Fast Schulze Voting Using Quickselect

Abstract

The Schulze voting method aggregates voter preference data using maxmin-weight graph paths, achieving the Condorcet property that a candidate who would win every head-to-head contest will also win the overall election. Once the voter preferences among $m$ candidates have been arranged into an $m\times m$ matrix of pairwise election outcomes, a previous algorithm of Sornat, Vassilevska Williams and Xu (EC '21) determines the Schulze winner in randomized expected time $O(m^2\log^4 m)$. We improve this to randomized expected time $O(m^2\log m)$ using a modified version of quickselect.