What Makes Something a Cause? A Guide to Causal Models

Imagine two kids, Billy and Suzy, standing in front of a window. Suzy throws a rock, and the window shatters. Billy doesn’t throw his rock. It’s obvious that Suzy caused the window to break, right?

But now imagine a slightly different story. Billy and Suzy decide that Suzy will throw first. If Suzy throws, Billy won’t. If Suzy doesn’t throw, Billy will throw, and his rock will break the window. In this version, Suzy does throw, the window breaks, and Billy doesn’t throw. Did Suzy cause the window to break? Intuitively, yes. But here’s the puzzle: if Suzy hadn’t thrown, Billy would have, and the window would still have broken. So the window doesn’t depend on Suzy’s throw in the way we usually think a cause should. And yet, it seems wrong to say Suzy didn’t cause it.

This is the kind of puzzle that leads people into the study of causal models. Causal models are a way of thinking about causes that uses math, diagrams, and sometimes probabilities. They were invented by people in statistics, computer science, and philosophy who wanted to get clearer about what it means for one thing to cause another. The basic idea turns out to be surprisingly useful—not just for philosophy, but for medicine, economics, and even figuring out how to make good decisions.

The Basic Tools: Variables and Diagrams

The first thing you need in a causal model is a set of variables. A variable is just something that can take different values. Suppose we want to model Billy-and-Suzy situation. We might use three variables:

S = 1 if Suzy throws, 0 if she doesn’t
B = 1 if Billy throws, 0 if he doesn’t
W = 1 if the window breaks, 0 if it doesn’t

The values of these variables depend on each other. In the first story (where Billy just watches), we might say that W depends on S and B like this: W = max(B, S). That is, the window breaks if either Billy or Suzy throws a rock. And in this story, S = 1, B = 0, so W = 1.

But the real power of causal models comes from the fact that they also represent what would happen under different circumstances. We can draw a diagram that shows the causal relationships between variables. We draw an arrow from one variable to another when the first directly influences the second. In our simple story, S and B both have arrows pointing to W.

These diagrams can get complicated. A directed acyclic graph (DAG) is just a fancy name for a diagram where all the arrows go one way and there are no loops. (If A causes B and B causes A, you’d have a problem, since you could never get a stable answer.) A DAG is like a family tree for causes: it shows which variables are “parents” of which others, and which are “descendants.”

What Would Happen If…? Interventions and Counterfactuals

Here’s where things get interesting. A causal model doesn’t just tell you what did happen. It also lets you ask: what would happen if you changed something? Philosophers call these “counterfactuals”—sentences of the form “If X had been different, then Y would have been different.”

In the causal model approach, we figure this out by thinking about interventions. An intervention is when you reach into the system and force a variable to take a certain value, breaking the normal causal connections that would otherwise determine it. Think of a science experiment where you decide randomly which subjects get a drug and which get a placebo. That random assignment is an intervention: it overrides the normal factors that would determine who takes the drug.

To figure out what would happen under an intervention, you literally change the equations in your model. Suppose in our first story, we wanted to know: what if Suzy had not thrown her rock? We would replace the equation that normally determines S with “S = 0.” Then we solve the new system to see what happens. In the first story, this gives us W = 0 (since Billy didn’t throw either). But in the second story (where Billy throws if Suzy doesn’t), setting S = 0 means B becomes 1, and W still becomes 1. So the counterfactual “if Suzy hadn’t thrown, the window wouldn’t have broken” is true in the first story but false in the second.

This is exactly the difference that causes trouble for simple theories of causation. In the second story, the window breaking doesn’t counterfactually depend on Suzy’s throw. And yet we still want to say Suzy caused it. So what’s going on?

The Puzzle of Actual Causation

This is where philosophers have spent a lot of energy. They want a definition of actual causation—the relation that holds between Suzy’s throw and the window breaking in the actual situation, not just in hypotheticals.

