The fall of Syria’s Bashar al-Assad regime on 8 December 2024 was a shocking and welcome piece of geopolitical news that brought an end to thirteen years of fighting. Assad’s position had seemed stable following Russian direct military intervention in the conflict in 2015, as rebel groups were unable to make real progress without incurring devastating Russian airstrikes. But, in the face of a renewed offensive by opposition forces in December, additional Russian support was not forthcoming, and instead Syria’s leader fled to Moscow. This reversal of fortune can be explained, in large part, by shifting Russian priorities and resources – ‘after Mr. Putin invaded Ukraine in 2022, Syria plummeted down the Kremlin’s priority list … Warplanes that Russia may have otherwise sent to reprise the brutal bombing campaigns were instead committed to Ukraine’.Footnote ¹

These events highlight the interdependent and contingent nature of international co-operation. Resources are finite, and states are at times forced to make hard choices in the face of scarcity. Russia’s decision to abandon Syria and focus resources on Ukraine demonstrates the trade-offs states face in stark terms.Footnote ² Smaller states observe the decisions major powers make in cases like this, and while the initial intervention in Syria bolstered Russia and Putin’s reputations, failure will likely have the opposite effect. An observer of Russian and Eurasian politics, Eugene Rumer, commented on Russia’s behavior at the end of the Syrian Civil War: ‘What good is Russia as a partner if it cannot save its oldest client in the Middle East from a ragtag band of militias?’Footnote ³

There are thus two dynamics in play here. Major powers are aware of the reputational consequences of removing support from allies and seek (all else equal) to maintain credible commitments and support their partners. Resources and attention, however, are not unlimited and shocks (either domestic or interstate) may occur, forcing states into choices that risk their hard-won reputations. Our expectation is that smaller states, in making choices about which major power to align with, observe the actions of these powers and update their strategies accordingly.

We look at these dynamics in the context of two of the largest stories in international politics in the past two decades. First, China’s ascent during this time period along with an assertive Russian foreign policy has given rise to a more competitive landscape in terms of state alignments. China, in particular, has emerged as a formidable competitor to the United States, both militarily and through diplomatic efforts such as its Belt and Road initiative – a policy focused on foreign investment in developing countries.

Second, the United States focused considerable resources during this time period on wars in Iraq and Afghanistan. This consumed a great deal of attention and (more recently) generated disputes over the ability of the US military to prepare for conventional conflicts while at the same time fighting counter-insurgencies and engaging in nation-building (Tammen Reference Tammen2006).Footnote ⁴

We contend that examining states’ alignment choices over the last two decades with major powers is incomplete without considering both dynamics simultaneously: the rise of Chinese power alongside the burdensome commitments of the United States.Footnote ⁵ While there are certainly other factors that constrain US foreign policy, such as leadership preferences or economic interdependencies, we center our analysis here on military commitments. Conflicts such as those in Iraq and Afghanistan were unambiguous drains on the United States’ capacity to respond to additional crises. They also offer clear empirical measures (for example troop levels, casualty figures) through which third parties can infer US bandwidth. Although policy preferences or isolationist leadership styles might similarly affect US engagement, they are more challenging to measure consistently over time and are not the focus of our work here.Footnote ⁶

Our investigation into the changing alignment of states in the international system is driven by the belief that studying these dynamics offers valuable insight into conflict and co-operation between states. Empirical studies focusing solely on interstate conflict have always faced challenges; conflict is relatively rare, different time periods are not directly comparable, issues of selection abound, and much of our data are geographically limited.Footnote ⁷

Here, we explore the other side of the coin: co-operation between states, specifically the decision of states to align with either the United States or China. Following Keohane (Reference Keohane1984), we define co-operation as ‘when actors adjust their behavior to the actual or anticipated preferences of others’. Although the causal mechanisms leading to war and co-operation are likely distinct, previous research has demonstrated that, all else being equal, states engaged in co-operative relationships are much less likely to participate in military conflict (Bailey et al. Reference Bailey, Strezhnev and Voeten2017; Gallop and Minhas Reference Gallop and Minhas2021). By examining the causes of co-operation between states, we can bypass the statistical issues involved in studying interstate conflict directly and concentrate on the more abundant data generated by decisions states make over who they align with. Genuine year-to-year variance in state relationships enables us to examine a broader set of mechanisms that explain co-operation. Further, understanding how states connect with one another on co-operative dimensions can shed light on changes in the capacity of major actors – such as the United States and China – to influence the international system.

