Complex Dependencies in the Alliance Network

The multifaceted and strategic interactions inherent in the formation of international military pacts render the alliance decisions of states highly interdependent. Our aim here is to model the network of alliances in such a way as to capture the effects of covariates and account for the complex dependencies inherent in the network. Regression analysis, due to its foundational assumption of conditional independence, cannot be used to analyze alliance decisions specifically and interdependent decisions generally. We demonstrate how alliance decisions are interdependent and define the problems associated with the regression analysis of nonindependent dyads. We then show that alliances can naturally be conceived of as constituting a network, where alliance formation is an inherently interdependent process. We proceed by introducing the exponential random graph model for analyzing interdependence in the alliance network and estimating the effect of covariates on alliances. The inherent complexity of alliance relationships presents analysts of international politics with an equally complex task in thoroughly explaining the realizations of these relationships. We argue that the study of interdependent processes like alliance formation are complicated both theoretically and empirically by the fact that states account for the behaviors of other states when determining their own behaviors. In other words, if states consider the alliance relationships of other states when deciding whether and how to adjust their alliance portfolios, then both our theories and our empirical tests must account for that consideration. While theoretical work has examined the interdependent nature of alliances for some time, the empirical study of alliances has lagged behind because of a lack of empirical tools for testing and accounting for the interdependent nature of alliance links. The existing empirical tool that, for lack of a better alternative, has been widely used is regression with a relational (dyadic) variable as the outcome. Regression analysis – counter to many of the substantive theories in the field – treats individual relationships between states as conditionally independent. This causes two closely related problems: (1) because the theoretical story represented by the empirical model is inaccurate, misspecification bias is induced and (2) confidence intervals are too small because of the smaller number of independent observations under study than the number assumed in the regression modeling process. Our aim is to address a substantial empirical challenge facing the study of alliances: explaining one or more alliances with reference to one or more of the other alliances extant in the international system, all while accounting for important state and dyad level covariates. We show that if the international system is treated as a network of nations, both theoretically and empirically, then the major problems with regression on the dyad can be resolved without abandoning the ability to estimate the effect of covariates on the individual alliances embedded in the network. We demonstrate our approach in the context of alliances, but the problems and solutions we discuss are by no means restricted to the study of alliances, but rather can easily be applied to international conflict (see e.g. Cranmer and Desmarais