One promising idea goes like this: Suzy’s throw is an actual cause of the window breaking if we can find some set of variables to “hold fixed” such that the window does counterfactually depend on Suzy’s throw. In the second story, if we hold Billy’s action fixed at its actual value (B = 0), then changing Suzy’s throw does change whether the window breaks. The intuition is that Suzy’s throw caused the window to break along the “direct path” from S to W, even though there’s another causal path (through B) that would have compensated if she hadn’t thrown.

This idea gets technical quickly—there are many versions, and philosophers still argue about which one is right. Some involve distinguishing between “normal” and “abnormal” conditions (maybe we should treat Billy’s throwing as a backup mechanism that only kicks in when Suzy doesn’t throw). Others involve more complicated mathematics. None of the existing definitions perfectly captures everyone’s intuitions, and some philosophers think the whole project is hopeless.

This part gets complicated, but here’s what it accomplishes: it shows that causation isn’t a simple thing. It involves multiple interacting pathways, hidden backup plans, and subtle decisions about what counts as “normal.” The causal model framework gives us a precise language to argue about these things, even if it doesn’t give us final answers.

Adding Probability: What We Can Learn from Correlations

So far, we’ve been thinking about deterministic causes: if this happens, that must happen. But real life is messier. Smoking doesn’t guarantee lung cancer, but it makes it more likely. So causal models often include probability.

Here’s a simple example. Imagine a variable K that represents whether someone has a potassium deficiency. K causes two things: it makes a person more likely to eat bananas (B), and it makes them more likely to get migraines (M). But K itself is hidden—the person doesn’t know whether they have it. If you look at the data, you’ll find that eating bananas is correlated with migraines. But that’s not because bananas cause migraines—it’s because both are caused by the hidden potassium deficiency.

Causal models give us a way to reason about this. One key principle is the Markov Condition. Roughly, it says that if you know the values of a variable’s direct causes (its “parents”), then knowing anything else that isn’t one of its effects doesn’t give you any extra information about it. In our example, if you know whether someone has the potassium deficiency, knowing whether they eat bananas tells you nothing extra about their migraine risk.

This condition turns out to be incredibly powerful. It means that from the pattern of correlations among variables, you can sometimes figure out the causal structure. But not always. If you only have correlations, you can often only narrow things down to a “Markov equivalence class”—a set of possible causal diagrams that all imply the same patterns of dependence and independence.

For instance, with three variables X, Y, and Z, if X and Z are independent but become dependent when you condition on Y, the only causal diagram that explains this is Y being a common effect of X and Z (so X causes Y and Z causes Y). But if X and Z are dependent unconditionally and independent given Y, there are several possible diagrams: X causes Y causes Z, X is caused by Y is caused by Z, or Y is a common cause of X and Z. You can’t tell which one is right just from the correlations.

This is why experiments are so valuable. If you intervene on a variable—say, you force people to eat bananas—you break the arrow from K to B, and you can see what really happens. In our banana example, without intervention, eating bananas looks bad (it’s correlated with migraines). But if you intervene to make people eat bananas, the correlation disappears, and you see that bananas are harmless or even beneficial.

Making Decisions: When Correlations Are Misleading

This matters for real decisions. Here’s a version of the banana example from the perspective of someone trying to decide what to do.

Cheryl sometimes has a potassium deficiency. When she does, she’s very likely to eat a banana and very likely to get a migraine. When she doesn’t, she’s unlikely to eat a banana and unlikely to get a migraine. Cheryl doesn’t know whether she has the deficiency. She enjoys bananas but hates migraines. Should she eat a banana?

If she just looks at the correlations—people who eat bananas are much more likely to get migraines—she might decide not to. That’s what evidential decision theory would recommend. But that seems wrong: eating the banana doesn’t cause the migraine. If she thinks of her choice as an intervention—she’s deciding to eat a banana regardless of what else is going on—she breaks the link between the deficiency and her banana-eating. Then she sees that the banana gives her pleasure without increasing her migraine risk. This is what causal decision theory recommends.