To assess these dynamics, we create a novel empirical measure of US distraction and commitment and examine how fluctuations in the United States’ focus impact other states’ alignment with either the United States or China. We pay particular attention to differences between democratic and non-democratic regimes, as our intuition suggests that non-democratic regimes may be especially inclined to align more closely with China during periods of US distraction – a finding that adds evidence to the prior research on this topic (Werner and Lemke Reference Werner and Lemke1997; Voeten Reference Voeten2004; Binder and Payton Reference Binder and Payton2022).

In our examination of the link between conflict and co-operation, we contribute to an extensive literature on state alignment in international relations. The realist tradition, based on structural factors and emphasizing the role of power in explaining alignment, has proposed various arguments: states may align themselves against more powerful states in the system to ensure their survival (Waltz Reference Waltz1979); against more threatening or proximate states, or those perceived as having aggressive intentions (Waltz Reference Waltz2010); or with more powerful states to maximize their benefit from future conflicts (Schweller Reference Schweller1994). Generally, states with similar regimes, particularly democratic states, are more likely to align, whether through economic co-operation (Remmer Reference Remmer1998; Mansfield et al. Reference Mansfield, Milner and Rosendorff2000, Reference Mansfield, Milner and Rosendorff2002) or military alliances (Gibler and Sarkees Reference Gibler and Sarkees2004; Leeds Reference Leeds2003; Kinne Reference Kinne2018; Walt Reference Walt1997; van Beek et al. Reference van Beek, Lopate, Goodhart, Peterson, Edgerton, Xiong, Alam, Tiglay, Kent and Braumoeller2024). Previous research has also explored the effects of power on state alignment, including the potential of foreign aid and trade to purchase policy alignment (de Mesquita and Smith Reference de Mesquita and Smith2007; Alesina and Dollar Reference Alesina and Dollar2000), military sales and transfers serving the same purpose, and Nye’s concept of soft power making a state’s policies more appealing to third parties (Nye Reference Nye1990). In the specific case of alignment with China, studies have demonstrated that trade with China has led to policy alignment on economic issues, but not necessarily on political and diplomatic issues (Kastner Reference Kastner2016); studies have also shown that in diplomatic contexts like the UN, most states align more closely with China and Russia than the United States, but this is least true for members of NATO (Nurullayev and Papa Reference Nurullayev and Papa2023). However, the question of whether a realignment in the international system vis-à-vis China occurred during the two-decade period in which the United States’ focus was on South Asia and the Middle East has not received adequate attention.

One of the significant challenges each of these theories faces is that we cannot directly measure alignment but must infer it from observable behaviors. We rely on the fact that, just as alliances (Warren Reference Warren2010; Cranmer et al. Reference Cranmer, Desmarais and Menninga2012); multinational military exercises (Galambos Reference Galambos2024); and conflict (Maoz Reference Maoz2012; Ward et al. Reference Ward, Siverson and Cao2007) occur in networks between states, so does co-operation. Crucially, these networks capture how changes in one relationship can reverberate across many others. Consider, for example, how Russia’s preoccupation with the war in Ukraine led it to scale back material support for the Assad regime in Syria – an adjustment that other Middle Eastern states interpreted not just as a Russia–Syria matter, but also as a signal about Russia’s broader reliability as a security partner. To systematically capture these wider ripple effects, we employ a latent factor model (LFM) to measure how states relate to each other in a network context (Hoff et al. Reference Hoff, Fosdick, Volfovsky and Stovel2013; Minhas et al. Reference Minhas, Hoff and Ward2019). Our approach uses co-operative interactions as inputs, projects them onto a lower-dimensional space that describes the overall co-operation between states, and positions actors closer together if they frequently co-operate or have a high level of co-operation with the same third parties. Substantively, this parallels other techniques that estimate a reduced-dimensional map – such as ideal points for legislators (Poole and Rosenthal Reference Poole and Rosenthal1985) or topic models for text (Roberts et al. Reference Roberts, Stewart and Tingley2016; de Marchi et al. Reference de Marchi, Dorsey and Ensley2021) – but it does so while explicitly accounting for the underlying interdependencies across the entire system of states.

