The Book of Why: The New Science of Cause and Effect (Penguin Science)

by Judea Pearl

First and most important, you don’t see U (the Smoking Gene) anywhere. This was the whole point. We have successfully deconfounded U even without possessing any data on it. Any statistician of Fisher’s generation would have seen this as an utter miracle. Second, way back in the Introduction I talked about an estimand as a recipe for computing the quantity of interest in a query. Equations 7.1 and 7.2 are the most complicated and interesting estimands that I will show you in this book. The left-hand side represents the query “What is the effect of X on Y?” The right-hand side is the estimand, a recipe for answering the query. Note that the estimand contains no do’s, only see’s, represented by the vertical bars, and this means it can be estimated from data.

Glynn and Kashin’s results show why the front-door adjustment is such a powerful tool: it allows us to control for confounders that we cannot observe (like Motivation), including those that we can’t even name. RCTs are considered the “gold standard” of causal effect estimation for exactly the same reason. Because front-door estimates do the same thing, with the additional virtue of observing people’s behavior in their own natural habitat instead of a laboratory, I would not be surprised if this method eventually becomes a useful alternative to randomized controlled trials.

The prospect of making these determinations by purely mathematical means should dazzle anybody who understands the cost and difficulty of running randomized controlled trials, even when they are physically feasible and legally permissible. The idea dazzled me, too, in the early 1990s, not as an experimenter but as a computer scientist and part-time philosopher. Surely one of the most exhilarating experiences you can have as a scientist is to sit at your desk and realize that you can finally figure out what is possible or impossible in the real world—especially if the problem is important to society and has baffled those who have tried to solve it before you. I imagine this is how Hipparchus of Nicaea felt when he discovered he could figure out the height of a pyramid from its shadow on the ground, without actually climbing the pyramid. It was a clear victory of mind over matter.

In 1994, when I first proposed the do-calculus, I selected these three rules because they were sufficient in any case that I knew of. I had no idea whether, like Ariadne’s thread, they would always lead me out of the maze, or I would someday encounter a maze of such fiendish complexity that I could not escape. Of course, I hoped for the best. I conjectured that whenever a causal effect is estimable from data, a sequence of steps using these three rules would eliminate the do-operator. But I could not prove it.

In this modern-day labyrinth tale, two groups of researchers played the role of Ariadne to my wandering Theseus: Yiming Huang and Marco Valtorta at the University of South Carolina and my own student, Ilya Shpitser, at the University of California, Los Angeles (UCLA). Both groups independently and simultaneously proved that Rules 1 to 3 suffice to get out of any do-labyrinth that has an exit.

Few people took note of Snow’s conclusion at the time. He printed a pamphlet of the results at his own expense, and it sold a grand total of fifty-six copies. Nowadays, epidemiologists view his pamphlet as the seminal document of their discipline. It showed that through “shoe-leather research” (a phrase I have borrowed from David Freedman) and causal reasoning, you can track down a killer.

If you’re sixty years old, your arteries have already sustained sixty years of damage. For that reason it’s very likely that Mendelian randomization overestimates the true benefits of statins. On the other hand, starting to reduce your cholesterol when you’re young—whether through diet or exercise or even statins—will have big effects later.

chapters—Sewall Wright’s path diagrams and their extension to structural causal models (SCMs). We got a good taste of this in Chapter 1, in the example of the firing squad, which showed how to answer counterfactual questions such as “Would the prisoner be alive if rifleman A had not shot?” I will compare how counterfactuals are defined in the Neyman-Rubin paradigm and in SCMs, where they enjoy the benefit of causal diagrams. Rubin has steadfastly maintained over the years that diagrams serve no useful purpose. So we will examine how students of the Rubin causal model must navigate causal problems blindfolded, lacking a facility to represent causal knowledge or to derive its testable implications.

Next, I will discuss the application of counterfactuals to climate change. Until recently, climate scientists have found it very difficult and awkward to answer questions like “Did global warming cause this storm [or this heat wave, or this drought]?” The conventional answer has been that individual weather events cannot be attributed to global climate change. Yet this answer seems rather evasive and may even contribute to public indifference about climate change. Counterfactual analysis allows climate scientists to make much more precise and definite statements than before. It requires, however, a slight addition to our everyday vocabulary. It will be helpful to distinguish three different kinds of causation: necessary causation, sufficient causation, and necessary-and-sufficient causation. (Necessary causation is the same as but-for causation.) Using these words, a climate scientist can say, “There is a 90 percent probability that man-made climate change was a necessary cause of this heat wave,” or “There is an 80 percent probability that climate change will be sufficient to produce a heat wave this strong at least once every 50 years.”

