Computing the Schulze Method for Large-Scale Preference Data Sets

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.