Peer-reviewed Publications

GPIRT: A Gaussian Process Model for Item Response Theory

Duck-Mayr, JBrandon, Roman Garnett, and Jacob Montgomery. 2020. “GPIRT: A Gaussian Process Model for Item Response Theory.” In Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), 124:520–529. Proceedings of Machine Learning Research.

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Replication archive here (opens in new tab)

Abstract The goal of item response theoretic (IRT) models is to provide estimates of latent traits from binary observed indicators and at the same time to learn the item response functions (IRFs) that map from latent trait to observed response. However, in many cases observed behavior can deviate significantly from the parametric assumptions of traditional IRT models. Nonparametric IRT models overcome these challenges by relaxing assumptions about the form of the IRFs, but standard tools are unable to simultaneously estimate flexible IRFs and recover ability estimates for respondents. We propose a Bayesian nonparametric model that solves this problem by placing Gaussian process priors on the latent functions defining the IRFs. This allows us to simultaneously relax assumptions about the shape of the IRFs while preserving the ability to estimate latent traits. This in turn allows us to easily extend the model to further tasks such as active learning. GPIRT therefore provides a simple and intuitive solution to several longstanding problems in the IRT literature.

Attention to Precedent in a Judicial Hierarchy
(with Thomas G. Hansford and James F. Spriggs, II)

Conditionally accepted at Journal of Law and Courts

Abstract Who controls the federal judicial agenda? Judicial agenda setting studies typically focus on the Supreme Court's agenda setting ability by considering individual case selection or attention to broad issue areas by the Court. We re-conceptualize the judicial agenda as attention to precedent and study the agenda setting ability of courts at all levels of the federal judicial hierarchy. We use decades of Supreme Court, appeals court, and district court citations to all Supreme Court cases decided between 1946 and 1986 to estimate a series of vector autoregression models that allow us to identify how each level of court initiates or responds to variation in the attention to a given precedent in other levels of court. The results reveal a new empirical regularity: while the Supreme Court may exert some top-down control of the federal judicial agenda, lower courts play an important role in influencing attention to precedent at the Court.

Working Papers

Explaining Confusion in the Law

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Abstract Judges, scholars, and commentators decry confusing areas of judicially created policy. This could hurt courts’ policy making efficacy, so why do judges allow it to happen? Existing accounts explain inconsistent decisions, but not inconsistent rule formulation. I show policy can become confusing when judges explain rules in more abstract terms than they decide cases. To do so, I expand standard case-space models of judicial decision making to account for relationships between specific facts and broader doctrinal dimensions. This model of judicial decision making as a process of multi-step reasoning reveals that preference aggregation in such a context can lead to inconsistent collegial rules. I also outline a class of preference configurations on collegial courts in which this problem cannot arise.

Ends Against the Middle: Scaling Votes when Ideological Opposites Behave the Same for Antithetical Reasons
(with Jacob Montgomery)

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Abstract Standard methods for measuring ideology from voting records assume that individuals at the ideological ends should never vote together in opposition to moderates. In practice, however, there are many times when individuals from both extremes vote identically but for opposing reasons. Both liberal and conservative justices may dissent from the same Supreme Court decision but provide ideologically contradictory rationales. In legislative settings, ideological opposites may join together to oppose moderate legislation in pursuit of antithetical goals. We introduce a scaling model that accommodates ends against the middle voting and provide a novel estimation approach that improves upon existing routines. We apply this method to voting data from the United States Supreme Court and Congress and show it outperforms standard methods in terms of both congruence with qualitative insights and model fit. We argue our proposed method represents a superior default approach for generating one-dimensional ideological estimates in many important settings.

Judicial Independence and Political Competition: Comparing Democracies Over Time
(with Joshua Boston and David Carlson)

Abstract Scholars of comparative courts have long been fascinated with variations in judicial independence across states, regimes, and time. Whether independence, in turn, depends on political competition remains an open question, as extant research has reached uncertain conclusions, often relying on questionable assumptions and data sources. This paper presents a formal model predicting the conditions under which legislative political competition causes a political power vacuum, which necessitates judicial independence and policy making. In short, when an ineffectual legislature cannot address a policy-seeker’s proposal, the courts can intervene, causing a *de facto* increase in judicial independence. Empirical results confirm these theoretically derived expectations, as aggregate measures of political competition across space and time cause significant changes in *de facto* judicial independence. Our findings have practical implications regarding when we might observe policy-seekers litigating issues rather than seeking legislation.