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BRICS Under Stress: A Crisis-Adjusted Divergence Index for Measuring Coalition Alignment Under Systemic Pressure

This paper introduces the Crisis-Adjusted Divergence Index (CADI), a leading indicator that models systemic stress as a dynamic reweighting of five structural dimensions to predict coalition alignment, demonstrating through BRICS case studies that structural heterogeneity drives divergence under pressure while similarity does not guarantee cohesion.

Original authors: Antoine Bachelin Sena

Published 2026-07-28

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Antoine Bachelin Sena

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Great Alliance Puzzle: When Friends Drift Apart Under Pressure

Imagine a group of friends who love hanging out together when everything is going well. They share meals, laugh at the same jokes, and post group photos that look perfectly united. But what happens when a massive storm hits? Do they all huddle together in the same corner, or do they scatter to different parts of the house to protect their own specific interests? This is the big question scientists in the field of international relations have been asking about a powerful group of nations called BRICS (Brazil, Russia, India, China, and South Africa).

For years, experts have argued over whether this group is a tight-knit team or just a loose collection of countries that happen to agree on some things. The trouble is, most ways of measuring friendship only look at what people do after the fact—like checking who voted for whom in a meeting or who signed a treaty. It's like trying to understand a relationship only by looking at the breakup letter. We need a way to predict how the pressure of a crisis changes the dynamic before the breakup happens. To do this, we need to understand a few key ideas: "structural exposure" (which is just a fancy way of saying how much a country relies on others for things like security, money, or technology), and "systemic stress" (the level of global tension or danger in the world). The big question is: as the world gets more dangerous, does the group stay glued together, or do the cracks start showing?

The "Stress-Test" for Friendships

Enter a new tool called the Crisis-Adjusted Divergence Index (CADI), created by researcher Antoine Bachelin Sena. Think of CADI not as a thermometer that measures how hot a relationship is after it burns, but as a weather forecast that predicts how the wind will blow the friends apart before the storm hits.

The paper argues that the old way of looking at BRICS was too simple. It treated the group like a solid block of stone. But CADI treats each country like a unique character in a video game, defined by five specific "stats" or vulnerabilities:

Security Exposure: How much do they rely on others for safety?
Defense-Industrial Dependence: Do they need to buy weapons from someone else?
Trade Concentration: How much of their business is with just a few partners?
Technological Dependency: Do they need high-tech gadgets from abroad?
Regulatory-Financial Alignment: Are their money rules and laws similar to the big Western powers?

The magic of CADI is a special "stress dial" (represented by the Greek letter sigma, σ). When the world is calm (the dial is at 0), all five stats matter equally. It's like a casual hangout where everyone's hobbies are equally important. But when a crisis hits—like a war or a major geopolitical shock—the dial turns up. As the stress rises, the "weight" of the stats changes dramatically. Suddenly, the survival stuff (security and weapons) becomes super important, while the "nice-to-have" stuff (trade and tech) gets pushed to the background.

What Happens When the Dial Turns Up?

The researchers tested this idea using Brazil, India, and China. They ran the numbers to see what happens when the stress dial goes from "Chill" (0) to "Maximum Panic" (2), which happened during the 2022 Ukraine crisis.

Here is the surprising result: It depends on who you are.

The Drifters (Brazil and India): These two countries have very different "stats." Brazil is heavily tied to Western trade and finance, while India is heavily tied to security and defense. When the stress dial turned up, the CADI showed their differences exploding. The index for their divergence jumped by 86% for Brazil and India, and 81% for Brazil and China. It's like two friends who usually agree on music and food suddenly finding that when the house is on fire, one wants to run to the fire station while the other wants to call the insurance company. They aren't fighting; they are just pulled in opposite directions by their different structural needs.
The Twins (India and China): This is the most interesting part. India and China have very similar "stats"—they both rely heavily on security and technology. You might think a crisis would make them fight, but the CADI predicted they would not drift apart structurally. And guess what? The index stayed flat. Their "structural distance" barely changed. The paper suggests that while they might be political rivals, their underlying "gear" is so similar that the stress of the crisis didn't pull them apart in the way it did for the others.

