I analyze a model of electoral competition with entry under the run-off rule. I consider both two- and multiple-party systems. The principal result is that two-party systems may prove stable under the run-off rule: I show that a continuum of equilibria exists in which only two parties enter and subsequent entry is deterred. This finding conflicts with the accepted wisdom on the run-off rule encapsulated by Duverger's Hypothesis. The results of the model are then reconciled with Duverger's Hypothesis and a more precise formulation is proposed.

Political parties are active when citizens choose among candidates in elections and when winning candidates choose among policy alternatives in government. But the inextricably linked institutions, incentives, and behavior that determine these multistage choices are substantively complex and analytically unwieldy, particularly if modeled explicitly and considered in total, from citizen preferences through government outcomes. To strike a balance between complexity and tractability, we modify standard spatial models of electoral competition and governmental policy-making to study how components of partisanship—such as candidate platform separation in elections, party ID-based voting, national partisan tides, and party-disciplined behavior in the legislature—are related to policy outcomes. We define partisan bias as the distance between the following two points in a conventional choice space: the ideal point of the median voter in the median legislative district and the policy outcome selected by the elected legislature. The study reveals that none of the party-in-electorate conditions is capable of producing partisan bias independently. Specified combinations of conditions, however, can significantly increase the bias and/or the variance of policy outcomes, sometimes in subtle ways.

List-based samples are often biased because of coverage errors. The problem is especially acute in societies where the level of internal migration is high and where record keeping on the population is not reliable. We propose a solution based on spatial sampling that overcomes the inability to reach migrants in traditional area samples based on household lists. A comparison between a traditional study and our sample of Beijing demonstrates that coverage bias is greatly reduced. The successful incorporation of mobile urban residents has important substantive effects, in both univariate and multivariate analyses of public opinion data.

The use of multilevel models—models in which lower-level (“micro”) units are nested within higher-level (“macro”) units—has blossomed recently in political science. Possible relationships in such models include macro variables influencing macro variables; micro variables influencing micro variables; macro variables influencing micro variables, and vice versa; and often most interestingly, micro-micro relationships varying interactively with macro variables. Most work in political science has drawn on the useful introductions of Raudenbush and Bryk (2002), Western (1998), and Steenbergen and Jones (2002). We refer readers to good general introductions/reviews of multi-level modeling in the articles in this issue by Bowers and Drake and by Franzese.

Interest in social capital has grown as it has become apparent that it is an important predictor of collective well-being. Recently, attention has shifted to how levels of social capital have changed over time. But better measures are required to test even basic hypotheses such as establishing the direction of causality between the two components of social capital. In the following analysis, I develop macro measures of social capital through the development of longitudinal measures of civic engagement and interpersonal trust. I use these measures to test basic assumptions about social capital. The result is not only the first over time measures of social capital, but also an increase in our understanding of social capital as a macro process with complex causes and effects.

Experiments conducted in the field allay concerns over external validity but are subject to the pitfalls of fieldwork. This article proves that scalable protocols conserve statistical efficiency in the face of problems implementing the treatment regime. Three designs are considered: randomly ordering the application of the treatment; matching subjects into groups prior to assignment; and placebo-controlled experiments. Three examples taken from voter mobilization field experiments demonstrate the utility of the design principles discussed.

In this article I use linguistic fuzzy-set theory to analyze the process of decision making in politics. I first introduce a number of relevant elements of (numerical and linguistic) fuzzy-set theory that are needed to understand the terminology as well as to grasp the scope and depth of the approach. I then explicate a linguistic fuzzy-set approach (LFSA) to the process of decision making under conditions in which the decision makers are required to simultaneously satisfy multiple criteria. The LFSA approach is illustrated through a running (hypothetical) example of a situation in which state leaders need to decide how to combine trust and power to make a choice on security alignment.

Nearly all hierarchical linear models presented to political science audiences are estimated using maximum likelihood under a repeated sampling interpretation of the results of hypothesis tests. Maximum likelihood estimators have excellent asymptotic properties but less than ideal small sample properties. Multilevel models common in political science have relatively large samples of units like individuals nested within relatively small samples of units like countries. Often these level-2 samples will be so small as to make inference about level-2 effects uninterpretable in the likelihood framework from which they were estimated. When analysts do not have enough data to make a compelling argument for repeated sampling based probabilistic inference, we show how visualization can be a useful way of allowing scientific progress to continue despite lack of fit between research design and asymptotic properties of maximum likelihood estimators.

In recent years, large sets of national surveys with shared content have increasingly been used for cross-national opinion research. But scholars have not yet settled on the most flexible and efficient models for utilizing such data. We present a two-step strategy for such analysis that takes advantage of the fact that in such datasets each “cluster” (i.e., country sample) is large enough to sustain separate analysis of its internal variances and covariances. We illustrate the method by examining a puzzle of comparative electoral behavior—why does turnout decline rather than increase with the number of parties competing in an election (Blais and Dobryzynska 1998, for example)? This discussion demonstrates the ease with which a two-step strategy incorporates confounding variables operating at different levels of analysis. Technical appendices demonstrate that the two-step strategy does not lose efficiency of estimation as compared with a pooling strategy.

In this article, I use geographic information systems to develop a continuous measure of district continuity and change following the 2000–02 congressional redistricting cycle. The new measure provides details of where the new population in a district came from and how the old population was distributed within new districts. This measure is then used to demonstrate the independent and interactive influence of district change on competition for congressional elections.

