Chapter 1: The Ladder of Causation: Unedited Working Copy, Do Not Quote
Chapter 1: The Ladder of Causation: Unedited Working Copy, Do Not Quote
Chapter 1: The Ladder of Causation: Unedited Working Copy, Do Not Quote
The Book of Why: The New Science of Cause and Effect – Pearl and Mackenzie
In the Beginning…
I was probably six or seven years old when I first read the story of Adam and Eve in the
Garden of Eden. My classmates and I were not at all surprised by God’s capricious demands,
forbidding Adam from eating from the Tree of Knowledge. Deities have their reasons, we
thought. What we were more intrigued by was the idea that as soon as they ate from the Tree of
Knowledge, Adam and Eve became conscious, like us, of their nakedness.
As teenagers, our interest shifted slowly to the more philosophical sides of the story. (In
Israeli schools, Genesis is read several times a year.) Of primary concern to us was the notion
that the emergence of human knowledge was not a joyful process but a painful one, accompanied
by disobedience, guilt, and punishment. Was it worth giving up the carefree life of Eden? Some
asked. Were the agricultural and scientific revolutions that followed worth the economic
hardships, military conquests, and social injustices that modern life entails?
Don’t get me wrong: we were no creationists; even our teachers were Darwinists at heart.
We knew, however, that the author who choreographed the story of Genesis struggled to answer
the most pressing philosophical questions of his time. We likewise suspected that this story bore
the cultural footprints of the actual process by which Homo sapiens gained dominion over our
planet. What, then, was the sequence of steps in this speedy, super-evolutionary process?
it was reignited suddenly in the 1990s, when I was writing my book Causality, and came to
As I re-read Genesis for the hundredth time, I noticed a nuance that had somehow eluded
my attention for all those years. When God finds Adam hiding in the garden, he asks: “Have you
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eaten from the tree which I forbade you?” And Adam answers: The woman you gave me for a
companion, she gave me fruit from the tree and I ate. “What is this you have done?” God asks
As we know, this blame game did not work very well on the Almighty, who banished
both of them from the garden. The interesting thing, though, is that God asked what and they
answered why. God asked for the facts, and they replied with explanations. Moreover, both were
thoroughly convinced that naming causes would somehow paint their actions in a different color.
For me, these nuances carried three profound messages. First, that very early in our
evolution, humans came to realize that the world is not made up only of dry facts (what we might
call data today), but that these facts are glued together by an intricate web of cause-effect
relationships. Second, that causal explanations, not dry facts, make up the bulk of our
knowledge, and that satisfying our craving for explanation should be the cornerstone of machine
intelligence. Finally, that our transition from processors of data to makers of explanations was
not gradual—it required an external push from an uncommon fruit. This matched perfectly what
I observed theoretically in the Ladder of Causation: no machine can derive explanations from
find the Tree of Knowledge, but we still see a major unexplained transition. We understand now
that humans evolved from ape-like ancestors over a period of 5-6 million years, and that such
gradual evolutionary processes are not uncommon to life on Earth. But in roughly the last 50,000
years, something unique happened, which some call the Cognitive Revolution and others (with a
touch of irony) call the Great Leap Forward. Humans acquired the ability to modify their
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For example, over millions of years, eagles and owls have evolved truly amazing
Humans have produced these miracles in a matter of centuries. I call this phenomenon the
“super-evolutionary speedup.” Some readers might object to my comparing apples and oranges,
evolution to engineering, but that is exactly my point. Evolution has endowed us with the ability
to engineer our lives, a gift she has not bestowed upon eagles and owls, and the question is again,
Why? What computational facility did humans suddenly acquire that eagles lacked?
Many theories have been proposed, but there is one I like because it is especially
pertinent to the idea of causation. In his book Sapiens, historian Yuval Harari posits that our
ancestors’ capacity to imagine non-existent things was the key to everything, for it allowed them
to communicate better. Before this change, they could only trust people from their immediate
family or tribe. Afterward their trust extended to larger communities, bound by common beliefs
and common expectations (for example, beliefs in invisible yet imaginable deities, in the
afterlife, and in the divinity of the leader). Whether you agree with Harari’s theory or not, the
connection between imagining and causal relations is almost self-evident. It is useless to know
the causes of things unless you can imagine their consequences. Conversely, you cannot claim
that Eve caused you to eat from the tree unless you can imagine a world in which, counter to
Back to our H. sapiens ancestors: their newly acquired causal imagination enabled them
to do many things more efficiently, through a tricky process we call “planning.” Imagine a tribe
preparing for a mammoth hunt. What would it take for them to succeed? My mammoth-hunting
skills are rusty, I must admit, but as a student of thinking machines I have learned one thing. The
only way a thinking entity (computer, caveman, or professor) can accomplish a task of such
magnitude is to plan things in advance. To decide how many hunters to recruit; to gauge, given
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the wind conditions, what direction to approach the mammoth; and more. In short, to imagine
and compare the consequences of several hunting strategies. To do this, it must possess, consult,
Each dot in the diagram represents a cause of success. Note that there are multiple causes,
and that none of them are deterministic. That is, we cannot be sure that more hunters will enable
us to succeed, or that rain will prevent us from succeeding; but these factors do change our
probability of success.