In developing our measure of co-operation, we aim to capture specific patterns that often occur when reducing the dimensionality of a network. One such pattern is stochastic equivalence. Stochastic equivalence refers to the idea that there are communities of nodes in a network, and actors within a community act similarly towards those in other communities. Thus, the community membership of an actor provides us with information on how that actor will act towards others in the network. Put more concretely, a pair of actors ij are stochastically equivalent if the probability of i relating to, and being related to, by every other actor is the same as the probability for j (Anderson et al. Reference Anderson, Wasserman and Faust1992). For example, in an international co-operation network, we might see relatively isolated rogue states, like North Korea and Iran, as being stochastically equivalent, because they have limited co-operation with states like China and Russia, and generally conflictual relations with wealthy Western states (Hafner-Burton et al. Reference Hafner-Burton, Kahler and Montgomery2009).Footnote ⁸ Similarly, close allies of the United States (for example Canada and the United Kingdom) will exhibit high degrees of stochastic equivalence, be likely to co-operate with other affluent Western states, and direct conflictual acts towards said rogue states. This concept speaks to the assertion that we can learn something about how an actor will interact with an entire network based on, for example, the existing set of relationships that they are enmeshed in.

Another dependence pattern that often manifests in networks is homophily – the tendency of actors to form transitive links. The presence of homophily in a network implies that actors may cluster together because they share some latent attribute. In the context of clustering in alliance relationships, we are likely to find that states like the United States, United Kingdom, and Germany may cluster together because of shared liberal norms. We would overlook salient information if we did not use, for example, the United Kingdom’s behavior towards third parties when trying to understand whether those third parties aligned with the United States. Doing so is likely to paint an incomplete picture of the co-operative networks and alignment patterns that states have with one another.

The LFM accounts for these higher-order dependence patterns and ensures that similarity in alignment is likely to be transitive. For example, if the United States aligns with the United Kingdom, and the United Kingdom aligns with France, the United States and France should also be aligned. Furthermore, the most useful feature of the LFM for our purpose is that it summarizes the interdependencies between actors in a relational k-dimensional latent vector space. From this vector space, we can both understand how states in the system are tied to others in the system and ask more specific questions about the dominance of particular actors in the system, such as China.

Our plan for the rest of the article is straightforward. First, we will outline the two competing theories for how the United States’ constraint could affect relationships in the international system. Second, we will establish our measure of the level of constraint of the United States during the period from 2000 to 2020. Third, we will detail the LFM and output measures for this time period. Lastly, we will present the results of our downstream regressions that detail the impact on co-operation as a function of constraint.

Methods

To test the competing dynamics of the distraction and credibility models, we develop a measure of ‘constraint’ that captures limits on the United States’ capacity or, alternatively, shifts external perceptions of its resolve. Our focus here is on conflict-based variables drawn primarily from the scale of active US military engagements, deployments, and associated casualties.Footnote ⁹ The main advantage of focusing on conflict-based variables is that they are readily observable indicators of expenditures of national resources and attention and also have substantial variance across the time period of interest.Footnote ¹⁰

Under the distraction model, constraints such as overseas conflicts and extensive force commitments reduce the United States’ bandwidth to engage elsewhere, making it more difficult to respond to states shifting their alignment. Under the credibility model, these same commitments demonstrate the United States’ willingness to bear costs, thereby bolstering its reputation for resolve. In this way, the very factors that might signify reduced capacity can also be interpreted as heightened credibility, depending on the perspective taken.

Broadly speaking, we operationalize US constraints as a function of two potential sources:

1. 1. Active conflicts the United States is involved in, especially those with high material commitments and US casualties;

2. 2. US force commitments around the globe, including troop deployments and defense expenditures.

We argue that each of these sources can plausibly indicate both distraction and credibility, which is why we treat them collectively as measures of US constraints.Footnote ¹¹ A simple latent variable model of the categories produced two features, representing active US conflicts (F ₁) and US defense spending/commitments (F ₂).Footnote ¹² Figure 1 visualizes how the two factors have changed over time.

Figure 1. Visualization of F ₁ and F ₂ over time.