The difference is subtle but important. It comes up in real life whenever we’re deciding whether to do something that’s correlated with bad outcomes but doesn’t cause them. (Here’s a non-medical example: in some neighborhoods, people who go to college are more likely to move away from their families. Does going to college cause you to move away, or are both caused by something else—like ambition or opportunity? The answer matters for your decision.)

What We Still Don’t Know

Causal models are powerful tools, but they haven’t solved all the puzzles. Philosophers still argue about:

The definition of actual causation. There are dozens of proposals, and none satisfies everyone. The problem is that our intuitions about causation are shaped by context, and it’s hard to capture that in a mathematical formula.

The Markov Condition. Is it a metaphysical truth about how causation works, or just a useful assumption? Some philosophers argue it’s always true if you include enough variables; others say it can fail for genuinely random systems.

The role of probability. When we say that smoking causes lung cancer, we don’t mean it always does—we mean it increases the probability. But how much increase is enough? And what about cases where the probability increase is real but small?

Default vs. deviant values. In the Billy-and-Suzy case, we want to say Billy’s throw is “deviant” or “abnormal” because it would only happen as a backup. But how do we define “normal” in a way that works for all cases? Different cultures and different contexts have different ideas about what’s normal, and it’s not obvious that causation should depend on that.

These debates are still alive. That’s part of what makes causal models interesting—they give us a shared language to argue about things we don’t fully understand.

Key Terms

Term	What it does in this debate
Variable	A basic building block that can take different values (e.g., “Suzy throws” can be 1 or 0)
Intervention	Forcing a variable to have a particular value, overriding its normal causes
Counterfactual	A claim about what would have happened if something had been different
Directed Acyclic Graph (DAG)	A diagram with arrows showing causal relationships, with no loops
Markov Condition	A principle saying that a variable is independent of its non-effects, given its direct causes
Actual causation	The relation that holds between particular events that really happened (like Suzy’s throw breaking the window)
Causal Bayes Net	A causal model that combines a DAG with probabilities

Key People

Judea Pearl – A computer scientist and philosopher who developed many of the key ideas in causal models, including the do-calculus for reasoning about interventions.
Peter Spirtes, Clark Glymour, and Richard Scheines – A team of philosophers and statisticians who developed a complementary approach focusing on how to discover causal structures from data.
David Lewis – A philosopher who developed influential theories of causation and counterfactuals that causal models build on and challenge.

Things to Think About

In the Billy-and-Suzy case, we said Suzy caused the window to break even though it would have broken anyway. But what if there were three potential rock-throwers, all with different backup arrangements? Can you design a case where your intuition about who caused the break gets fuzzy?
The difference between evidential and causal decision theory comes up whenever you’re deciding whether to do something that’s correlated with bad outcomes. Can you think of a real situation where you’d want to use one rather than the other? What would you actually do?
Causal models assume we can pick the right variables to include. But what if you leave out an important variable? How would you know? And does the model’s answer depend on what you include or leave out?
The Markov Condition says that once you know the direct causes of something, other non-effects give you no extra information. But in the quantum world, this seems to fail—particles can be correlated without any common cause. Does this mean causation is different in the quantum world, or that our models need to change?

Where This Shows Up

Medicine. Doctors use causal models to figure out whether a treatment causes recovery or is just correlated with it. The famous question “does this drug work?” is really a question about causation.
Law. Courts need to decide whether someone’s actions caused harm. The “but for” test (“but for the defendant’s action, would the harm have occurred?”) is a counterfactual test, and causal models help make it precise.
Machine learning and AI. Researchers are building causal models into AI systems so they can reason about interventions and counterfactuals, not just correlations. This is a hot area right now.
Economics and social science. Researchers use causal models to figure out whether policies (like increasing the minimum wage) actually cause the effects we see (like changes in employment).
Your own decisions. Every time you decide whether to do something based on what you expect to happen, you’re implicitly using a causal model—whether you know it or not.