Toward Completing the Picture of Control in Schulze and Ranked Pairs Elections

TL;DR

This paper advances understanding of electoral control in Schulze and ranked pairs voting rules by solving open problems, fixing previous flaws, and analyzing related graph problems.

Contribution

It resolves several open questions about control by replacing candidates or voters and corrects a flaw in prior resistance proofs for Schulze elections.

Findings

Schulze is resistant to certain control types.

Fixed a flaw in previous resistance proofs.

Identified vulnerabilities in destructive control by deleting candidates.

Abstract

Both Schulze and ranked pairs are voting rules that satisfy many natural, desirable axioms. Many standard types of electoral control (with a chair seeking to change the outcome of an election by interfering with the election structure) have already been studied. However, for control by replacing candidates or voters and for (exact) multimode control that combines multiple standard attacks, many questions remain open. We solve a number of these open cases for Schulze and ranked pairs. In addition, we fix a flaw in the reduction of Menton and Singh [IJCAI 2013] showing that Schulze is resistant to constructive control by deleting candidates and re-establish a vulnerability result for destructive control by deleting candidates. In some of our proofs, we study variants of s-t vertex cuts in graphs that are related to our control problems.