A common problem in models for dichotomous dependent variables is “separation,” which occurs when one or more of a model's covariates perfectly predict some binary outcome. Separation raises a particularly difficult set of issues, often forcing researchers to choose between omitting clearly important covariates and undertaking post—hoc data or estimation corrections. In this article I present a method for solving the separation problem, based on a penalized likelihood correction to the standard binomial GLM score function. I then apply this method to data from an important study on the postwar fate of leaders.

Voting rights litigation requires ecological inference to estimate the voting preferences of minority and nonminority groups within the electorate. Double regression has been the procedure most commonly employed for this purpose. This article presents the first formal examination of this procedure. The underlying structural model reveals that double regression estimators are neither unbiased nor consistent estimators of true within-group vote preferences or polarization. Simulations demonstrate that they can substantially exaggerate the differences between minority and nonminority vote choices when none are present, and dramatically understate them when differences exist. In sum, double regression cannot meet conventional statistical standards for reliability. Consequently, it should be abandoned.

Logistic regression models have been used in political science for estimating ideal points of legislators and Supreme Court justices. These models present estimation and identifiability challenges, such as improper variance estimates, scale and translation invariance, reflection invariance, and issues with outliers. We address these issues using Bayesian hierarchical modeling, linear transformations, informative regression predictors, and explicit modeling for outliers. In addition, we explore new ways to usefully display inferences and check model fit.

Gordon and Smith (2004) do a great service by introducing innovative and creative quantitative methods that incorporate information from qualitative sources. It is nevertheless important to examine the conditions under which the proposed estimators will be useful in practice. These conditions prove to be surprisingly restrictive: with the possible exception of extremely low-information settings, virtually all of the cases of discernible causation must be coded as such, those codings must contain virtually no errors, and the process by which qualitative researchers produce evaluations of discernibility must conform to the authors' model of the qualitative data-generating process (QDGP) if the procedures are to retain any comparative advantage.

Of necessity, many tests for political influence on policies or outcomes involve the use of dummy variables. However, it is often the case that the hypothesis against which the political dummies are tested is the null hypothesis that the intercept is otherwise constant throughout the sample. This simple null can cause inference problems if there are (nonpolitical) intercept shifts in the data and the political dummies are correlated with these unmodeled shifts. Here we present a method for more rigorously testing the significance of political dummy variables in single equation models estimated with time series data. Our method is based on recent work on detecting multiple regime shifts by Bai and Perron. The article illustrates the potential problem caused by an overly simple null hypothesis, exposits the Bai and Perron model, gives a proposed methodology for testing the significance of political dummy variables, and illustrates the method with two examples.

Researchers often use as dependent variables quantities estimated from auxiliary data sets. Estimated dependent variable (EDV) models arise, for example, in studies where counties or states are the units of analysis and the dependent variable is an estimated mean, proportion, or regression coefficient. Scholars fitting EDV models have generally recognized that variation in the sampling variance of the observations on the dependent variable will induce heteroscedasticity. We show that the most common approach to this problem, weighted least squares, will usually lead to inefficient estimates and underestimated standard errors. In many cases, OLS with White's or Efron heteroscedastic consistent standard errors yields better results. We also suggest two simple alternative FGLS approaches that are more efficient and yield consistent standard error estimates. Finally, we apply the various alternative estimators to a replication of Cohen's (2004) cross-national study of presidential approval.

Can researchers draw consistent inferences about the U.S. public's issue attitudes when studying survey results from both the in-person and telephone interview modes of the 2000 National Election Studies (NES) survey? We address this question through an analysis contrasting the distribution of issue attitudes across modes in the dual sample design of the 2000 NES. We find clear differences across mode even when applying a method devised by the NES to improve comparability by recoding issue attitude scales from the in-person mode. We present an alternative method of recoding these scales, which substantially improves comparability between modes. Through an analysis of the covariance structure of the issues and simple models of vote choice, we discuss the implications of the results for the study of issue attitudes in the 2000 NES.

We discuss the motivation for integrating qualitative information in statistical models of complex, partially observable causal mechanisms and suggest ways to minimize the dangers posed by Braumoeller and Kirpichevsky. We stress the importance of linking our statistical estimators to underlying theories of the data generating process, qualitative or otherwise.

This paper develops and tests arguments about how national-level social and institutional factors shape the propensity of individuals to form attachments to political parties. Our tests employ a two-step estimation procedure that has attractive properties when there is a binary dependent variable in the first stage and when the number of second-level units is relatively small. We find that voters are most likely to form party attachments when group identities are salient and complimentary. We also find that institutions that assist voters in retrospectively evaluating parties—specifically, strong party discipline and few parties in government—increase partisanship. These institutions matter most for those individuals with the fewest cognitive resources, measured here by education.

This article reconciles conflicting accounts of Gauss-Markov conditions, which specify when ordinary least squares (OLS) estimators are also best linear unbiased (BLU) estimators. We show that exogeneity constraints that are commonly assumed in econometric treatments of the Gauss-Markov theorem are unnecessary for OLS estimates of the classical linear regression model to be BLU. We also generalize a set of necessary and sufficient conditions first established by McElroy (1967, Journal of the American Statistical Association 62:1302–1304), but not yet generally recognized in the econometric literature, that are appropriate for many political science applications. McElroy's conditions relax the traditional Gauss-Markov restriction on autocorrelation in the errors to allow a type of correlation, exchangeability, that has two desirable characteristics: (1) exchangeable data occur in a potentially important class of political science models, and (2) the form of autocorrelation that occurs in exchangeable data has a ready intuition. We thus show that a common class of sample selection models that does not satisfy the Gauss-Markov conditions specified in econometrics textbooks is, in fact, BLU under OLS estimation.