The "Revealed Preference" Check

To make sure this wasn't just a cool math trick, the authors compared their predictions to real-world behavior. They looked at how these countries actually voted in the United Nations General Assembly (the "revealed preferences").

The results were a match. When the CADI predicted that Brazil and China would drift apart, their voting records in the UN showed a massive gap (their distance nearly tripled). When the CADI said India and China would stay structurally similar, their voting records showed a different story: they actually drifted apart in voting, but the paper explains this is because of a specific "rivalry" factor that the index doesn't measure. This proves the tool is doing exactly what it's supposed to: measuring the structural pressure that pushes countries apart, not the political drama that might pull them apart for other reasons.

The Takeaway: It's Not About "Unity," It's About Layers

The paper concludes that the debate over whether BRICS is "united" or "broken" is actually a misunderstanding. The group is both!

Layer 1 (The Low-Stress Layer): When things are calm, or when the crisis isn't life-or-death, the countries stay united. They hold summits, sign joint statements, and keep the New Development Bank running. This is the "diplomatic façade" that looks like unity.
Layer 2 (The High-Stress Layer): When the stress dial hits the red zone, the countries diverge based on their specific vulnerabilities. They don't break up the group; they just stop cooperating on the things that matter most for survival.

The paper suggests that for policymakers, the old way of thinking—treating BRICS as a single block to be either contained or ignored—is wrong. Instead, they should look at the "stress map." If you are a country trying to negotiate with BRICS, you need to know that under high stress, Brazil might be open to trade deals (because that's their weak spot), while India might be open to security talks (because that's theirs).

In short, the paper gives us a new lens to see that in a multipolar world, alliances aren't fixed. They are elastic. They stretch and shrink depending on how hard the wind blows, and the CADI is the tool that finally lets us measure exactly how much they will stretch before they snap.

Technical Summary: BRICS Under Stress and the Crisis-Adjusted Divergence Index (CADI)

Problem Statement
Existing literature on the BRICS coalition (Brazil, Russia, India, China, South Africa) presents a paradox: the group appears cohesive during periods of geopolitical calm but fractures selectively during acute crises, such as the 2022 Russian invasion of Ukraine. While scholars have documented this regularity—distinguishing between diplomatic cohesion (summits, communiqués) and behavioral divergence (voting, trade shifts)—there is a lack of formal instruments to measure when, how fast, and along which structural dimensions this fragmentation occurs. Current quantitative measures of alignment (e.g., UN General Assembly ideal points, voting similarity scores) are "lagging indicators" that capture revealed preferences only after behavior has occurred. They fail to model the underlying structural pressure that precedes these choices or to account for how systemic stress dynamically reweights the salience of different policy domains.

Methodology: The Crisis-Adjusted Divergence Index (CADI)
The paper introduces the CADI, a formal, transparent, and replicable instrument designed to measure structural pressure on alignment conditional on systemic stress. The methodology proceeds through three core components:

Structural Exposure Vectors: Each state is modeled as a five-dimensional vector ( $v_i \in [0, 1]^5$ ) representing objective structural circumstances rather than preferences. The dimensions are:
- Security exposure
- Defence-industrial dependence
- Trade concentration
- Technological dependency
- Regulatory-financial alignment
  These vectors are constructed from publicly available data (SIPRI, UN Comtrade, World Bank, etc.) and min-max normalized across the sample.
Systemic Stress Scalar ( $\sigma$ ): Stress is treated as a continuous scalar ranging from 0 (baseline stability) to 2 (peak geopolitical pressure). It is calibrated externally using the country-level Geopolitical Risk (GPR) index (Caldara and Iacoviello, 2022), anchored to the 2015–2019 mean and the 2022 Ukraine peak.
Stress-Sensitive Reweighting (Softmax Function): The core mechanism treats systemic stress as a variable that dynamically reweights the salience of the five dimensions. A softmax function transforms linear scores ( $\alpha_k + \beta_k \sigma$ ) into weights ( $w_k$ ).
- Survival-proximate dimensions (Security, Defence-industrial) are assigned positive stress-sensitivity coefficients ( $\beta > 0$ ), meaning their salience increases exponentially as stress rises.
- Optimisation-oriented dimensions (Trade, Technology, Regulatory-financial) are assigned negative coefficients ( $\beta < 0$ ), meaning their salience compresses under stress.
- At $\sigma = 0$ , all dimensions have equal weight (0.20). As $\sigma$ increases, the model shifts focus toward survival-proximate vulnerabilities.
Index Calculation: The CADI for a dyad $(i, j)$ is the Euclidean distance between their stress-weighted exposure vectors:
$CADI_{ij}(\sigma) = \|\tilde{v}_i(\sigma) - \tilde{v}_j(\sigma)\|_2$
This measures the divergence of structural profiles under specific stress conditions.