The mental model is the arena where imagination takes place. It enables us to experiment
with different scenarios, by making local alterations to the model. Somewhere in our hunters’
mental model was a subroutine that evaluated the effect of the number of hunters. When they
considered adding more, they didn’t have to evaluate every other factor from scratch. They could
make a local change to the model, replacing “Hunters = 8” by “Hunters = 9” and re-evaluating
I don’t mean to imply, of course, that early humans actually drew a pictorial model like
this one. Of course not! But when we seek to emulate human thought on a computer, or indeed
when we try to solve unfamiliar scientific problems, drawing an explicit dots-and-arrows picture
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is extremely useful. You will see many in this book, and I will call them causal diagrams. They
are the computational core of the “causal inference engine” described in Chapter 1.
So far I may have given the impression that the ability to organize our knowledge of the
world into causes and effects was monolithic and acquired all at once. But in fact, my research
on machine learning has taught me that there are at least three distinct levels that need to be
The first cognitive ability, seeing or observation, is the detection of regularities in our
environment, and it is shared by many animals as well as early humans before the Cognitive
Revolution. The second ability, doing, stands for predicting the effect(s) of deliberate alterations
of the environment, and choosing among these alterations to produce a desired outcome. Only a
small handful of species have demonstrated elements of this skill. Usage of tools, provided they
are designed for a purpose and not just picked up by accident or copied from one’s ancestors,
could be taken as a sign of reaching this second level. Yet even tool users do not necessarily
possess a “theory” of their tool that tells them why their tool works and what to do when it
doesn’t. For that, you need to be at a level of understanding that permits imagining. It was
primarily this third level that prepared us for further revolutions in agriculture and science, and
led to a sudden and drastic change in our species’ impact on planet Earth.
I cannot prove this, but what I can prove mathematically is that the three levels are
fundamentally different, each unleashing capabilities that the ones below it do not. The
framework I will use to show this goes back to Alan Turing, the pioneer of research in artificial
intelligence, who proposed to classify a cognitive system in terms of the queries it can answer.
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Figure 2. The Ladder of Causation, with representative organisms at each level. Most animals as
well as present-day learning machines are on the first rung, learning from association. Tool
users, such as early humans, are on the second rung, if they act by planning and not merely by
imitation. We can also use experiments to learn the effects of interventions, and presumably this
is how babies acquire much of their causal knowledge. On the top rung, counterfactual learners
can imagine worlds that do not exist and infer reasons for observed phenomena.
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This is an exceptionally fruitful approach when we are talking about causality, because it
bypasses long and unproductive discussions of “What is causality exactly?” and focuses instead
on the concrete and answerable question, “What can a causal reasoner do?” Or more precisely,
what can an organism possessing a causal model compute that one lacking such a model cannot?
While Turing was looking for a binary classification—human or non-human—ours has three
tiers, corresponding to progressively more powerful causal queries. Using these criteria, we can
assemble the three levels of queries into one Ladder of Causation (Figure 2), a metaphor that we
Let’s take some time to consider each rung of the ladder in detail. At the first level,
Association, we are looking for regularities in observations. This is what an owl does when it
observes how a rat moves and figures out where it is likely to be a moment later, and it is what a
computer go program does when it studies a database of millions of go games so that it can
figure out which moves are associated with a higher percentage of wins. We say that one event is
associated with another if observing one changes the likelihood of observing the other.
The first rung of the ladder calls for predictions based on passive observations. It is
characterized by the question: “What if we see [X]?” For instance, imagine a marketing director
at a department store, who asks, “How likely is it that a customer who bought toothpaste will
also buy dental floss?” Such questions are the bread and butter of statistics, and they are
answered, first and foremost, by collecting and analyzing data. In our case, the question can be
answered by first taking the data consisting of the shopping behavior of all customers, selecting
only those who bought toothpaste, and, focusing on the latter group, computing the proportion
who also bought dental floss. This proportion, also known as a “conditional probability,”
measures (for large data) the degree of association between “buying toothpaste” and “buying
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floss.” Symbolically, we can write it as P(Floss|Toothpaste). The “P” stands for “probability,”
Statisticians have developed many elaborate methods to reduce a large body of data and
identify associations between variables. A typical measure of association, which we will mention
often in this book, is called “correlation” or “regression,” which involves fitting a line to a
collection of data points and taking the slope of that line. Some associations might have obvious
causal interpretations. Other associations may not. But statistics alone cannot tell which is the
cause and which is the effect, toothpaste or floss. From the point of view of the sales manager, it
may not really matter. Good predictions need not have good explanations. The owl can be a good
hunter without understanding why the rat always goes from point A to point B.
Some readers may be surprised to see that I have placed present-day learning machines
squarely on rung one of the Ladder of Causation, sharing their wisdom with an owl. We hear
almost every day, it seems, about rapid advances in machine learning systems—self-driving cars,
speech-understanding systems, and especially in recent years, deep-learning algorithms (or deep
neural networks). How could it be that they are still only at level one?
The successes of deep learning have been truly remarkable, and have caught many of us
by surprise. Nevertheless, deep learning has succeeded primarily by showing that certain
questions or tasks we thought were difficult are in fact not so difficult. It has not addressed the
truly difficult questions that continue to prevent us from achieving human-like AI. The result is
that the public believes that “strong AI,” machines that think like humans, is just around the
corner or maybe even here already. In reality, nothing could be farther from the truth. I fully
agree with Gary Marcus, a neuroscientist at New York University, who recently wrote in the
New York Times that the field of artificial intelligence is “bursting with microdiscoveries”—the
sort of things that make good press releases—but that machines are still disappointingly far from
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human-like cognition. My colleague in computer science at UCLA, Adnan Darwiche, has just (as
Abilities?” which I think frames the question in just the right way. The goal of strong AI is to
produce machines with human-like intelligence, able to converse with humans and guide us.
