Toward a Network Theory of Alliance Formation

Abstract

We propose a network-based theory of alliance formation. Our theory implies that, in addition to key state and dyad attributes already established in the literature, the evolution of the alliance network from any given point in time is largely determined by its structure. Specifically, we argue that closed triangles in the alliance network—where i is allied with j is allied with k is allied with i — produce synergy effects in which state-level utility is greater than the sum of its dyadic parts. This idea can be generalized to n-state closure, and, when considered along with factors that make dyadic alliance formation more attractive, such as military prowess and political compatibility, suggests that the network will evolve toward a state of several densely connected clusters of states with star-like groupings of states as an intermediary stage. To evaluate our theory, we use the temporal exponential random graph model and find that the roles of our network effects are robustly supported by the data, whereas the effects of non-network parameters vary substantially between periods of recent history. Our results indicate that network structure plays a greater role in the formation of alliance ties than has been previously understood in the literature.

Keywords:

• alliance formation
• alliances
• endogenous dependencies
• exponential random graph models (ERGMs)
• networks

Acknowledgments

The authors thank James Fowler, Justin Gross, Mark Pickup, Randolph Siverson, and Tom Snijders for helpful comments. Replication data are available at http://dvn.iq.$$$$harvard.edu/dvn/dv/internationalinteractions.

Notes

¹It makes little sense for states to enter into alliances if they do not expect fruitful and reliable cooperation; there is evidence to suggest that states consider the reputations for reliability of prospective allies in the alliance formation process (Crescenzi et al., forthcoming, 2012; Downs, Rocke and Barsoom 1996; Gibler 2008; Leeds 1999; Miller 2003) and rivals consider the reliability of a state's allies before initiating hostile action (Gartner and Siverson 1996; Smith 1996). Leeds, Long, and Mitchell (2000) suggest that most promises are honored, that democracies are more reliable partners than autocracies (see Leeds 1999;see Gartzke and Gleditsch 2004 for a challenge to this finding), and failures to honor alliances are generally produced by major changes in the structures of governments or when the costs of reneging are especially low (Leeds 2003).

²Note however, that such an argument is not antithetical to the idea of political compatibility: it simply suggests that the presence of a common threat may lower the threshold for basic political compatibility, if only temporarily. An obvious example of this are the World War II alliances between communist and capitalist states in order to counter the common foe of fascist states.

³We should also emphasize that we have limited ourselves theoretically (and empirically below) to defensive alliances (offensive alliances are quite rare historically, particularly since the infamous “blank check” Germany provided to Austria-Hungary at the opening of World War I), thus negating any obligation of allied states to support an ally who comes into conflict as a result of its own antagonism and limiting a given state's exposure to unwanted conflicts to the case in which one of its allies is attacked without alliance-voiding provocation.

⁴We are forced to restrict our analysis to the period after World War I because of data limitations. Prior to World War I, the sparsity of the alliance network is such that reliable statistical inferences cannot be drawn. Said more simply, there is too little variation in alliances prior to World War I for reasonable statistical inference. Additionally, as Achen (2002, 2005) points out, there is a great deal of causal heterogeneity over such long time periods that would be difficult to control for in a statistical analysis. The fact that the data are so sparse prior to World War I suggests a very different set of causes may be at work in that time period. To combine such distinct samples into a single sample is to invite a host of statistical problems into our model.

⁵See Gilpin (1981) and Organski (1968) for seminal theories suggesting unipolar stability and Waltz (1979) for a seminal theory suggesting unipolar instability.

⁶ Duncan and Siverson (1982) used a data set expanded from Singer and Small's (1967) original alliance data and was restricted to major powers only.

⁷A detailed technical review of the TERGM is beyond the scope of the present discussion. See original work by Hanneke, Fu, and Xing (2010) and reviews by Cranmer and Desmarais (2011)and Desmarais and Cranmer (2012) for technical details.

⁸We note one additional common misperception about SIENA vis-a-vis ERGM. Snijders (2001) derives a model whereby the network evolves by one actor changing the network by one tie at a time.When an actor has the opportunity to change a tie, a change (including the option of no change) is selected, with some error, to optimize an “objective function.” In the literature on political networks, this is often characterized as a “utility function” in the game-theoretic sense. The objective function that is optimized in SIENA is defined on the entire network and is proportional to the loglikelihood in the ERGM. It is misleading to interpret this objective function as an actor-specific utility function in that each actor derives the exact same utility from the creation or dissolution of a particular tie in the network—the change in the network-level objective function. Though Snijders (2001) provides a useful framework for the actor-level decomposition of a dynamic process that results in an ERGM-like network distribution, it is not analogous to the equilibrium of actor-specific stochastic utility maximization.

⁹Autocorrelation in the conflict network is greater than 0.7 when estimated by dyad-year GEE logistic regression.

¹⁰For the sake of robustness with respect to our measurement of political compatibility, we ran a model to which we added the measure of interstate policy “Interest Similarity” from Gartzke and Hewitt (2010). This measure is derived from the similarity of voting records in the United Nations General Assembly. Including it changes the coefficients on the other terms in the model very little, and does not in any way alter the substantive conclusions derived from the results. The results including the U.N. vote similarity measure are available from the authors upon request.

¹¹This statistic is measured as, , where POLITY is defined as the difference between autocracy and democracy scores of a country and is a dummy variable coded one if two countries dissolved a tie and zero otherwise.