Abstract Coalition research increasingly emphasizes party-level explanations of coalition outcomes. However, this work does not account for the complex multilevel structure between parties and governments: many parties participate in multiple governments and governments often comprise multiple parties. In this paper, I show that this crisscrossing structure creates dependencies among observations both across and within governments. If ignored, these dependencies produce downward-biased uncertainty estimates that cluster-robust standard errors fail to fully correct. To address this issue, I then introduce a model that extends the Multiple Membership Multilevel Model to represent the multilevel structure of coalition government data. The model accounts for party-level dependencies across governments through party-specific effects in each coalition they join, and for dependencies within governments by representing the total party effect on a government as a weighted sum of its members’ contributions. By allowing party weights to vary with covariates describing their interrelationships, the model enables researchers to examine the interdependent nature of coalition outcomes. I validate the model through simulation and an empirical application to coalition government survival, showing that ignoring party-level dependencies can produce misleading conclusions at all levels of analysis. The model is estimated via Bayesian MCMC and implemented in the accompanying R package ‘bml’.

Abstract One of the most robust empirical findings in political science is that in multiparty democracies cabinet ministries are distributed in rough proportion to parties’ legislative seat shares, a pattern known as Gamson’s Law. Yet existing research often overlooks the fact that portfolio and seat shares are compositional—mutually dependent parts of a whole. Standard methods treat them as unconstrained, risking bias, misleading uncertainty estimates, and flawed inference. Unfortunately, the most common strategy for handling compositions—the additive log-ratio (ALR) transformation combined with seemingly unrelated regression (SUR)—fails when the number and identity of compositional elements (like parties) vary across cases. We propose the isometric log-ratio (ILR) transformation—new to political science—as an alternative that both respects compositional geometry and adapts to differing compositional structures. Monte Carlo simulations show that ILR sharply outperforms standard approaches, reducing bias, improving coverage probability, and increasing statistical power. While we apply it to portfolio allocation, ILR provides a general solution for modeling compositional outcomes with other potential uses, including in electoral competition, where ALR+SUR has required strong assumptions or ad hoc adjustments. Using this improved methodology, we find that seat–portfolio proportionality is weaker overall than conventionally reported and varies substantially across governments.

Anthony Crysler is a recent graduate of Seton Hall University. He earned his B.A. in Political Science in December 2024 and currently is a law clerk at Graves Andrews LLC in Morristown, New Jersey. This topic was briefly presented in Dr. Pallitto’s Fall 2024 Constitutional Law class which inspired his interest in this topic. Anthony also plans to attend law school in the fall. He has an interest in immigration law, which was another impetus for this paper

Abstract Online panels have become an important resource for research in political science, but the compensation offered to panelists incentivizes them to become “survey professionals,” raising concerns about data quality. We provide evidence on survey professionalism exploring three US samples of subjects who donated their browsing data, recruited via Lucid, YouGov, and Facebook (total $n = 3,886$ ). Survey professionalism is common, but varies across samples: by our most conservative estimate, we find 1.7% of respondents on Facebook, 7. $\color {black}6$ % on YouGov, and 34 $\color {black}.7$ % on Lucid to be professionals (under the assumption that professionals are as likely as non-professionals to donate data after conditioning on observable demographics available from all online survey takers). However, evidence that professionals lower data quality is limited: they do not systematically differ demographically or politically from non-professionals and do not exhibit more response instability. They are, however, somewhat more likely to speed, straightline, and attempt to take questionnaires repeatedly. To address potential selection issues in donating of browsing data, we present sensitivity analyses with lower bounds for survey professionalism. While concerns about professionalism are warranted, we conclude that survey professionals do not, by and large, distort inferences of research based on online panels.

Abstract In experimental social science, precise treatment effect estimation is of utmost importance, and researchers can make design choices to increase precision. Specifically, block-randomized and pre-post designs are promoted as effective means to increase precision. However, implementing these designs requires pre-treatment covariates, and collecting this information may decrease sample sizes, which in and of itself harms precision. Therefore, despite the literature’s recommendation to use block-randomized and pre-post designs, it remains unclear when to expect these designs to increase precision in applied settings. We use real-world data to demonstrate a counterintuitive result: precision gains from block-randomized or pre-post designs can withstand significant sample loss that may arise during implementation. Our findings underscore the importance of incorporating researchers’ practical concerns into existing experimental design advice.