Key Contributions
The paper claims three primary contributions to the literature:

Leading Indicator of Structural Pressure: Unlike existing tools that measure revealed preferences, CADI is a leading indicator that quantifies the ex ante structural pressure shaping alignment choices before they are observed.
Formalization of "Shrinking Hedging Space": The index operationalizes the theoretical claim that as rivalry intensifies, the space for hedging shrinks. It does so by mathematically demonstrating how rising stress systematically elevates the weight of security/autonomy dimensions while suppressing trade/financial dimensions.
Falsifiable Scope Conditions: The framework explicitly defines its scope. It predicts divergence for structurally heterogeneous dyads under stress but predicts stability for structurally similar dyads, even if political rivalry exists. This allows the index to fail informatively (as seen in the India–China case) rather than forcing a fit.

Results
The index was applied to three dyads (Brazil–India, Brazil–China, India–China) using 2015–2024 data:

Heterogeneous Dyads (Brazil–India, Brazil–China): As stress ( $\sigma$ $σ$ ) rose from 0 to 2 (the 2022 peak), the CADI increased significantly.
- Brazil–India CADI rose by 86% (from 0.160 to 0.298).
- Brazil–China CADI rose by 81% (from 0.181 to 0.329).
- The trajectories were non-linear, accelerating as security weights approached dominance.
Structurally Similar Dyad (India–China): Despite high geopolitical tension, the CADI remained flat (0.068 to 0.065). This confirms Hypothesis G2: because India and China share similar high-β exposure profiles (high security and tech dependence), stress-induced reweighting does not pull their structural profiles apart.
External Validation: The CADI trajectories were compared against UN General Assembly ideal-point distances (Bailey et al., 2017).
- For heterogeneous dyads, the correlation between CADI and revealed divergence was 0.68.
- For the India–China dyad, the correlation was negative (-0.34), confirming that the index correctly identifies structural similarity while external data reveals divergence driven by bilateral rivalry (a factor the index deliberately excludes).
- The stress-reweighting mechanism reduced prediction error by 36% relative to a static-distance null model.

Significance and Claims
The paper argues that the debate over whether BRICS "held together" or "fractured" post-2022 is not an empirical dispute but a disagreement about analytical layers.

Reconciling Readings: The CADI demonstrates that both readings can be true simultaneously. The coalition remains cohesive in "low-β" domains (diplomacy, development banking, joint communiqués) which remain cheap to sustain under stress. However, it diverges sharply in "high-β" domains (security, defence-industrial autonomy) where survival-proximate pressures dominate.
Policy Implications: For policymakers, the index suggests treating BRICS not as a monolithic bloc but as a collection of differentiated exposure profiles. Engagement strategies should be tailored to specific structural anchors (e.g., security cooperation for India, trade stability for Brazil) rather than the coalition label.
Modest Scope: The authors explicitly state that the index measures structural exposure divergence, not political alignment direction. The India–China case serves as a boundary condition: low profile divergence is necessary but not sufficient for political alignment. The paper does not claim to predict specific policy outcomes but rather to map the structural constraints that make certain outcomes more or less likely under varying levels of systemic stress.