Directed Acyclic Graphs
2026-03-11; revised: 2026-03-19
Part I: Prologue
A Primer on Causal Diagrams: How a Simple Visual Language Helps Us Understand—and Prevent—Conflict
Most people think of war as a tangle of motives, histories, and unpredictable decisions. And it’s true: international conflict is complex. But complexity does not mean chaos. Beneath the headlines and the noise, there are patterns—patterns of cause and effect that shape how crises unfold. This book introduces a tool that helps us see those patterns clearly: the Directed Acyclic Graph, or DAG.
If you’ve never heard of a DAG, don’t worry. You already use the underlying logic every day. When you say, “If this happens, then that will follow,” you’re thinking in causal terms. A DAG simply draws those relationships on paper so we can examine them with clarity and discipline.
Think of a DAG as a map of causes. Not a map of geography, but a map of how events push and pull on one another.
- Nodes represent events or conditions.
- Arrows represent causal relations—what leads to what.
- Acyclic means the arrows never loop back on themselves; time moves forward.
That’s it. No equations required.
Yet this simple structure has transformed fields as diverse as epidemiology, economics, and artificial intelligence. It gives us a way to distinguish what merely correlates from what truly causes. And once we understand causes, we can design interventions—actions that change outcomes.
This book applies that same logic to one of humanity’s oldest problems: how to prevent war and build peace.
Why DAGs Matter for Peace
When a conflict erupts, it often feels like a chain reaction: one country attacks, another responds, alliances activate, fears escalate, and soon the situation spirals beyond control. But if we draw the causal chain, we can see where the escalation happens—and where it can be interrupted.
A DAG lets us:
- Identify the triggers that turn a crisis into a war.
- Spot the mediators—the mechanisms through which escalation spreads.
- Recognize confounders—background conditions that push multiple actors toward conflict.
- Find leverage points—places where a well‑designed intervention can redirect the entire trajectory.
In other words, DAGs help us see not just what happened, but what could have happened differently. They reveal the architecture of escalation—and therefore the architecture of peace.
From War Pathways to Peace Pathways
In the chapters that follow, you’ll see how a typical conflict can be represented as a causal diagram. For example:
- A country attacks a neighbor.
- An ally feels compelled to join.
- Fear of retaliation spreads.
- The alliance structure amplifies the crisis.
- A joint attack becomes almost inevitable.
This is the war pathway—a sequence of causal arrows that channel the crisis toward violence. But DAGs also allow us to imagine—and design—alternative pathways:
- Instead of alliance pressure leading to joint attack, it could lead to automatic mediation.
- Instead of fear driving escalation, monitoring and verification could reduce uncertainty.
- Instead of retaliation, incentives for restraint could shift the calculus.
- Instead of spiraling violence, the crisis could trigger a ceasefire mechanism.
By redrawing the arrows, we can redesign the system.This is the central idea of the book: Peace is not only a moral aspiration—it is a causal possibility. If we understand the structure of escalation, we can build the structure of de‑escalation.
What This Primer Prepares You For
The chapters ahead will show you:
- How to read and draw DAGs
- How to identify confounders, proxies, mediators, and effect modifiers in real conflicts
- How to analyze escalation as a causal process
- How to design interventions that break the chain of war
- How to build a “Peace‑DAG”—a causal architecture that channels crises toward ceasefire and settlement
You will see that peace is not an abstraction. It is a outcome of a system of causes which, when misdirected, produce wars. The pathways of war can be redesigned. This primer is your invitation into that way of seeing.
Node table
| Code | Name | Role in DAGs |
|---|---|---|
| B | Z attacks I | Exposure (crisis event) |
| K | Alliance pressure/coordination | Escalation mediator (war‑DAG) |
| C | U attacks I | Escalation mediator (war‑DAG) |
| Y | Joint attack on I | War outcome |
| A | Alliance structure | Confounder (affects B and C/Y) |
| S | Strategic environment | Confounder (threat context, affects B and C/Y) |
| P_u | U’s domestic politics | Confounder (affects C and support for war/peace) |
| P_z | Z’s domestic politics | Confounder (affects B and Z’s choices) |
| R | Relative power | Confounder and effect modifier (modifies B→C) |
| M | Mediation mechanism | Positive mediator (peace‑DAG) |
| Q | Monitoring & verification | Path‑blocking node (reduces misperception, proxies) |
| D | De‑escalation incentives | Positive mediator of restraint |
| C′ | U’s de‑escalatory response | De‑escalatory action (peace‑DAG) |
| Z′ | Z’s de‑escalatory response | De‑escalatory action (peace‑DAG) |
| CF | Ceasefire | Co‑incident peace node (joint restraint) |
| P | Peace process | Long‑term settlement / resolution |
| T | Triggering event (general model) | Exposure in generalized conflict DAG |
| E | Amplifiers of escalation | Layer of confounders/effect modifiers (A, S, P_u, P_z, R) |
| A_gen | Escalatory actions (general) | Mediators in generalized conflict DAG |
| C_gen | Conflict entrenchment | Co‑incident node in generalized conflict DAG |
| V | Monitoring & verification (general) | Same role as Q in generalized model |
| R_gen | Incentives for restraint | Same role as D in generalized model |
| D_gen | De‑escalatory actions | Same role as C′/Z′ layer in generalized model |
| S_gen | Settlement | Same role as P in generalized model |
Notes:
- For definitions, see glossary.
- The “_gen” variants can be omitted when reusing the same letters across the specific and general models; separated them here only for clarity.