Nearly Group-Separable Elections

2026-09-27

AI Summary

This study addresses the challenge of computing election proximity to near-single-peakedness in computational social choice, measuring structural distance via the number of adjacent candidate swaps. Methodologically, grounded in fixed-parameter tractability (FPT) theory, it designs algorithms parameterized by either the number of candidates or the number of swaps, enabling efficient computation for domains characterized by finitely many forbidden subelections. The primary contribution lies in resolving a long-standing open problem by providing the first practical FPT algorithms for all such finite forbidden subelection domains. Furthermore, experimental analyses validate the feasibility and superior performance of the proposed algorithms across diverse social choice domains.

Abstract

We study the problem of computing how close a given election is to being group-separable, measuring proximity by swaps of adjacent candidates in the votes. We also consider several other domains, including caterpillar group-separable, balanced group-separable, single-peaked, and single-crossing ones. Our problem is generally intractable, but we find practical FPT algorithms parameterized by the number of candidates or swaps. For the latter case, our algorithm applies to all domains characterized by finite forbidden subelections, resolving a well-established open problem. We supplement our theoretical findings with experimental analysis.

Problem

• Group-Separable Elections
• Kendall tau distance
• Swap distance
• Preference domains
• Forbidden subelections

Innovation

• Group-Separable Elections
• Fixed-Parameter Tractability (FPT)
• Forbidden Subelections
• Adjacent Swaps
• Preference Domains