States form defensive military alliances to enhance their security in the face of potential or realized interstate conflict. The network of these international alliances is increasingly interconnected, now linking most of the states in a complex web of ties. These alliances can be used both as a tool for securing cooperation and to foster peace between direct partners. However, do indirect connections—such as the ally of an ally or even further out in the alliance network—result in lower probabilities of conflict? We investigate the extent to which military alliances produce peace between states that are not directly allied. We find that the peacemaking horizon of indirect alliances extends through the network up to three degrees of separation. Within this horizon of influence, a lack of decay in the effect of degrees of distance indicates that alliances do not diminish with respect to their ability to affect peace regardless of whether or not the states in question are directly allied. Beyond the three-degree horizon of influence, we observe a sharp decline in the effect of indirect alliances on bilateral peace. Further investigation reveals that the community structure of the alliance network plays a role in establishing this horizon, but the effects of indirect alliances are not spurious to the community structure.

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INTRODUCTION

The tendency of political organizations to ally likely dates back to the earliest permanent human settlements and certainly predates the modern political state by at least two millennia (1). The formation of modern military alliances is multifaceted: States ally to counter common threats, to bolster one another’s security, and even to help facilitate peace between potential rivals (2, 3). Military alliances are typically understood as a tool for securing defensive cooperation and fostering peace between direct allies (4–9). Despite the long history of the practice of forming alliances, the effect of the alliance network’s structure on bilateral peace is poorly understood.

The past century has seen the advent of alliances meant to exist in times of peace as well as war, and the corresponding increase in the interconnectedness of the alliance network has been dramatic. The system has gone from 8 individual alliance ties in 1900 to 1115 in 2000, including bilateral and multilateral defense pacts.

Much research has shown that allies are less likely to fight one another (6, 10), but we lack any understanding of higher-order effects. That is, are states whose only connection is a common ally—those separated by two degrees—less likely to fight? What about pairs connected at three or more degrees? To answer this question, we examine the conflict propensities of indirectly allied states through the concept of path length. Within the alliance networks, direct allies have a path length of one degree, the allies of allies have a path length of two degrees, and so on (fig. S1 and tables S1 to S3). That is, if state i is allied to j, j is allied to k, and k is allied with l, then the path length between i and l is three. Figure 1 shows the concept of distance in a network—the shortest number of links required to connect one state to another—and the focal question of bilateral conflict.

Fig. 1 Illustration of degrees of separation in the alliance network. Examples of alliances at one to four degrees of separation are presented, with the focal states embedded within the global alliance network. The paths linking the focal pair of states are in red, whereas the rest of the states in the network are in light yellow. Our research investigates the probability of conflict between states at different degrees of separation in the alliance network.

Many states that have never signed a formal defensive pact have at some point experienced the pacifying effect of higher-order alliances. One example is Turkey and Iran, who did not enter into conflict at any level from 1965 to 1979, during which period they were indirectly connected in the alliance network at two degrees of separation. After losing this connection in 1980, disputes arose between the neighbors, reaching a peak in 1987 when Turkey was mediating the conflict between Iran and Iraq and became involved itself in a militarized dispute with fatalities.

In another case, Spain and its former colony Morocco had several disputes with one another in the 1970s, including an incident in 1972 when the states deployed naval forces to exchange fire after failing to reach a new fishery agreement. However, the states have maintained peaceful relations since they established an indirect alliance at three degrees of separation beginning in 1981. Using state-of-the-art statistical models for network data, we investigate the importance of path length and identify the horizon within which indirect alliances contribute to bilateral peace.

Defensive alliances are formal promises “to assist a partner actively in the event of an attack on the partner’s sovereignty or territorial integrity” (11). Hence, they signal a basic level of agreement and affinity between the allied states. Although alliance partners may not agree on every issue, an alliance is unlikely to be sustained if the partners have large differences in their preferences with respect to the security environment. That is, the basic condition that must be met for a defensive alliance to form and persist is that the allied parties must agree that major changes to the status quo are in neither of their best interests at that time. We use this as our operational understanding of an alliance.

Although some scholars have argued that alliances can actually increase the risk of conflict incidence or escalation, by drawing more actors into ongoing conflicts or by encouraging states to behave more recklessly than they otherwise would have (12–14), there are compelling reasons to discount these arguments. First, alliances are sometimes formed to address already tense security situations, making a positive association between alliances and wars potentially spurious (10). Further, recent evidence suggests that defensive pacts (the alliances with which our study is concerned) are associated with less conflict, not more (15). On balance, we therefore expect defensive alliance ties to be associated with a reduced risk of conflict. Our study starts from this premise about direct alliance ties and considers the ramifications of indirect ties with the expectation that these ties should reduce the risk of conflict but should have a less pronounced effect than direct alliances.