What we have gotten from deep learning instead is machines with abilities—truly impressive
abilities—but no intelligence. The difference is profound, and lies in the absence of a model of
reality.
Just as they did 30 years ago, machine-learning programs (including those with deep
neural networks) operate almost entirely in an associational mode. They are driven by a stream
of observations to which they attempt to fit a function, in much the same way that a statistician
tries to fit a line to a collection of points. Deep neural networks have added many more layers to
the complexity of the fitted function but still, what drives the fitting process is raw data. They
continue to improve in accuracy as more data are fitted, but they do not benefit from the “super-
evolutionary speedup” that we encountered above. They end up with a brittle, special-purpose
system that is inscrutable even to its programmers. The architects of a program like AlphaGo
(which recently defeated the best human go players) do not really know why it works, only that it
does. The lack of flexibility, adaptability, and transparency is not in the least bit surprising; it is
inevitable in any system that works at the first level of the Ladder of Causation.
We step up to the next level of causal queries when we begin to change the world. A
typical question for this level is, “What will happen to our floss sales if we double the price of
toothpaste?” This already calls for a new kind of knowledge, absent from the data, which we find
Intervention ranks higher than Association because it involves not just seeing what is, but
changing what is. Seeing smoke tells us a totally different story about the likelihood of fire than
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making smoke. Questions about interventions cannot be answered by using passively collected
data, no matter how big the data or how deep your neural network. It has been quite traumatic for
many scientists to learn that none of the methods they learn in statistics are sufficient even to
articulate, let alone answer, a simple question like, “What happens if we double the price?” I
know this because I have had many occasions to help them climb to the next rung of the ladder.
Why can’t we answer our floss question just by observation? Why not just go into our
vast database of previous purchases and see what happened previously when toothpaste cost
twice as much? The reason is that on the previous occasions, the price may have been higher for
different reasons. For example, the product may have been in short supply, and every other store
also had to raise its price. But now you are considering a deliberate intervention that will set a
new price regardless of market conditions. The result might be quite different from what it was
when the customer couldn’t find a better deal anywhere else. If you had data on the market
conditions that existed on the previous occasions, perhaps you could figure it out… but what data
do you need? And then, how would you figure it out? Those are exactly the questions the science
One very direct way to predict the result of an intervention is to experiment with it under
carefully controlled conditions. Big Data companies like Facebook know this, and they
constantly perform experiments to see what happens if items on the screen are arranged
differently, or if the customer is given a different prompt (or even a different price).
What is more interesting, and less widely known—even in Silicon Valley—is that
successful predictions of the effects of interventions can sometimes be made even without an
experiment. For example, the sales manager could develop a model of consumer behavior that
includes market conditions. Even if she doesn’t have data on every factor, she might have data
on enough key surrogates to make the prediction. A sufficiently strong and accurate causal
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model can allow us to use rung-one (observational) data to answer rung-two (interventional)
queries. Without the causal model, we could not go from rung one to rung two. This is why
deep-learning systems (as long as they use only rung-one data and do not have a causal model)
will never be able to answer questions about interventions, which by definition break the rules of
As these examples illustrate, the defining query of the second rung of the Ladder of
Causation is, “What if we do?” What will happen if we change the environment? We can write
this kind of query as P(Floss|do(Toothpaste)), the probability that we will sell floss at a certain
Another popular question at the second level of causation is “How?”, which is a cousin of
“What if we do?” For instance, the manager may tell us that we have too much toothpaste in our
warehouse. “How can we sell it?” he asks. That is, at what price should we set it? Again, the
question refers to an intervention, which we want to perform mentally before we decide whether
Interventions occur all the time in our daily lives, although we don’t usually use such a
fancy term for them. For example, when we take aspirin to cure a headache, we are intervening
on one variable (the quantity of aspirin in our body) in order to affect another one (our headache
status). If we are correct in our causal belief about aspirin, the “outcome” variable will respond
While reasoning about interventions is an important step on the causal ladder, it still does
not answer all questions of interest. We often wish to ask: My headache is gone now, but why?
Was it the aspirin I took? The food that I ate? The good news I heard? These queries take us to
the top rung of the Ladder of Causation, the level of Counterfactuals, because to answer them we
must go back in time, change history and ask, “What would have happened if I had not taken the
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aspirin?” No experiment in the world can deny treatment to an already treated person and
compare the two outcomes, so we must import a whole new kind of knowledge.
Counterfactuals have a particularly problematic relationship with data because data are,
by definition, facts. They cannot tell us what will happen in a counterfactual or imaginary world,
in which some observed facts are bluntly negated. Yet the human mind does make such
explanation-seeking inferences, reliably and repeatably. Eve did it when she identified “The
serpent deceived me” as the reason for her action. This is the ability that most distinguishes
human from animal intelligence, as well as model-blind versions of AI and machine learning.
