The uncovered set has frequently been proposed as a solution concept for majority rule settings. This paper tests this proposition using a new technique for estimating uncovered sets and a series of experiments, including five-player computer-mediated experiments and 35-player paper-format experiments. The results support the theoretic appeal of the uncovered set. Outcomes overwhelmingly lie in or near the uncovered set. Furthermore, when preferences shift, outcomes track the uncovered set. Although outcomes tend to occur within the uncovered set, they are not necessarily stable; majority dominance relationships still produce instability, albeit constrained by the uncovered set.

Analysts of cluster-randomized field experiments have an array of estimation techniques to choose from. Using Monte Carlo simulation, we evaluate the properties of point estimates and standard errors (SEs) generated by ordinary least squares (OLS) as applied to both individual-level and cluster-level data. We also compare OLS to alternative random effects estimators, such as generalized least squares (GLS). Our simulations assess efficiency across a variety of scenarios involving varying sample sizes and numbers of clusters. Our results confirm that conventional OLS SEs are severely biased downward and that, for all estimators, gains in efficiency come mainly from increasing the number of clusters, not increasing the number of individuals within clusters. We find relatively minor differences across alternative estimation approaches, but GLS seems to enjoy a slight edge in terms of the efficiency of its point estimates and the accuracy of its SEs. We illustrate the application of alternative estimation approaches using a clustered experiment in which Rock the Vote TV advertisements were used to encourage young voters in 85 cable TV markets to vote in the 2004 presidential election.

Increasingly, political science researchers are turning to Markov chain Monte Carlo methods to solve inferential problems with complex models and problematic data. This is an enormously powerful set of tools based on replacing difficult or impossible analytical work with simulated empirical draws from the distributions of interest. Although practitioners are generally aware of the importance of convergence of the Markov chain, many are not fully aware of the difficulties in fully assessing convergence across multiple dimensions. In most applied circumstances, every parameter dimension must be converged for the others to converge. The usual culprit is slow mixing of the Markov chain and therefore slow convergence towards the target distribution. This work demonstrates the partial convergence problem for the two dominant algorithms and illustrates these issues with empirical examples.

This paper develops a procedure for locating proposals and legislators in a multidimensional policy space by applying agenda-constrained ideal point estimation. Placing proposals and legislators on the same scale allows an empirical test of the predictions of the spatial voting model. I illustrate this procedure by testing the predictive power of the uncovered set—a solution concept of the multidimensional spatial voting model—using roll call data from the U.S. Senate. Since empirical tests of the predictive power of the uncovered set have been limited to experimental data, this is the first empirical test of the concept's predictive power using real-world data.

Although political methodologists are well aware of measurement issues and the problems that can be created, such concerns are not always front and center when we are doing substantive research. Here, we show how choices in measuring legislative preferences have influenced our understanding of what determines legislative outputs. Specifically, we replicate and extend Binder's highly influential analysis (Binder, Sarah A. 1999. The dynamics of legislative gridlock, 1947–96. American Political Science Review 93:519–33; see also Binder, Sarah A. 2003. Stalemate: Causes and consequences of legislative gridlock. Washington, DC: Brookings Institution) of legislative gridlock, which emphasizes how partisan, electoral, and institutional characteristics generate major legislative initiatives. Binder purports to show that examining the proportion, rather than the absolute number, of key policy proposals passed leads to the inference that these features, rather than divided government, are crucial for explaining gridlock. However, we demonstrate that this finding is undermined by flaws in preference measurement. Binder's results are a function of using W-NOMINATE scores never designed for comparing Senate to House members or for analyzing multiple Congresses jointly. When preferences are more appropriately measured with common space scores (Poole, Keith T. 1998. Recovering a basic space from a set of issue scales. American Journal of Political Science 42:964–93), there is no evidence that the factors that she highlights matter.

Chiou and Rothenberg raise important questions about how to measure key concepts in the study of legislative stalemate in the U.S. Congress. In challenging my choice of measures to capture bicameral differences, Chiou and Rothenberg argue that my findings are the artifact of measurement error. In this reply, I review the hurdles involved in measuring policy views over time and across institutions and suggest that the preferred measure of Chiou and Rothenberg falls short for measuring bicameral differences. Second, I assess the extent to which measurement choices affect the robustness of my findings about the determinants of gridlock. Drawing on new measures and model specifications, I show that my results are robust to alternative specifications. I conclude with an assessment of the broader challenges posed by how we measure critical concepts in the study of congressional performance.

Binder (n.d., Taking the measure of Congress: Reply to Chiou and Rothenberg. Political Analysis. Forthcoming) highlights areas of agreement and disagreement with our discussion of preference measurement and legislative gridlock. We now both agree that W-NOMINATE scores—employed in Binder (1999, The dynamics of legislative gridlock. American Political Science Review 9:519–33) to measure key independent variables, including bicameral differences—should not be used when examining multichamber legislatures over time. We continue to disagree over whether Common Space scores or Binder's conference vote measure is superior. In this response, we show that, although several of the theoretical and statistical objections that Binder (n.d.) raises to our Common Space measure do not apply, they are all relevant for her conference vote analog. Additionally, we detail how, despite protests to the contrary, the conference vote measure is plagued by insufficient data. Finally, we demonstrate how new efforts to show that Binder's (1999) results continue to hold are not robust.