Computing the Schulze Method for Large-Scale Preference Data Sets

TL;DR

This paper introduces a highly optimized parallel algorithm for computing the Schulze voting method using Pregel, enabling efficient processing of large-scale preference data sets and highlighting its suitability for parallel computation.

Contribution

The paper develops a scalable, optimized parallel algorithm for the Schulze method and provides theoretical analysis comparing its computational complexity to the ranked pairs method.

Findings

The algorithm efficiently handles large preference data sets.

The Schulze method is more suitable for parallel computation than ranked pairs.

Winner determination for the Schulze method is NL-complete.

Abstract

The Schulze method is a voting rule widely used in practice and enjoys many positive axiomatic properties. While it is computable in polynomial time, its straight-forward implementation does not scale well for large elections. In this paper, we develop a highly optimised algorithm for computing the Schulze method with Pregel, a framework for massively parallel computation of graph problems, and demonstrate its applicability for large preference data sets. In addition, our theoretic analysis shows that the Schulze method is indeed particularly well-suited for parallel computation, in stark contrast to the related ranked pairs method. More precisely we show that winner determination subject to the Schulze method is NL-complete, whereas this problem is P-complete for the ranked pairs method.