You may be skeptical that science can make any useful statement about “would haves,”
worlds that do not exist and things that have not happened. But it does, and it always has. The
laws of physics, for example, can be interpreted as counterfactual assertions, such as: Had the
weight on this spring doubled, its length would have doubled as well (Hooke’s Law). This
anointed with the term “law,” physicists interpret it as a functional relationship that governs this
very spring, at this very moment of time, under hypothetical values of the weight. All of these
different worlds, where the weight is x pounds and the length of the spring is Lx inches, are
treated as being objectively knowable, and simultaneously active, even though only one of them
actually exists.
Going back to the toothpaste example, a top-rung question would be, “What is the
probability that a customer who bought toothpaste would still have bought it if we had doubled
the price?” We are comparing the real world (where we know that the customer bought the
toothpaste at the current price) to a fictitious world (where the price is twice as high).
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The rewards of having a causal model that can answer counterfactual questions are
immense. Finding out why a blunder occurred allows us to take the right corrective measures in
the future. Finding out why a treatment worked on some people and not on others can lead to a
new cure for a disease. Answering the question “What if things had been different?” allows us to
learn from history and from the experience of others, something that no other species appears to
do. It is not surprising that the ancient Greek philosopher Democritus (460-370 BC) said, “I
The position of counterfactuals at the top of the Ladder of Causation explains why I place
such emphasis on them as a key moment in the evolution of human consciousness. I totally agree
with Yuval Harari that the depiction of imaginary creatures was a manifestation of a new ability,
which he calls the cognitive revolution. His prototypical example is the Lion Man sculpture,
found in Stadel Cave in southwestern Germany and now held at the Ulm Museum (see Figure 3).
The Lion Man, roughly 40 thousand years old, is a mammoth tusk that has been sculpted in the
We do not know who sculpted the Lion Man or what its purpose was, but we do know it
was made by anatomically modern humans and that it represents a break with any art or craft that
had gone before. Previously, humans had fashioned tools and representational art, from beads to
flutes to spear points to elegant carvings of horses and other animals. The Lion Man is different:
As a manifestation of our newfound ability to imagine things that have never existed, the
Lion Man is the precursor to every philosophical theory, scientific discovery, and technological
innovation, from microscopes to airplanes to computers. Every one of these had to take shape in
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Figure 3. The Lion Man of Stadel Cave. The earliest known representation of an imaginary
creature (half man and half lion), it is emblematic of a newly developed cognitive ability, the
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This leap forward in cognitive ability was as profound and important to our species as
any of the anatomical changes that made us human. Within 10,000 years after the Lion Man’s
creation, all other hominids (except for the very geographically isolated Flores hominids) had
become extinct. And humans have continued to change the natural world with incredible speed,
using our imagination to survive, adapt, and ultimately take over. The advantage we gained from
imagining counterfactuals was the same then as it is today: flexibility, the ability to reflect on
and improve upon past actions and, perhaps even more significant, our willingness to take
As shown in Figure 2, the characteristic queries for the third rung of the Ladder of
Causation are “What if I had done…?” and “Why?” Both of these involve comparing the
alone. While rung one deals with the seen world, and rung two deals with a brave new world that
is seeable, rung three deals with a world that cannot be seen (because it contradicts what is seen).
To bridge the gap, we need a model of the underlying causal process, sometimes called a
“theory” or even (in cases where we are extraordinarily confident) a “law of nature.” In short, we
need understanding.This is, of course, one of the holy grails of any branch of science—the
development of a theory that will enable us to predict what will happen in situations we have not
even envisioned yet. But it goes even further: having such laws permits us to violate them
selectively, so as to create worlds that contradict ours. Our next section will feature such
violations in action.
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In 1950, Alan Turing asked what it would mean for a computer to think like a human. He
suggested a practical test, which he called “the imitation game,” but every AI researcher since
then has called it the “Turing test.” For all practical purposes, a computer could be called a
thinking machine if an ordinary human, communicating with the computer by typewriter, would
not be able to tell whether he was talking with a human or a computer. Turing was very
confident that this was within the realm of feasibility. “I believe that in about fifty years’ time it
will be possible to program computers,” he wrote, “… to make them play the imitation game so
well that an average interrogator will not have more than a 70 percent chance of making the right
Turing’s prediction was slightly off. Every year the Loebner Prize competition identifies
the most human-like “chatbot” in the world, with a gold medal and $100,000 offered to any
program that succeeds in fooling all four judges into thinking that it is human. As of 2015, in 25
years of competition, not a single program has fooled all the judges or even half of them.
Turing didn’t just suggest the “imitation game,” he also proposed a strategy to pass it.
“Instead of trying to produce a program to simulate the adult mind, why not rather try to produce
one which simulates the child’s?” he asked. If you could do that, then you could just teach it the
same way you would teach a child and presto, twenty years later (or less, given a computer’s
greater speed), you would have an artificial intelligence. “Presumably the child brain is
something like a notebook as one buys it from the stationer’s,” he wrote. “Rather little
mechanism, and lots of blank sheets.” He was wrong about that: the child’s brain is rich in
Nonetheless, I think that Turing’s instinct had more than a kernel of truth. We probably
will not succeed in creating human-like intelligence until we can create child-like intelligence,
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How can machines acquire causal knowledge? That is still a major challenge which
undoubtedly will involve an intricate combination of inputs from active experimentation, passive
observation, and (not least) input from the programmer—much the same inputs that a child
receives, with evolution, parents, and peers substituted for the programmer.
