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Nonparametric Ideal-Point Estimation and Inference

Published online by Cambridge University Press:  08 March 2018

Alexander Tahk*
Assistant Professor, Department of Political Science, University of Wisconsin–Madison, North Hall Rm 110, 1050 Bascom Mall, Madison, WI 53706, USA. Email:


Existing approaches to estimating ideal points offer no method for consistent estimation or inference without relying on strong parametric assumptions. In this paper, I introduce a nonparametric approach to ideal-point estimation and inference that goes beyond these limitations. I show that some inferences about the relative positions of two pairs of legislators can be made with minimal assumptions. This information can be combined across different possible choices of the pairs to provide estimates and perform hypothesis tests for all legislators without additional assumptions. I demonstrate the usefulness of these methods in two applications to Supreme Court data, one testing for ideological movement by a single justice and the other testing for multidimensional voting behavior in different decades.

Copyright © The Author(s) 2018. Published by Cambridge University Press on behalf of the Society for Political Methodology. 

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Author’s note: I thank R. Michael Alvarez, Bret Hanlon, Simon Jackman, Jeff Lewis, Nolan McCarty, and Keith Poole. All mistakes are my own. Open-source software for the method proposed in this article is available at as a package for the statistical software R. Replication materials for all of the results in this article are provided in the online Dataverse archive associated with this article (Tahk 2017).

Contributing Editor: R. Michael Alvarez


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