The graphs in Figure 1 display considerable variance that aligns with our priors on constraints resulting from US military conflicts over the past two decades: the measure of distraction based on military spending declines sharply following the end of the Cold War, rises dramatically after the 9/11 attacks, and then gradually diminishes as the United States starts allocating less attention and resources to the wars in Afghanistan and Iraq; the measure based on active US conflicts increases as the Cold War ends and the United States begins fighting several small wars during the 1990s, peaks during the wars in Iraq and Afghanistan, and then decreases to a still relatively high equilibrium in the 2010s.

Measuring Alignment

We also need a measure of how closely states are aligned and how these relationships change over time. One approach would be to simply examine a raw measure of co-operation between states, but this presents several problems. First, states vary in their overall levels of voting participation at the UN – a higher co-voting rate between the United States and France, for instance, does not necessarily reflect deeper political alignment than a lower rate between France and a smaller or less engaged country. Rather, the United States and France might both regularly vote ‘Yes’ on widely supported resolutions, inflating their co-voting score. Second, abstentions and low voting participation can mask genuine disagreement versus mere disinterest: a pair of states may rarely vote in tandem not out of antagonism but because one or both frequently abstain on certain resolutions. By treating co-voting patterns as a form of relational data, we can better distinguish low co-voting driven by actual contention from low co-voting born of ambivalence or passive engagement. A network approach thus allows us to capture these higher-order interdependencies – such as clustering, transitivity, and indirect ties – when inferring a latent measure of alignment from UN voting behavior. Both of these issues can be addressed by treating measures of co-operation as a form of relational data and employing a network approach to infer our latent measure of alignment. A network approach enables us to capture the different orders of interdependencies in relational data, which will be discussed in more detail in this section.

Our raw measure of co-operation is based on the similarity in states’ UN voting records (Voeten Reference Voeten2013). We examine the percentage of votes at the United Nations General Assembly in which states voted the same way.Footnote ¹³ Although we operationalize alignment primarily through UN co-voting behavior, we view ‘alignment’ as a broader phenomenon encompassing co-operation on policy. Diplomatic co-operation – like co-sponsoring UN resolutions – provides a tangible indicator of alignment, but states can also align through defense co-operation, trade agreements, or foreign policy stances (for example joining a US-led coalition or building deeper ties with China). Hence, while our empirical measure relies on voting data for systematic, globally comparable coverage, we acknowledge that alignment extends beyond diplomatic interactions to include economic and military domains as well. Our focus on co-voting thus captures one crucial dimension of foreign policy co-ordination, especially relevant for understanding how states navigate superpower competition when the United States is ‘distracted’. We use this longitudinal network of voting data to estimate state affinity via an LFM.Footnote ¹⁴

The LFM is a network model designed to account for three different orders of interdependencies in relational data. First, it considers the tendency of some actors to be both the initiator and target of conflict and co-operation by including sender and receiver random effects. Second, it accounts for the fact that co-operation is often reciprocal through the composition of the error term. Finally, the aspect that sets the LFM apart from other network estimators is how it addresses third-order dependencies. Two specific types of third-order dependencies that the LFM can handle are homophily (the tendency for actors sharing an unobserved characteristic to interact more with each other) and stochastic equivalence (the notion that actors playing similar roles in a network are more likely to co-operate with the same third party). Stochastic equivalence differs from homophily in that actors close to one another in a network do not necessarily interact more. Instead, actors within the same group in a network share similar relationship patterns with actors in other groups, such as a connection to a common actor.

The LFM manages these third-order dependencies with a multiplicative random effect based on matrix decomposition procedures.Footnote ¹⁵ This third-order term is valuable for coping with left censoring in the data, since we can use common or contrasting voting patterns with third parties at the United Nations to ascertain whether states truly share alignment in the broader diplomatic network, or if their divergence extends further. We formulate the latent factor model as follows:

(1) $$\eqalign{& {y_{ij}}\; = \;f({\theta _{ij}}),\;{\rm{where}}\; \cr & {\theta _{ij}}\; = \;{{\bf{\beta }}_0} + {a_i} + {b_j} + {\varepsilon _{ij}} \cr & \quad\quad+ {\bf{u}}_i^ \top {\bf{D}}{{\bf{v}}_j} \cr} $$

where $y_{ij}$ represents the observed level of co-operation between states $i$ and $j$ ; $\beta_{0}$ is the intercept; $a_{i}$ and $b_{j}$ are sender and receiver random effects, respectively; $\theta_{ij} = u_{i}^{\top} v_{j}$ is the multiplicative term capturing third-order dependencies such as homophily and stochastic equivalence; and $\varepsilon_{ij}$ is an error term.