However, we can answer a slightly less ambitious question: How can machines (and
people) represent causal knowledge, in a way that would enable them to access the necessary
information swiftly, answer questions correctly, and do it with ease, as a three-year-old child
I call this the mini-Turing test. The idea is to take a simple story, encode it on a machine
in some way, and then test to see if the machine can correctly answer causal questions that a
human can answer. It is “mini” for two reasons. First, because it is confined to causal reasoning,
excluding other aspects of human intelligence such as vision and natural language. Second, we
allow the contestant to encode the story in any convenient representation, unburdening the
machine from the task of acquiring the story from its own personal experience. Passing this mini-
test has been my life’s work—consciously for the last twenty-five years, and subconsciously
needs to precede the question of acquisition. Without a representation, we wouldn’t know how to
store information for future usage. Even if we could let our robot manipulate its environment at
will, whatever information we learned this way is destined to be forgotten, unless our robot is
endowed with a template to encode the results of those manipulations. One major contribution of
AI to the study of cognition has been the paradigm: “Representation first, acquisition second.”
Often it turned out that the quest for a good representation led to insights on how the knowledge
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When I describe the mini-Turing test to people, one common reaction is to claim that it
can easily be defeated by cheating. For example, take the list of all possible questions, store their
correct answers, and then read them out from memory when asked. There is no way to
distinguish (so the argument goes) between a machine that stores a dumb question-answer list
and one that answers the way that you and I do it, that is, by understanding the question and
producing an answer using a mental causal model. So what would the mini-Turing test prove, if
cheating is so easy?
This cheating possibility, known as the “Chinese Room Argument,” was introduced in
1980 by the philosopher John Searle to challenge Turing’s claim that the ability to fake
intelligence amounts to having intelligence. Searle’s challenge has only one flaw: cheating is not
easy; in fact it is impossible. Even with a small number of variables, the number of possible
questions grows astronomically. Say that we have 10 causal variables, each of which takes only
two values (0 or 1). There are roughly 30 million possible queries that we could ask, such as
“What is the probability that the outcome is 1, given that we see variable X equals 1 and we
make variable Y equal 0 and variable Z equal 1?” If there were more variables, or more than two
states for each one, the number of possibilities would grow beyond our ability to even imagine.
Searle’s list would need to have more entries than the number of atoms in the universe. So it is
clear that a dumb list of questions and answers will never be able to simulate the intelligence of a
Humans must have some compact representation of the information needed in their
brains, as well as an effective procedure to interpret each question properly and extract the right
answer from the stored representation. To pass the mini-Turing test, therefore, we need to equip
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Such a representation not only exists, but it has childlike simplicity: a causal diagram. We
have already seen one example, the diagram for the mammoth hunt. Considering the extreme
ease with which people can communicate their knowledge with dot-and-arrow diagrams, I
believe that our brains indeed use a representation something like this. But more important for
our purposes, these models pass the mini-Turing test; no other model is known to do so. Let’s
events has to occur for this to happen. First, the court has to order the execution. The order goes
to a captain, who signals the soldiers on the firing squad (A and B) to fire. We’ll assume that
they are obedient and expert marksmen, so they only fire on command and if either one of them
Captain (C )
A B
Death (D)
Figure 4. Causal diagram for the firing squad example. A and B represent (the actions of)
soldiers A and B.
D = True means the prisoner is dead, D = False means the prisoner is alive. CO = False means
the court order was not issued, CO = True means it was, and so on.
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Using this diagram, we can start answering causal questions from different rungs of the
ladder. First, we can answer questions of association, i.e., what one fact tells us about another. If
the prisoner is dead, does that mean the court order was given? We (or a computer) can inspect
the graph, trace the rules behind each of the arrows, and using ordinary logic, conclude that the
two soldiers wouldn’t have fired without the captain’s command. Likewise, the captain wouldn’t
have given the command if he didn’t have the order in his possession. Therefore the answer to
our query is Yes. Alternatively, suppose we find out that A fired. What does that tell us about B?
By following the arrows, the computer concludes that B must have fired, too. (A would not have
fired if the captain hadn’t signaled, so B must have fired as well.) This is true even though A
Going up the Ladder of Causation, we can ask questions of intervention. What if soldier
A decides on his own initiative to fire, without waiting for the captain’s command? Will the
This question in fact already has a contradictory flavor to it. I just told you that A only
shoots if commanded to, and yet now we are asking what happens if he fired without a
command. If you’re just using the rules of logic, as computers typically do, the question is
meaningless. As the Robot in the 1960s sci-fi TV series Lost in Space used to say in such
If we want our computer to understand causation, we have to teach it how to break the
rules. We have to teach it the difference between merely observing an event as compared to
making it happen. “Whenever you make an event happen,” we tell the computer, “remove all
arrows that point to that event and continue the analysis by ordinary logic, as if the arrows had
never been there.” Thus, we erase all the arrows leading into the intervened variable (A). We
also set that variable manually to its prescribed value (True). The rationale for this peculiar
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“surgery” is simple: making an event happen means that you emancipate it from all other
influences and subject it to one and only one influence—that which enforces its happening.
In our example, the resulting causal diagram is shown in Figure 5. Under this
intervention, the result is inevitably the prisoner’s death. That is the causal meaning of the arrow
leading from A to D.
