Ideal point estimation methods face a significant challenge when legislators engage in protest voting -- strategically voting against their party to express dissatisfaction. Such votes introduce attenuation bias, making ideologically extreme legislators appear artificially moderate. We propose a novel statistical framework that extends the fast EM-based estimation approach of \cite{Imai2016} using $\ell_0$ regularization method to handle protest votes. Through simulation studies, we demonstrate that our proposed method maintains estimation accuracy even with high proportions of protest votes, while being substantially faster than MCMC-based methods. Applying our method to the 116th and 117th U.S. House of Representatives, we successfully recover the extreme liberal positions of ``the Squad'', whose protest votes had caused conventional methods to misclassify them as moderates. While conventional methods rank Ocasio-Cortez as more conservative than 69\% of Democrats, our method places her firmly in the progressive wing, aligning with her documented policy positions. This approach provides both robust ideal point estimates and systematic identification of protest votes, facilitating deeper analysis of strategic voting behavior in legislatures.

翻译：理想点估计方法面临一个重大挑战：当立法者进行抗议性投票时——即策略性地投票反对自己所属政党以表达不满。此类投票会引入衰减偏差，使得意识形态极端的立法者被人为地表现为温和派。我们提出了一种新颖的统计框架，该框架通过ℓ₀正则化方法扩展了\cite{Imai2016}提出的基于快速EM算法的估计方法，以处理抗议性投票。通过模拟研究，我们证明即使在高比例抗议性投票的情况下，所提出的方法仍能保持估计准确性，同时其计算速度显著快于基于MCMC的方法。将我们的方法应用于美国第116届和第117届众议院的数据，我们成功还原了“小队”成员的极端自由主义立场——其抗议性投票曾导致传统方法将他们错误分类为温和派。传统方法将奥卡西奥-科尔特斯的保守程度排在高于69%民主党人的位置，而我们的方法则将其明确归入进步派阵营，这与她记录在案的政策立场相一致。该方法不仅提供了稳健的理想点估计，还能系统性地识别抗议性投票，有助于深入分析立法机构中的策略性投票行为。