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

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.