Note that this conclusion agrees with our intuitive judgment that A’s unauthorized firing
will lead to the prisoner’s death, because the surgery leaves the arrow A D intact. Also, our
judgment would be that B (in all likelihood) did not shoot; nothing about A’s decision should
affect variables in the model that are not effects of A’s shot. This bears repeating. If we see A
Captain (C )
A = True B
Death (D)
Figure 5. Reasoning about interventions. Soldier A decides to fire; arrow from C to A is deleted
shoot, then we conclude that B shot too. But if A decides to shoot, or if we make A shoot, then
the opposite is true2. This is the difference between seeing and doing. Only a computer capable
2
Another way to say this is that when evaluating an intervention in a causal model, we make the
minimum changes possible to enforce its immediate effect. So we “break” the model where it
comes to A, but not B.
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Note also that merely collecting big data would not have helped us go up the ladder and
answer the above questions. Assume that you are a reporter collecting records of execution
scenes day after day. Your data will consist of two kinds of events: either all five variables are
true, or all of them are false. There is no way that this kind of data, in the absence of an
understanding of who listens to whom, will enable you (or any machine learning algorithm) to
Finally, to illustrate the third rung of the Ladder of Causation, let’s answer a
counterfactual question. Suppose the prisoner is lying dead on the ground. From this we can
conclude (using level one) that A shot, B shot, the captain gave the signal, and the court gave the
order. If, contrary to fact, A had decided not to shoot, would the prisoner be alive? This question
requires us to compare the real world with a fictitious and contradictory world where A didn’t
shoot. In the fictitious world, the arrow leading into A is erased and A is set to False, but the past
history of A stays the same as it was in the real world. So the fictitious world looks like Figure 6.
To pass the mini-Turing test, our computer must conclude that the prisoner would be
dead in the fictitious world as well, because B’s shot would have killed him. So A’s courageous
change of heart would not have saved his life. Undoubtedly this is one of the reasons firing
squads exist. They guarantee that the court’s order will be carried out, and they also lift some of
the burden of responsibility off the individual shooters, who can say with a (somewhat) clean
conscience that their action did not cause the prisoner’s death: “He would have died anyway.”
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Captain (C ) = True
A = False B = True
Death (D) = ?
Figure 6. Counterfactual reasoning. We observe that the prisoner is dead, and ask what would
It may seem as if we are going to a lot of trouble to answer toy questions whose answer
was obvious anyway. I completely agree! Causal reasoning is easy for you because you are
human, and you were once a three-year-old, and you had a marvelous three-year-old brain that
understood causation better than any animal or computer. The whole point of the “mini-Turing
problem” is to make causal reasoning feasible for computers, too; in the process, we might learn
something about how humans do it. As we have seen in all three examples, we have to teach the
computer how to selectively break the rules of logic. Computers are not good at breaking rules, a
skill at which children excel. (Cavemen too! The Lion Man could not have been created without
breaking the rules about what head goes with what body.)
However, let’s not get too complacent about human superiority. There are a great many
situations where humans may have a much harder time reaching correct causal conclusions. For
example, there could be many more variables, and they might not be simple binary (true-false)
variables. Instead of predicting whether a prisoner is alive or dead, we might want to predict how
much the unemployment rate would go up in the event of a raise in the minimum wage. This
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kind of quantitative causal reasoning is generally beyond the power of our intuition. Also, in the
firing squad example we ruled out uncertainties: maybe the captain gave his order a split second
after rifleman A decided to shoot, maybe rifleman B’s gun jammed, etc. To handle uncertainty
Let me give you an example in which probabilities make all the difference. It echoes the
public debate that erupted in Europe when smallpox vaccination was first introduced.
Unexpectedly, data showed that more people died from smallpox inoculations than from
smallpox itself. Naturally, some people used this information to argue that inoculation should be
banned when, in fact, it was saving lives by eradicating smallpox. Let’s look at some fictitious
Suppose that out of 1 million children, 99 percent are vaccinated and 1 percent are not. If
a child is vaccinated, he or she has 1 chance in 100 of developing a reaction, and the reaction has
1 chance in 100 of being fatal. On the other hand, he or she has no chance of developing
smallpox. Meanwhile, if a child is not vaccinated, he or she obviously has zero chance of
developing a reaction to the vaccine, but he or she has 1 chance in 50 of developing smallpox.
I think you would agree that vaccination looks like a good idea. The odds of having a
reaction are less than the odds of getting smallpox, and the reaction is much less dangerous than
the disease. But now let’s look at the data. Out of 1 million children, 990 thousand get
vaccinated; 9,900 get the reaction; and 99 die from the reaction. Meanwhile, 10 thousand don’t
get vaccinated, 200 get smallpox, and 40 die from the disease. In summary, more children die
I can empathize with the parents who might march to the health department with signs
saying, “Vaccines killed our children!” And the data seem to be on their side; the vaccinations
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indeed are causing more death than smallpox itself. But is logic on their side? Should we ban
vaccination, or take into account the deaths prevented? We can make this clear using the causal
Vaccination
Reaction Smallpox
Death
When we began, the vaccination rate was 99 percent. We now ask the counterfactual
question: What if we had set the vaccination rate to 0? Using the probabilities I gave you above,
we can conclude that out of 1 million children, 20 thousand would have gotten smallpox and
4,000 would have died. Comparing the counterfactual world with the real world, we see that the
cost of not vaccinating was the death of 3,861 children (the difference between 4,000 and 139).