Abstract If instant runoff voting (IRV) mitigates strategic voting, is that because the rules of the system mechanically reduce strategic opportunities, or because of other more indirect effects? In single-vote plurality elections, a voter can be pivotal if adding one vote to a candidate would cause that candidate to win. In IRV, it is more complicated to identify when one voter can be pivotal. This letter derives all the ways that a single ballot can change the result of an IRV election, for any number of candidates and voters. I obtain an expression for the probability of casting a pivotal vote in IRV by phrasing the probability that any pivotal event occurs as a function of all the rankings cast by other voters. This expression facilitates modeling vote choice in IRV, and enables the estimation of voters’ strategic opportunities in IRV contests between any number of candidates. I present some illustrative simulations estimating pivotal probabilities in both IRV and Single-Member District Plurality for stylized electorates with identical preference structures. These simulations produce similar estimated pivotal probabilities in the two systems, suggesting that these systems may provide similar opportunities to strategically cast a decisive vote.

Abstract Analysts often seek to compare representations in high-dimensional space, e.g., embedding vectors of the same word across groups. We show that the distance measures calculated in such cases can exhibit considerable statistical bias, that stems from uncertainty in the estimation of the elements of those vectors. This problem applies to Euclidean distance, cosine similarity, and other similar measures. After illustrating the severity of this problem for text-as-data applications, we provide and validate a bias correction for the squared Euclidean distance. This same correction also substantially reduces bias in ordinary Euclidean distance and cosine similarity estimates, but corrections for these measures are not quite unbiased and are (non-intuitively) bimodal when distances are close to zero. The estimators require obtaining the variance of the latent positions. We (will) implement the estimator in free software, and we offer recommendations for related work.

Abstract Confidence intervals are ubiquitous in the presentation of social science models, data, and effects. When several intervals are plotted together, one natural inclination is to ask whether the estimates represented by those intervals are significantly different from each other. Unfortunately, there is no general rule or procedure that would allow us to answer this question from the confidence intervals alone. It is well known that using the overlaps in 95% confidence intervals to perform significance tests at the 0.05 level does not work. Recent scholarship has developed and refined a set of tools for inferential confidence intervals that permit inference on confidence intervals with the appropriate type I error rate in many different bivariate contexts. These are all based on the same underlying idea of identifying the multiple of the standard error (i.e., a new confidence level) such that the overlap in confidence intervals matches the desired type I error rate. These procedures remain stymied by multiple simultaneous comparisons. We propose an entirely new procedure for developing inferential confidence intervals that decouples the testing and visualization that can overcome many of these problems in any visual testing scenario. We provide software in R and Stata to accomplish this goal.

Abstract We develop a new class of spatial voting models for binary preference data that can accommodate both monotonic and non-monotonic response functions, and are more flexible than alternative “unfolding” models previously introduced in the literature. We then use these models to estimate revealed preferences for legislators in the U.S. House of Representatives and justices on the U.S. Supreme Court. The results from these applications indicate that the new models provide superior complexity-adjusted performance to various alternatives and that the additional flexibility leads to preferences’ estimates that more closely match the perceived ideological positions of legislators and justices.

Abstract Political scientists commonly use Grambsch and Therneau’s (1994, Biometrika 81, 515–526) ubiquitous Schoenfeld-based test to diagnose proportional hazard violations in Cox duration models. However, some statistical packages have changed how they implement the test’s calculation. The traditional implementation makes a simplifying assumption about the test’s variance–covariance matrix, while the newer implementation does not. Recent work suggests the test’s performance differs, depending on its implementation. I use Monte Carlo simulations to more thoroughly investigate whether the test’s implementation affects its performance. Surprisingly, I find the newer implementation performs very poorly with correlated covariates, with a false positive rate far above 5%. By contrast, the traditional implementation has no such issues in the same situations. This shocking finding raises new, complex questions for researchers moving forward. It appears to suggest, for now, researchers should favor the traditional implementation in situations where its simplifying assumption is likely met, but researchers must also be mindful that this implementation’s false positive rate can be high in misspecified models.