The No-show Paradox in Single Transferable Vote under One-dimensional Preferences
一维偏好下单一可转移投票中的缺席悖论
Farhad Mohsin
AI总结 研究一维偏好模型下单一可转移投票(STV)的群体缺席悖论,发现极端选民弃权易引发悖论,且随候选人数增加概率显著上升。
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群体缺席悖论(GNSP)是指一组选民弃权后,新获胜者更受他们偏好。先前研究表明,即使对于易受此悖论影响的投票规则,在实际选举和多种假设下,该悖论也罕见发生。然而,我们发现,在一维偏好模型(如1D-Euclidean、单峰或单交叉偏好)下,流行的 runoff 规则——单一可转移投票(STV)——极易受到 GNSP 的影响。这与另一类易受 GNSP 影响的规则——Condorcet 规则——形成鲜明对比,后者在这些一维偏好下不会出现悖论。我们从理论上识别了 STV 在一维偏好模型下发生 GNSP 的易于处理且普遍存在的充分条件。通过理论结果和来自这些领域的合成偏好配置实验,我们证明一维频谱两端的选民特别容易因弃权而引发 GNSP。此外,随着备选方案数量的增加,发生的可能性显著增加。
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.