A basic argument about the transitive properties of positive affinity in social networks holds that the friend of my friend should be my friend or at least not my enemy. If an actor i has enough in common with another actor j to form a positive bond, and j has enough in common with a third actor k to form a positive bond, then this would suggest that actors i and k have a fair amount in common. They may not be friends, but enmity between the two would be surprising. We can then ask how far this logic extends. If the ally of my ally should, at minimum, not be my enemy, what about the ally of my ally of my ally? Unlike existing studies, which have examined the effects of direct alliances on the conflict propensities of states and have used measures like alliance portfolio similarity to consider the consequences of shared security preferences (16), our study is designed to capture the effects of the emergent complexity inherent in the international alliance network. This approach is different from that of studies testing classic hypotheses about the relationship between direct alliance ties and conflict between states. We both test the general expectation that indirect alliance ties have an effect on conflict propensity and probe the radius within which indirect connections can effectively foster peace.

If states i and k both agree substantially with j on the security status quo, this would suggest that i and k should also have a fair amount in common, and that they should agree with one another, at least in broad strokes. A naive expectation drawn from this argument could be that a chain of allies, however long, should lead to peaceful relations between the members of the chain. That is, allies of allies of allies would be expected to behave peaceably, as would allies of allies of allies of allies and so on. This simple transitive logic leads to our first network hypothesis about indirect alliance effects: The ability of higher-order alliances to suppress conflict is constant, regardless of the degree of the connection.

The network of international defensive alliances in the post–World War II period forms a giant cluster (or it can be said to be “percolated”): The web of alliance connections includes nearly all actors in the system, and there are few isolated clusters of alliances. This means that most of the states are connected to each other indirectly at some degree. If the first network hypothesis were on target, then it should be the case that conflict is quite rare between any states having one or more defensive alliances. However, the increasing density of the alliance network has not been accompanied by a reduction in military conflict (17).

To square the transitive argument about higher-order alliances with the empirical reality of alliance network percolation and the lack of near-complete global peace, we return to our consideration of the three states: i allied to j allied to k. If i and k agree with one another on the security status quo, then they might well decide to ally with each other. This is the sort of transitive agreement on security that we would expect to lead to triadic closure—i, j, and k all being allied—and broad multilateral alliances. Not only has this pattern of multilateral alliances been posited in the literature, but it also has robust empirical support (17, 18). This pattern of alliances has a strong effect on conflict between the states under consideration: Not only is the probability of military conflict lower between allies (6, 10, 19), but also having allies in common further lowers the probability of conflict.

If trilateral (or multilateral) agreement on the status quo tends to lead to trilateral (or multilateral) alliances and the lower probability of conflict between allies that accompanies them, then the fact that i and k are not directly allied sends a distinctly different signal than if they were. It might be the case that the ij alliance pertains to one aspect of the status quo and the jk alliance to another, meaning that the ik pair might lack the common ground to form an alliance between them. Yet, although i and k may not have sufficient common ground to form an alliance, it seems relatively unlikely that their interests and attitudes toward the security status quo would be so diametrically opposed as to lead to conflict between the two of them. Thus, we expect a second-order alliance like that between i and k to reduce the probability of military conflict between the two of them relative to a pair of states that share no alliance connections.

The same dynamic applies to third- and fourth-order alliances. If the lack of a direct alliance between states that share a common ally carries information, then we can expect that every time the order of the alliance is increased, the two states under consideration have progressively less and less in common in terms of their attitudes toward the security status quo. One can think of this like a game of telephone, with each additional degree of separation introducing some decrease in the amount of agreement between the originating state and the terminating state. This dynamic takes on the form of a decay: the extent to which originating state i and some other state in the chain of alliance connections p agree on the security status quo decays, possibly nonlinearly, because the distance between those two states in the alliance network increases. As the degree of agreement on the status quo decreases with each step, the probability of conflict between the two states sees a corresponding increase. It is important to note that this increase is not relative to the conflict propensity of two unconnected states but relative to two states that are directly allied. The theorized decay in the peacemaking ability of alliances at higher degrees results in our second network hypothesis that the probability of conflict is lower for dyads closer to each other in the alliance network than for dyads connected through higher degrees of separation.

However, these processes do not function independently of regional dynamics. Specifically, past research has shown that alliance dynamics interact strongly with geographic contiguity (20). Contemplating this persistent interaction, it is difficult to imagine two contiguous states at any location in an alliance chain having the same probability of conflict as a similarly located noncontiguous pair, and there are very few states, however close their geographic distance, that have the power to project serious conflict over another state. Thus, it is reasonable to account for power projection capabilities by including a dichotomous measure of state contiguity. We hypothesize that the effect of degrees of separation in the alliance network is strongly interactive with geographic contiguity; the effect is expected to be stronger for contiguous states.

Last, our analysis also considers the effects of the communities that states form within the alliance network. Communities here refer to sets of countries that are joined together in tightly interconnected groups, between which the connections are sparse (21). This sort of community structure, which has been studied extensively in social and biological networks, is also observed in the alliance network. It is also worth noting that a state can simultaneously participate in several multinational alliances, but this view of network communities places each state into exactly one community, as identified by a specific partition algorithm. Members of a community share a greater common interest in the security status quo than outside states do. The community also provides forums through which members can strive for peaceful dispute settlements. States belonging to different communities may have opposing interests and are more likely to resort to force in the face of international disputes. Thus, we expect that the community structure of the alliance network contributes to the peacemaking effect of indirect alliances.