Our focus for measuring co-operation is on the ${\bf u}_i^{{\rm T}}{\bf D}{\bf v}_j$ term, which is included in the model to capture third-order dependencies. This captures the tendency of states to not only co-operate with each other but also to co-operate with similar third parties. Put simply, it allows us to quantify indirect ties. At its core, the ${\bf u}_i^{{\rm T}}{\bf D}{\bf v}_j$ term is similar to conducting a singular value decomposition (SVD) of a network after accounting for the general propensity of actors to form a tie (β ₀) and variation in how active some are in sending or receiving ties through a set of random effect terms (a _i and b _j , respectively).Footnote ¹⁶ To estimate the ${\bf u}_i^{{\rm T}}{\bf D}{\bf v}_j$ term, we need to specify a dimension for the multiplicative effects. If we choose one dimension, we could write this term in vector notation as: θ _ij = d ₁(u _i,1×v _j,1). Here, if we find, for example, that u _USA ≈ u _Canada, this would imply that the United States and Canada send ties to similar third parties, meaning they are stochastically equivalent to one another in terms of their sending relationships. Additionally, if u _USA ≈ v _Canada and d ₁ > 0, this implies that the United States is likely to send a tie to Canada due to homophily, which indicates that there is some latent nodal attribute Canada and the United States share that makes a tie between them more likely. We take the multiplicative effects term for every pair of countries in every year as a measure of alignment.Footnote ¹⁷

Face Validity

We turn to descriptive statistics of our measure, first, by looking at the overall network of relationships uncovered, and then by looking in more detail at the time series of certain prominent relationships. Our model maps each state into a latent vector space and we visualize this for our measure of Alignment for 2000 and 2019 in Figure 2.

Figure 2. Visualization of multiplicative effects for our measure of alignment. The left panel shows the results for 2000 and the right for 2019. Each circle designates a country and the color corresponds to the legend at the center of the visualization. Countries that are closer together are those that share indirect ties.

States with their vectors pointed in similar directions are more likely to influence each other and common third parties, whereas states whose vectors point in opposite directions have limited influence on each other. There are a few immediate takeaways from these networks. First, the diplomatic alignment measure based on UN voting shows three discernible clusters: the United States and Israel (and Canada in 2019) are relatively isolated but generally close to a larger cluster with most of the other major European powers, along with Japan, Australia, and New Zealand. The third cluster contains the vast majority of the Global South.Footnote ¹⁸ These figures show that the measures of diplomatic alignment correspond to many of our intuitions about influence in world politics while also maintaining important and novel characteristics based on the data used to generate them.

We also test the face validity of these measures by looking at how they characterize three important dyads. We choose the relationship between the United States and United Kingdom, which we expect to be generally close and amicable, and the United States’ relations with its two major competitors, China and Russia. As shown in Figure 3, this measure captures the general tenor of the relationships – the United States and United Kingdom have a consistently positive relationship, whereas the relationship the United States has with both China and Russia, based on UN voting, is characterized as more adversarial. The time series interestingly points to generally positive relationships in the immediate aftermath of 9/11, which deteriorate precipitously starting in 2003 with the Iraq war. While there are some marginal improvements, the relationships remain quite negative.

Figure 3. Level of diplomatic alignment for selected dyads over time.

Regression Models

Given the measure described in the previous section, our empirical approach to testing H1 and H2 is straightforward. The dependent variable (DV) is the affinity of actors to China as measured by our network-based approach using UN voting data. Higher values on this measure indicate that states are more diplomatically aligned, while lower values indicate the opposite.Footnote ¹⁹ Our unit of observation here is the country-year, with a sample of 118 countries measured annually between 2000 and 2020.Footnote ²⁰

Our key independent variable is our measures of US distraction, which we measure through active US conflicts (F ₁) and US defense expenditures and force commitments (F ₂).Footnote ²¹ For each country-year observation, we include the value of US distraction in the previous year to see how it relates to that country’s alignment with China.

