The symposium develops statistical models and methods for the study of path dependence. In this introductory essay, the connections between key areas in the path dependence and statistical literatures are illuminated. And some ways in which familiar time series and regression models embody these ideas are explained. The arguments in the articles in the symposium then are summarized and compared. Finally, directions for additional, statistically grounded research on path dependence are discussed.

In this article, we define a class of revised path—dependent processes and characterize their basic properties. A process exhibits revised-path dependence if the current outcome can revise the value of a past outcome. A revision could be a change to that outcome or a reinterpretation. We first define a revised path—dependent process called the accumulation process: in each period, a randomly chosen past outcome is changed to match the current outcome and show that it converges to identical outcomes. We then construct a general class of models that includes the Bernoulli process, the Polya process, and the accumulation process as special cases. For this general class, we show that, apart from knife-edge cases, all processes converge either to homogeneous equilibria or to an equal probability distribution over types. We also show that if random draws advantage one outcome over the other, then the process has a unique equilibrium.

Path dependence is commonly used to describe processes where “history matters,” which encompasses many different kinds of temporal dynamics. This essay distinguishes path-, or equilibrium-, dependent processes where early conditions continue to matter, from outcome-dependent processes where recent history matters and from outcome-independent processes where history does not matter. Others have argued for a precise and restrictive definition of path dependence. We build on this and distinguish among different types of outcome-dependent processes when these conditions for path dependence are not fully satisfied.

Spatial interdependence—the dependence of outcomes in some units on those in others—is substantively and theoretically ubiquitous and central across the social sciences. Spatial association is also omnipresent empirically. However, spatial association may arise from three importantly distinct processes: common exposure of actors to exogenous external and internal stimuli, interdependence of outcomes/behaviors across actors (contagion), and/or the putative outcomes may affect the dimensions along which the clustering occurs (selection). Accurate inference about any of these processes generally requires an empirical strategy that addresses all three well. From a spatial-econometric perspective, this suggests spatiotemporal empirical models with exogenous covariates (common exposure) and spatial lags (contagion), with the spatial weights being endogenous (selection). From a longitudinal network-analytic perspective, the same three processes are identified as potential sources of network effects and network formation. From that perspective, actors' self-selection into networks (by, e.g., behavioral homophily) and actors' behavior that is contagious through those network connections likewise demands theoretical and empirical models in which networks and behavior coevolve over time. This paper begins building such models by, on theoretical side, extending a Markov type-interaction model to allow endogenous tie-formation, and, on empirical side, merging a simple spatial-lag logit model of contagious behavior with a simple p*-logit model of network formation. One interesting consequence of network-behavior coevolution—identically, endogenous patterns of spatial interdependence—emphasized here is how it can produce history-dependent political dynamics, including equilibrium phat and path dependence (Page 2006). The paper concludes with an illustrative application to alliance formation and conflict behavior among the great powers in the first half of the twentieth century.

The concept of electoral competition is relevant to a variety of research agendas in political science, yet the question of how to measure electoral competition has received little direct attention. We revisit the distinction proposed by Giovanni Sartori between competition as a structure or rule of the game and competitiveness as an outcome of that game and argue that to understand which elections can be lost (and therefore when parties and leaders are potentially threatened by electoral accountability), scholars may be better off considering the full range of elections where competition is allowed. We provide a data set of all national elections between 1945 and 2006 and a measure of whether each election event is structured such that the competition is possible. We outline the pitfalls of other measures used by scholars to define the potential for electoral competition and show that such methods can lead to biased or incomplete findings. The new global data on elections and the minimal conditions necessary for electoral competition are introduced, followed by an empirical illustration of the differences between the proposed measure of competition and existing methods used to infer the existence of competition.

Is it possible to detect manipulation by looking only at electoral returns? Drawing on work in psychology, we exploit individuals' biases in generating numbers to highlight suspicious digit patterns in reported vote counts. First, we show that fair election procedures produce returns where last digits occur with equal frequency, but laboratory experiments indicate that individuals tend to favor some numerals over others, even when subjects have incentives to properly randomize. Second, individuals underestimate the likelihood of digit repetition in sequences of random integers, so we should observe relatively few instances of repeated numbers in manipulated vote tallies. Third, laboratory experiments demonstrate a preference for pairs of adjacent digits, which suggests that such pairs should be abundant on fraudulent return sheets. Fourth, subjects avoid pairs of distant numerals, so those should appear with lower frequency on tainted returns. We test for deviations in digit patterns using data from Sweden's 2002 parliamentary elections, Senegal's 2000 and 2007 presidential elections, and previously unavailable results from Nigeria's 2003 presidential election. In line with observers' expectations, we find substantial evidence that manipulation occurred in Nigeria as well as in Senegal in 2007.

Empirical researchers studying party systems often struggle with the question of how to count parties. Indexes of party system fragmentation used to address this problem (e.g., the effective number of parties) have a fundamental shortcoming: since the same index value may represent very different party systems, they are impossible to interpret and may lead to erroneous inference. We offer a novel approach to this problem: instead of focusing on index measures, we develop a model that predicts the entire distribution of party vote-shares and, thus, does not require any index measure. First, a model of party counts predicts the number of parties. Second, a set of multivariate t models predicts party vote-shares. Compared to the standard index-based approach, our approach helps to avoid inferential errors and, in addition, yields a much richer set of insights into the variation of party systems. For illustration, we apply the model on two data sets. Our analyses call into question the conclusions one would arrive at by the index-based approach. Software is provided to implement the proposed model.

In recent years, a consensus has developed that the conditional logit (CL) model is the most appropriate strategy for modeling government choice. In this paper, we reconsider this approach and make three methodological contributions. First, we employ a mixed logit with random coefficients that allows us to take account of unobserved heterogeneity in the government formation process and relax the independence of irrelevant alternatives (IIA) assumption. Second, we demonstrate that the procedure used in the literature to test the IIA assumption is biased against finding IIA violations. An improved testing procedure reveals clear evidence of IIA violations, indicating that the CL model is inappropriate. Third, we move beyond simply presenting the sign and significance of model coefficients, suggesting various strategies for interpreting the substantive influence of variables in models of government choice.