One philosopher who defied convention, David Lewis, called in his 1973 book Counterfactuals for abandoning the regularity account altogether and for interpreting “A has caused B” as “B would not have occurred if not for A.” Lewis asked, “Why not take counterfactuals at face value: as statements about possible alternatives to the actual situation?” Like Hume, Lewis was evidently impressed by the fact that humans make counterfactual judgments without much ado, swiftly, comfortably, and consistently. We can assign them truth values and probabilities with no less confidence than we do for factual statements. In his view, we do this by envisioning “possible worlds” in which the counterfactual statements are true.

But I think that his critics (and perhaps Lewis himself) missed the most important point. We do not need to argue about whether such worlds exist as physical or even metaphysical entities. If we aim to explain what people mean by saying “A causes B,” we need only postulate that people are capable of generating alternative worlds in their heads, judging which world is “closer” to ours and, most importantly, doing it coherently so as to form a consensus.

With these motivations I entered counterfactual analysis in 1994 (with my student Alex Balke). Not surprisingly, the algorithmization of counterfactuals made a bigger splash in artificial intelligence and cognitive science than in philosophy. Philosophers tended to view structural models as merely one of many possible implementations of Lewis’s possible-worlds logic. I dare to suggest that they are much more than that. Logic void of representation is metaphysics. Causal diagrams, with their simple rules of following and erasing arrows, must be close to the way that our brains represent counterfactuals.

In principle, counterfactuals should find easy application in the courtroom. I say “in principle” because the legal profession is very conservative and takes a long time to accept new mathematical methods. But using counterfactuals as a mode of argument is actually very old and known in the legal profession as “but-for causation.” The Model Penal Code expresses the “but-for” test as follows: “Conduct is the cause of a result when: (a) it is an antecedent but for which the result in question would not have occurred.” If the defendant fired a gun and the bullet struck and killed the victim, the firing of the gun is a but-for, or necessary, cause of the death, since the victim would be alive if not for the firing. But-for causes can also be indirect. If Joe blocks a building’s fire exit with furniture, and Judy dies in a fire after she could not reach the exit, then Joe is legally responsible for her death even though he did not light the fire.

Myles Allen, a physicist at the University of Oxford and author of the above quote, suggested a way to do better: use a metric called fraction of attributable risk (FAR) to quantify the effect of climate change. The FAR requires us to know two numbers: p0, the probability of a heat wave like the 2003 heat wave before climate change (e.g., before 1800), and p1, the probability after climate change. For example, if the probability doubles, then we can say that half of the risk is due to climate change. If it triples, then two-thirds of the risk is due to climate change.

One of the earliest examples of a controlled experiment was sea captain James Lind’s study of scurvy, published in 1747. In Lind’s time scurvy was a terrifying disease, estimated to have killed 2 million sailors between 1500 and 1800. Lind established, as conclusively as anybody could at that time, that a diet of citrus fruit prevented sailors from developing this dread disease. By the early 1800s, scurvy had become a problem of the past for the British navy, as all its ships took to the seas with an adequate supply of citrus fruit. This is usually the point at which history books end the story, celebrating a great triumph of the scientific method.

With hindsight, Koettlitz’s advice borders on criminal malpractice. How could the lesson of James Lind have been so thoroughly forgotten—or worse, dismissed—a century later? The explanation, in part, is that doctors did not really understand how citrus fruits worked against scurvy. In other words, they did not know the mediator.

To the best of my knowledge, the first person to explicitly represent a mediator with a diagram was a Stanford graduate student named Barbara Burks, in 1926. This very little-known pioneer in women’s science is one of the true heroes of this book. There is reason to believe that she actually invented path diagrams independently of Sewall Wright. And in regard to mediation, she was ahead of Wright and decades ahead of her time. Burks’s main research interest, throughout her unfortunately brief career, was the role of nature versus nurture in determining human intelligence.

