Where is the Squad? Robust ideal point estimation in the presence of protest votes

Kwangok Seo, Joungyoun Kim, Johan Lim and Jong Hee Park

Journal of Applied Statistics, 2026, vol. 53, issue 10, 2012-2027

Abstract: Ideal point estimation is a widely used statistical method for understanding the preferences of elected representatives in political science, statistics, and social sciences. However, protest votes – where individuals deliberately obscure their true ideal points to express dissatisfaction with their own political party – present a significant challenge to the accuracy of this method. In this paper, we first examine the impact of protest votes on ideal point estimation, demonstrating that they introduce substantial attenuation bias that leads to the misrepresentation of extreme legislators as moderates. After establishing the importance of this issue, we propose a novel method that corrects the bias stemming from protest votes, thereby allowing researchers to obtain more accurate estimates of legislators’ ideal points. Our method detects and masks votes suspected to be protest votes within a Bayesian framework, reducing the bias introduced by such votes in posterior inference of ideal points. We demonstrate the effectiveness of our proposed method in addressing the attenuation problem caused by protest votes using both simulated scenarios and real-world roll-call data.

Date: 2026
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DOI: 10.1080/02664763.2025.2585949

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