We should thank the language of counterfactuals for helping us to avoid such costs.3
The main lesson for a student of causality is that there is more to a causal model than
merely writing arrows. Behind the arrows, there are probabilities. When we draw an arrow from
X to Y, then implicitly we are saying that there is some probability rule or function specifying
how Y would change if X were to change. We might know what the rule is; more likely, we will
have to estimate it from data. One of the most intriguing features of the Causal Revolution,
3
I should also mention here that counterfactuals allow us to talk about causality in individual
cases: what would have happened to Mr. Smith, who was not vaccinated and died of smallpox, if
he had not been vaccinated? Such questions, the backbone of personalized medicine, cannot be
answered from rung-two information.
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though, is the fact that we can in many cases leave those mathematical details completely
unspecified. Very often the structure of the diagram itself enables us to estimate all sorts of
linear or non-linear.
From the computing perspective, another remarkable thing about our scheme for passing
the mini-Turing test is the fact that we used the same routine in all three examples: Translate the
story into a diagram, listen to the query, perform a surgery that corresponds to the given query
then use the modified causal model to compute the answer. We did not have to train the machine
on a multitude of new queries each time we changed the story. The approach is flexible enough
to work whenever we can draw a causal diagram, whether it has to do with mammoths, firing
squads, or vaccinations. This is exactly what we want for a causal inference engine: it is the kind
Of course, there is nothing inherently magic about a diagram. The success of the diagram
is attributable to the fact that it carries causal information; that is, when we constructed the
diagram we asked ourselves, “Who could be a direct cause of the prisoner’s death?” or “What
are the direct effects of vaccinations?” Had we constructed the diagram by asking about mere
associations, it would not have given us these capabilities. For example, in Figure 7, if we
reversed the arrow Vaccination Smallpox we would get the same associations in the data, but
Decades of experience with these kinds of questions have given me a firm conviction
that, in both a cognitive sense and a philosophical sense, the idea of causes and effects is much
more fundamental than the idea of probability. We begin learning causes and effects before we
understand language, and before we know any mathematics. (Research has shown that three-
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year-olds already understand the entire Ladder of Causation.) Likewise, the knowledge conveyed
in a causal diagram is typically much more robust than the knowledge encoded in a probability
distribution. For example, suppose that times have changed and a new vaccine is introduced
which is much safer and more effective. Suppose, further, that due to improved hygiene and
socioeconomic conditions, the danger of contracting smallpox has diminished. These changes
will drastically affect all of the probabilities involved, yet, remarkably, the structure of the
diagram would remain invariant. This is the key secret of causal modeling. Moreover, once we
go through the analysis and find how to estimate the benefit of vaccination from data, we do not
have to repeat the entire analysis from scratch. As discussed in the Introduction, the same
estimand (i.e., recipe for answering the query) will remain valid and, as long as the diagram does
not change, it can be applied to the new data and produce a new estimate for our query. It is
because of this robustness, I conjecture, that human intuition is organized around causal, not
statistical relations.
The recognition that causation is not reducible to probabilities has been very hard-won,
both for me personally and for philosophers and scientists in general. The drive to understand
what a “cause” means has been the focus of a long tradition of philosophers, from Hume and
Mill in the 1700s and 1800s to Hans Reichenbach and Patrick Suppes in the mid-1900s, to
Nancy Cartwright, Wolfgang Spohn and Christopher Hitchcock today. In particular, beginning
with Reichenbach and Suppes, philosophers have tried to define causation in terms of
probability, using the notion of “probability raising”: X causes Y if X raises the probability of Y.
This concept is solidly ensconced in intuition. We say, for example, “reckless driving
causes accidents” or “you will fail this course because of your laziness,” knowing quite well that
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the antecedents merely tend to make the consequences more likely, not absolutely certain. One
would expect, therefore, that probability raising should become the bridge between rung one and
rung two of the Ladder of Causation. Alas, this intuition has led to decades of failed attempts.
