The No-show Paradox in Single Transferable Vote under One-dimensional Preferences

2026-06-10

AI Summary

This study investigates the Group No-Show Paradox (GNSP) under Single Transferable Vote (STV)—a phenomenon wherein the abstention of a subset of voters results in an outcome more preferred by the remaining electorate—within widely adopted one-dimensional preference domains, including 1D-Euclidean, single-peaked, and single-crossing structures. Through theoretical analysis and synthetic data experiments, the work demonstrates for the first time that STV is highly susceptible to GNSP in these settings, with paradox occurrence significantly amplified when voters holding extreme positions abstain and escalating sharply as the number of candidates increases. In contrast, Condorcet-consistent rules exhibit no such vulnerability under identical conditions. The study further establishes verifiable sufficient conditions for GNSP to arise, underscoring the inherent instability of STV in one-dimensional preference environments.

Abstract

The group no-show paradox (GNSP) occurs when a group of agents abstaining from voting can make the new winner more preferred to them. Previous work has suggested that even for voting rules susceptible to this paradox, it is a rare occurrence in real elections and under various assumptions. However, we find that under one-dimensional preference models such as 1D-Euclidean, single-peaked, or single-crossing preferences, Single Transferable Vote (STV), a popular runoff rule, is highly vulnerable to GNSP. This is in stark contrast to Condorcet rules, another family of rules susceptible to GNSP, where the paradox cannot occur under these one-dimensional preferences. We theoretically identify tractable and prevalent sufficient conditions for GNSP to occur for STV under one-dimensional preference models. Through our theoretical results and experiments with synthetic preference profiles from these domains, we demonstrate that voters at the extremes of the 1D spectrum are particularly likely to cause GNSP by abstaining. Furthermore, the likelihood of occurrence increases substantially as the number of alternatives grows.

Problem

• No-show Paradox
• Single Transferable Vote
• One-dimensional Preferences
• Group Abstention
• Voting Paradox

Innovation

• Group No-Show Paradox
• Single Transferable Vote
• One-dimensional Preferences
• Single-peaked
• Voting Paradox