How Should We Understand Alliance Formation in a Multilateral World?

For several decades, bilateral modeling has been the central tool in much of the theoretical and empirical research on alliance formation. Theoretical investigations into alliance formation were traditionally rooted in dyadic game-theoretical frameworks that feature two primary parties. For example, these models might examine the trade-off of an alliance relationship where a weaker party gains security while ceding policy autonomy to a stronger party. Empirical research has also concentrated almost exclusively on pairs of states when designing research and testing hypotheses pertaining to alliance formation because this framework is favorable in formalizing arguments.

However, alliances cannot always be assumed to be bilateral given that international relations take place in a multilateral context. According to data from the Alliance Treaty Obligations and Provisions (ATOP), between 1815 and 2003 approximately 90 percent of bilateral alliances were formed through a multilateral pact. With the dominance of bilateral studies, this fact has received far less appreciation than it deserves. A recent study by Fordham and Poast states the need for international relations research on alliance formation to focus on a multilateral, rather than bilateral process. Because theoretical concepts and arguments made under dyadic models do not accurately reflect multilateral circumstances, dyadic analytical approaches fall short in terms of providing a complete understanding of many real-life instances of multilateral alliance formation.

Indeed, because alliances can involve more than two members, they often originate from a multilateral context. The formation of an alliance may hinge on the inclusion or exclusion of a particular entity; thus, an alliance might not make sense without considering the involvement of other parties. By redefining alliances to have originated from a multilateral process, the authors revisit the various influences on alliance formation. In particular, they reevaluate William Riker’s size principle, which states that politicians form optimal-size winning coalitions to maximize their respective votes. The authors find that the size principle is also applicable to military alliances.

Riker’s size principle suggests answers to questions that can only be tested in a multilateral framework: How much power should prospective allies contribute to an alliance? Should the alliance continue to add allies to escalate its total military capabilities? To what extent should the alliance aggregate military power? These questions insinuate that alliances should lead to an optimal level of aggregate capabilities and curb their expansion from that point onward. The underlying rationale lies in a simple claim that applies to any coalition where participants must distribute a finite stream of benefits: having more members implies that each receives a smaller share of the benefits. In other words, powerful coalitions should not invite additional allies when they add little or nothing to the probability of victory since they would diminish the benefits each member receives. In the case where additional members decrease the probability of victory, the expected benefits to each member will surely decline. Thus, the notion of “strength in numbers” does not always apply; coalitions that hold enough power should not invite additional members.

Bearing in mind a multilateral setting, the authors conduct a set of statistical tests to determine the optimal level of total capabilities as it relates to the high likelihood of alliance formation. Using a dataset containing ATOP data which captures alliance formation as well as the total Composite Index of National Capabilities (CINC) score, the authors first demonstrate that the probability of alliance formation is represented as a bell-shaped curve in terms of the coalition’s aggregate capabilities, with a single peak at a certain level of the combined power. The CINC score consists of military, economic, and demographic measures to represent national capabilities. As of 2012, the U.S., China, and Russia have values of around 0.14, 0.22 and 0.04, respectively.

The black curve in Figure 1 below illustrates the probability that alliance formation increases as the aggregate capabilities in the coalition rise, holding only until a CINC score of 0.30. Beyond this peak, the probability of alliance formation decreases gradually, implying that 0.30 is more or less the optimal level of total power in alliance formation that will maximize each signatory’s benefits from the alliance.

The authors additionally assumed that factors like diversity in interests, similarity in foreign policy, commonalities in the type of regime, threats facing the potential coalition, and the number of total states will be positively correlated to the probability of alliance formation, whereas geographic distance will be negatively correlated. By controlling for these “heterogeneous” factors, the authors model how these elements affect prospective allies. As compared to the black curve, the blue curve indicates that these heterogeneous elements affect the probability of alliance formation, but do not alter the total CINC score associated with the highest estimated probability of alliance formation. In other words, the peak of the probability of alliance formation still corresponds to 0.30 in total CINC, even while the entire curve becomes flatter. The heterogeneity considerations do have an impact on alliance formation but are all far less influential than aggregate power, which is often left out of dyadic studies on alliance formation. Combined, the two results suggest that there exists a certain level of aggregate capabilities in a group of allied states that maximizes their respective benefits from forming an alliance.

Because the prediction about the relationship between aggregate capabilities and alliance formation cannot be achieved in a dyadic, bilateral scheme, Riker’s statement about the role of power has garnered far less attention in contemporary studies on international relations than it perhaps should. Relative to the size principle, the authors find evidence that overwhelmingly large coalitions cannot exist in the global political system. The probability of forming an alliance is maximized when the total power of the alliance reaches a peak level, with much stronger and much weaker alliances being less likely to form. Since these findings could not have been achieved using a dyadic design, this study suggests that future research make the necessary switch in logic from a bilateral to a multilateral context. Unless alliance formation can be understood in a multilateral setting, any underlying rationale would remain incomplete.

Article source: Fordham, Benjamin, and Paul Poast. “All Alliances Are Multilateral: Rethinking Alliance Formation.” Journal of Conflict Resolution 60, no. 5 (2016): 840-865.

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