Schulze and Ranked-Pairs Voting are Fixed-Parameter Tractable to Bribe, Manipulate, and Control

TL;DR

This paper demonstrates that Schulze and ranked-pairs voting systems, despite their resistance to manipulation in general, are fixed-parameter tractable when considering the number of candidates, allowing efficient algorithms for bribery, control, and manipulation.

Contribution

It introduces fixed-parameter tractable algorithms for bribery, control, and manipulation in Schulze and ranked-pairs elections based on the number of candidates, including weighted variants.

Findings

Polynomial-time algorithms for bribery, control, and manipulation.

Fixed-parameter tractability with respect to candidate count.

Algorithms extend to certain weighted election variants.

Abstract

Schulze and ranked-pairs elections have received much attention recently, and the former has quickly become a quite widely used election system. For many cases these systems have been proven resistant to bribery, control, or manipulation, with ranked pairs being particularly praised for being NP-hard for all three of those. Nonetheless, the present paper shows that with respect to the number of candidates, Schulze and ranked-pairs elections are fixed-parameter tractable to bribe, control, and manipulate: we obtain uniform, polynomial-time algorithms whose degree does not depend on the number of candidates. We also provide such algorithms for some weighted variants of these problems.