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$\ell_0$-Regularized Item Response Theory Model for Robust Ideal Point Estimation

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.