We also include several country-level controls that might influence how closely a country is aligned to China diplomatically. Specifically, we control for a country’s population, their GDP, and the distance between their capital and Beijing. To address political factors that might make a country more or less closely aligned with China, we include Polity’s measure of a country’s level of democracy (the intuition being that autocratic regimes will be closer to other autocracies, like China, and democracies will be less close, all else being equal). To consider other structural factors, we estimate our models within a hierarchical framework. In the first set of results, we rely on random effects for the country, and later we examine how the effect of our key independent variables varies based on a state’s domestic political institutions.Footnote ²²

Empirical Results

In the first set of models depicted in Figure 4, we see results that generally conform to the distraction hypothesis. As F ₁ increases (listed as ‘United States Constraint Proxy’), denoting a higher level of US attention and resources devoted to the Middle East and South Asia, states consistently experience an increase in their diplomatic alignment with China (though our estimate of this result is measured with a high degree of uncertainty). When we move to the right panel, in which we are proxying US constraint with troop deployments and military spending, F ₂, we see a similar pattern: diplomatic alignment with China increases with our measures of US distraction.

Figure 4. Parameter estimates from a hierarchical model on diplomatic alignment with random country effects. Each column shows the results with a different distraction measure that is labeled in the facet on the top of the plots. Points represent average value of parameters, thicker line represents the 90 per cent confidence interval, and thinner the 95 per cent. GDP, gross domestic product.

For control variables, results are generally consistent with our expectations. Democracies are less likely to be aligned diplomatically with China, and the same is true for rich states. The distance to Beijing has a consistent positive effect across all models, indicating that there is closer alignment between China and more distant states, on average, which might speak to the wariness that some of China’s neighbors feel with regard to its growing importance.

Figure 5. Country random effect estimates, where the lower values in red indicate less alignment with China and higher values in blue indicate greater alignment. Countries in gray are those that were omitted from the model.

One possible explanation for the relatively high levels of uncertainty is that these models show the aggregate effect, but beneath the surface, different states react to US distraction in different ways. To understand whether or not we can find evidence of variation in how countries are responding to China, we visualize the country random effect estimates from the diplomatic alignment models in Figure 5. For both measures of alignment, we see notable variation in country random effect estimates.

While Figure 5 shows substantial heterogeneity in countries’ responses to US distraction, we now move towards examining this heterogeneity in a more systematic way. The most obvious and commonly used division in the study of international conflict and co-operation is to divide states based on their domestic political institutions. The diplomatic behavior of states occurs within and is conditioned by political institutions. Therefore, we might expect a common stimulus, like US distraction, to lead to different reactions when decisions are made by a hereditary autocrat than when they are the purview of a democratically elected legislature or executive.

We thus modify our hierarchical model to allow the effect of our US distraction variables to vary across types of political institutions. We measure political institutions using Polity scores, relying on the canonical division into consolidated democracies (Polity Score ≥ 7), consolidated autocracies (≤–6), and mixed regimes (all other states). In these models, we allow a random slope for the two distraction proxies in each tranche of the Polity score. These results are shown in Figure 6.Footnote ²³

For F ₁, both autocracies and mixed regimes (anocracies) show a positive relationship between US distraction and alignment with China, whereas consolidated democracies become less aligned with China when the United States is more distracted. A similar pattern emerges for F ₂, where non-democratic regimes again respond positively to US constraint, in contrast to democracies. Taken together, these results suggest that US distraction fosters greater alignment with China among regimes outside the democratic core.

Figure 6. Parameter estimates from a hierarchical model on diplomatic alignment with varying effects of the distraction measures by Polity categories. The top panel shows how the distraction measures vary by Polity categories, and the bottom panel shows the fixed effects, each column again representing the results of one model. Points represent the average value of parameters, the thicker line represents the 90 per cent confidence interval, and the thinner line represents the 95 per cent confidence interval.

Alignment with Russia

In the SI, we present in more detail an additional set of models that focus on alignment with Russia. These results are similar to the results on alignment with China – both our measures of constraint are associated with closer diplomatic alignment with Russia. When we look at the heterogeneous effect of constraint conditioned by regime type, we find similar patterns – constraint has the greatest impact in moving autocracies towards Russia, less impact on anocracies, and the least on democracies. The substantive similarity in results between our models of alignment with Russia and China increases our confidence in the robustness and generalizability of these dynamics, and highlights the importance of considering both constraint and domestic political institutions in order to understand co-operative behavior.