Stable Voting is PSPACE-Complete

2026-07-15

AI Summary

This study investigates the winner determination problem for Stable Voting and its simplified variant, Simple Stable Voting—two recursively defined Condorcet-consistent voting rules. Employing techniques from computational complexity theory and polynomial-time reductions, the paper establishes for the first time that both problems are PSPACE-complete, thereby precisely characterizing their worst-case computational complexity with matching upper and lower bounds. This result resolves a long-standing open question in computational social choice and reveals the inherent computational intractability of determining winners under these stable voting schemes.

Abstract

Stable Voting and Simple Stable Voting, introduced by Holliday and Pacuit, are Condorcet-consistent voting rules defined recursively: a candidate wins if they would win after removing some opponent they beat, taking the pair with the largest margin first. The computational complexity of winner determination under these rules has been an open question. We resolve this problem: winner determination is PSPACE-complete under both Stable Voting and Simple Stable Voting.

Problem

• Stable Voting
• Simple Stable Voting
• PSPACE-complete
• winner determination
• computational complexity

Innovation

• Stable Voting
• PSPACE-complete
• Condorcet-consistent
• voting rules
• computational complexity