In 1986, Reuben Baron and David Kenny articulated a set of principles for detecting and evaluating mediation in a system of equations. The essential principles are, first, that the variables are all related by linear equations, which are estimated by fitting them to the data. Second, direct and indirect effects are computed by fitting two equations to the data: one with the mediator included and one with the mediator excluded. Significant change in the coefficients when the mediator is introduced is taken as evidence of mediation. The simplicity and plausibility of the Baron-Kenny method took the social sciences by storm. As of 2014, their article ranks thirty-third on the list of most frequently cited scientific papers of all time. As of 2017, Google Scholar reports that 73,000 scholarly articles have cited Baron and Kenny. Just think about that! They’ve been cited more times than Albert Einstein, more than Sigmund Freud, more than almost any other famous scientist you can think of. Their article ranks second among all papers in psychology and psychiatry, and yet it’s not about psychology at all. It’s about noncausal mediation.

And in 2014, the father of the Baron-Kenny approach, David Kenny, posted a new section on his website called “causal mediation analysis.” Though I would not call him a convert yet, Kenny clearly recognizes that times are changing and that mediation analysis is entering a new era.

In his first five minutes on the job, Kragh had stumbled upon a sea change in trauma care that took place during the Iraq and Afghanistan wars. Though used for centuries, both on the battlefield and in the operating room, tourniquets have always been somewhat controversial. A tourniquet left on too long will lead to loss of a limb. Also, tourniquets have often been improvised under duress, from straps or other handy materials, so their effectiveness is unsurprisingly a hit-or-miss affair. After World War II they were considered a treatment of last resort, and their use was officially discouraged.

When I began my journey into causation, I was following the tracks of an anomaly. With Bayesian networks, we had taught machines to think in shades of gray, and this was an important step toward humanlike thinking. But we still couldn’t teach machines to understand causes and effects.

2014, the last year for which I’ve seen data, Facebook reportedly was warehousing 300 petabytes of data about its 2 billion active users, or 150 megabytes of data per user. The games people play, the products they like to buy, the names of all their Facebook friends, and of course all their cat videos—all of them are out there in a glorious ocean of ones and zeros.

In certain circles there is an almost religious faith that we can find the answers to these questions in the data itself, if only we are sufficiently clever at data mining. However, readers of this book will know that this hype is likely to be misguided. The questions I have just asked are all causal, and causal questions can never be answered from data alone.

If we understand the mechanism by which we recruit subjects for the study, we can recover from bias by collecting data on the right set of deconfounders and using an appropriate reweighting or adjustment formula. Bareinboim’s work allows us to exploit causal logic and Big Data to perform miracles that were previously inconceivable.

In recent years, the most remarkable progress in AI has taken place in an area called “deep learning,” which uses methods like convolutional neural networks. These networks do not follow the rules of probability; they do not deal with uncertainty in a rigorous or transparent way. Still less do they incorporate any explicit representation of the environment in which they operate. Instead, the architecture of the network is left free to evolve on its own. When finished training a new network, the programmer has no idea what computations it is performing or why they work. If the network fails, she has no idea how to fix it. Perhaps the prototypical example is AlphaGo,

All of this is exciting, and the results leave no doubt: deep learning works for certain tasks. But it is the antithesis of transparency. Even AlphaGo’s programmers cannot tell you why the program plays so well. They knew from experience that deep networks have been successful at tasks in computer vision and speech recognition. Nevertheless, our understanding of deep learning is completely empirical and comes with no guarantees. The AlphaGo team could not have predicted at the outset that the program would beat the best human in a year, or two, or five. They simply experimented, and it did.

This limitation does not hinder the performance of AlphaGo in the narrow world of go games, since the board description together with the rules of the game constitutes an adequate causal model of the go-world. Yet it hinders learning systems that operate in environments governed by rich webs of causal forces, while having access merely to surface manifestations of those forces. Medicine, economics, education, climatology, and social affairs are typical examples of such environments. Like the prisoners in Plato’s famous cave, deep-learning systems explore the shadows on the cave wall and learn to accurately predict their movements. They lack the understanding that the observed shadows are mere projections of three-dimensional objects moving in a three-dimensional space. Strong AI requires this understanding.

Once we have built a moral robot, many apocalyptic visions start to recede into irrelevance. There is no reason to refrain from building machines that are better able to distinguish good from evil than we are, better able to resist temptation, better able to assign guilt and credit. At this point, like chess and Go players, we may even start to learn from our own creation. We will be able to depend on our machines for a clear-eyed and causally sound sense of justice. We will be able to learn how our own free will software works and how it manages to hide its secrets from us. Such a thinking machine would be a wonderful companion for our species and would truly qualify as AI’s first and best gift to humanity.