine-Grained Complexity and Algorithms for the Schulze Voting Method](https://mlsanity.com/paper/2103.03959/) (2021)
- [Absolute Ranking: An Essential Normalization for Benchmarking Optimization Algorithms](https://mlsanity.com/paper/2409.04479/) (2024)
- [A Tutorial On Intersectionality in Fair Rankings](https://mlsanity.com/paper/2502.05333/) (2025)

## Abstract (arXiv)

We propose a new single-winner election method ("Schulze method") and prove that it satisfies many academic criteria (e.g. monotonicity, reversal symmetry, resolvability, independence of clones, Condorcet criterion, k-consistency, polynomial runtime). We then generalize this method to proportional representation by the single transferable vote ("Schulze STV") and to methods to calculate a proportional ranking ("Schulze proportional ranking"). Furthermore, we propose a generalization of the Condorcet criterion to multi-winner elections. This paper contains a large number of examples to illustrate the proposed methods.