The Schulze Method of Voting

TL;DR

The paper introduces the Schulze method for single-winner elections, proves its compliance with key criteria, and extends it to proportional representation and multi-winner elections, supported by numerous illustrative examples.

Contribution

It presents a new voting method satisfying many criteria and generalizes it for proportional and multi-winner elections, with comprehensive theoretical proofs and examples.

Findings

Schulze method satisfies key electoral criteria.

Generalization to proportional and multi-winner elections.

Method demonstrated with extensive examples.

Abstract

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.