What prevented the attempts from succeeding was not the idea itself but the way it was
articulated formally. Almost without exception, philosophers expressed the sentence, “X raises
the probability of Y” using conditional probabilities and wrote: P(Y|X) > P(Y). This
interpretation is wrong, as you surely noticed, because “raises” is a causal concept, connoting a
causal influence that X has over Y. The expression P(Y|X) > P(Y), on the other hand, speaks
only about observations, and means, “If we see X, then the probability of Y increases.” But this
increase may come about for other reasons, including Y being a cause of X or some other
variable (Z) being the cause of both of them. That’s the catch! It puts the philosophers back on
Probabilities, as given by expressions like P(Y|X), lie on the first rung of the Ladder of
Causation and they cannot ever (by themselves) answer queries on the second or third rung. Any
attempt to “define” causation in terms of simpler, first-rung concepts must fail. That is why I
have not attempted to define causation anywhere in this book; definitions demand reduction and
reduction demands going to a lower rung. Instead, I have pursued the ultimately more
constructive program of explaining how to answer causal queries and what information is needed
to answer them. If this seems odd, consider that mathematicians take exactly the same approach
to Euclidean geometry. Nowhere in a geometry book will you find a definition of the terms
“point” and “line.” Yet we can answer any and all queries about them on the basis of Euclid’s
axioms (or even better, the various modern versions of Euclid’s axioms).4
4
To be more precise: in geometry, undefined terms like “point” and “line” are primitives. The
But let’s look at this criterion of probability raising more carefully and see where it runs
aground. The issue of a common cause or confounder of X and Y, mentioned above, was one of
the most vexing ones for philosophers. If we take the probability-raising criterion at face value,
we would have to conclude that high ice cream sales cause crime, because the probability of
crime is higher in months when more ice cream is sold. In this particular case, we can explain the
phenomenon because both ice cream sales and crime are higher in summer, when the weather is
warmer. Nevertheless, the question remains: what general philosophical criterion could tell us
Philosophers tried hard to repair the definition by conditioning on what they called
“background factors” (another word for confounders), yielding the criterion P(Y|X, K = k) >
P(Y|K = k), where K stands for some background variables. In fact, this criterion works for our
ice cream example, if we treat temperature as a background variable. For example, if we look
only at days when the temperature is 90 degrees (K = 90), we will find no residual association
between ice cream sales and crime. It’s only when we compare 90-degree days to 30-degree days
Still, no philosopher has been able to give a convincingly general answer to the question:
Which variables need to be included in the background set K and conditioned on? The reason is
obvious; confounding too is a causal concept, hence defies probabilistic formulation. In 1983,
Nancy Cartwright broke this deadlock and enriched the description of the background context
with a causal component. She proposed that we should condition on any factor that is “causally
relevant” to the effect. By borrowing a concept from rung two of the Ladder of Causation she
essentially gave up on the idea of defining causes from probability alone. This was progress, but
it opens the door to the criticism that we are defining a cause in terms of itself.
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Philosophical disputes over the appropriate content of K continued for more than two
decades and reached an impasse. In fact, we will see a correct criterion in Chapter 4 and I will
not spoil the surprise here. It will suffice for the moment to say that this criterion is practically
In summary, confounding has always been the rock on which probabilistic causality has
foundered. Every time the adherents of probabilistic causation try to patch up the ship with a new
hull, the boat runs into the same rock and springs another leak. Once you misrepresent
patching will get you to the next rung of the ladder. As strange as it may sound, the notion of
The proper way to rescue the probability-raising idea would be with the do-operator: we
could say that X causes Y if P(Y| do(X)) > P(Y). Since intervention is a rung-two concept, this
definition can capture the causal notion of probability raising, and it can also be made
operational through causal diagrams. In other words, if we have a causal diagram and data on
hand and a researcher asks whether P(Y| do(X)) > P(Y), we can answer his question coherently
I usually pay a great deal of attention to what philosophers have to say about slippery
concepts such as causation, induction, and the logic of scientific inference. Philosophers have the
advantage of standing apart from the hurly-burly of scientific debate and the practical realities of
dealing with data. They have been less contaminated than other scientists by the anti-causal
biases of statistics. They can call upon a tradition of thought about causation that goes back at
least to Aristotle, and they can talk about causation without blushing or hiding it behind the label
of “association.”
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idea—philosophers were too quick to commit to the only uncertainty-handling language they
knew, the language of probability. They have for the most part gotten over this blunder, but
unfortunately similar ideas are being pursued in econometrics even now, under names like
Now I have a confession to make: I made the same mistake, too. I did not always put
causality first and probability second. Quite the opposite! When I started working in artificial
intelligence, in the early 1980s, I thought that the most important thing missing from AI’s was
Bayesian networks, which mimics how an idealized, decentralized brain might incorporate
probabilities into its decisions. Given that we see certain facts, Bayesian networks can swiftly
compute how likely it is that certain other facts are true or false. Not surprisingly, Bayesian
networks caught on immediately in the AI community, and even today they are considered one
Though I am delighted with the ongoing success of Bayesian networks, they failed to
bridge the gap between artificial and human intelligence. I’m sure you can figure out the missing
ingredient: causality. True, causal ghosts were all over the place. The arrows invariably pointed
from causes to effects, and practitioners often noted that diagnostic systems became
unmanageable when the direction of the arrows was reversed. But for the most part we thought
that this was a cultural habit, or an artifact of old thought patterns, not a central aspect of
intelligent behavior.
At the time, I was so intoxicated with the power of probabilities that I considered
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probabilistic dependencies, and for distinguishing relevant variables from irrelevant ones. In my
1988 book Probabilistic Reasoning in Intelligent Systems, I wrote, “Causation is a language with
which one can talk efficiently about certain structures of relevance relationships.” The words
embarrass me today, because “relevance” is so obviously a rung 1 notion. Even by the time the
book was published, I knew in my heart that I was wrong. To my fellow computer scientists, my
book became the bible of reasoning under uncertainty, but I was already feeling like an apostate.
Bayesian networks inhabit a world where all questions are reducible to probabilities, or
(to put it in the terminology of this chapter) degrees of association between variables; they could
not ascend to the second or third rungs of the Ladder of Causation. Fortunately, they required
only two slight twists to climb to the top. First, in 1991, the graph surgery idea empowered them
to handle both observations and interventions. Another twist, in 1994, brought them to the third
level and made them capable of handling counterfactuals. But these developments deserve a
fuller discussion in a later chapter. The main point is this: While probabilities encode our beliefs
about a static world, causality tells us whether and how probabilities change when the world
33