Category: Judea Pearl – The Book Of Why

Bias Versus Discrimination - Joe Abittan

Bias Versus Discrimination

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In The Book of Why Judea Pearl writes about a distinction between bias and discrimination from Peter Bickel, a statistician  from UC Berkeley. Regarding sex bias and discrimination in the workplace, Bickel carefully distinguished between bias and discrimination in a way that I find interesting. Describing his distinction Pearl writes the following:
“He [Bickel] carefully distinguishes between two terms, that in common English, are often taken as synonyms: bias and discrimination. He defines bias as a pattern of association between a particular decision and a particular sex of applicant. Note the words pattern and association. They tell us that bias is a phenomenon on rung one of the Ladder of Causation.”
Bias, Pearl explains using Bickel’s quote, is simply an observation. There is no causal mechanism at play when dealing with bias and that is why he states that it is on rung one of the Ladder of Causation. It is simply recognizing that there is a disparity, a trend, or some sort of pattern or association between two things.
Pearl continues, “on the other hand, he defines discrimination as the exercise of decision influenced by the sex of the applicant when that is immaterial to the qualification for entry. Words like exercise of decision, or influence and immaterial are redolent of causation, even if Bickel could not bring himself to utter that word in 1975. Discrimination, unlike bias, belongs on rung two or three of the Ladder of Causation.”
Discrimination is an intentional act. There is a clear causal pathway that we can posit between the outcome we observe and the actions or behaviors of individuals. In the case that Bickel used, sex disparities in work can be directly attributed to discrimination if it can be proven that immaterial considerations were the basis for not hiring women (or maybe men) for specific work. Discrimination does not happen all on its own, it happens because of something else. Bias can exist on its own. It can be caused by discrimination, but it could be caused by larger structural factors that themselves are not actively making decisions to create a situation. Biases are results, patterns, and associations we can observe. Discrimination is deliberate behavior that generates, sustains, and reinforces biases.
Mediating Variables

Mediating Variables

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Mediating variables stand in the middle of the actions and the outcomes that we can observe. They are often tied together and hard to separate from the action and the outcome, making their direct impact hard to pull apart from other factors. They play an important role in determining causal structures, and ultimately in shaping discourse and public policy about good and bad actions.
Judea Pearl writes about mediating variables in The Book of Why. He uses cigarette smoking, tar, and lung cancer as an example of the confounding nature of mediating variables. He writes, “if smoking causes lung cancer only through the formation of tar deposits, then we could eliminate the excess cancer risk by giving smokers tar-free cigarettes, such as e-cigarettes. On the other hand, if smoking causes cancer directly or through a different mediator, then e-cigarettes might not solve the problem.”
The mediator problem of tar still has not been fully disentangled and fully understood, but it is an excellent example of the importance, challenges, and public health consequences of mediating variables. Mediators can contribute directly to the final outcome we observe (lung cancer), but they may not be the only variable at play. In this instance, other aspects of smoking may directly cause lung cancer. An experiment between cigarette and e-cigarette smokers can help us get closer, but we won’t be able to say there isn’t a self-selection effect between traditional and e-cigarette smokers that plays into cancer development. However, closely studying both groups will help us start to better understand the direct role of tar in the causal chain.
Mediating variables like this pop up when we talk about the effectiveness of schools, the role for democratic norms, and the pros or cons of traditional gender roles. Often, mediating variables are driving the concerns we have for larger actions and behaviors. We want all children to go to school, but argue about the many mediating variables within the educational environment that may or may not directly contribute to specific outcomes that we want to see. It is hard to say which specific piece is the most important, because there are so many mediating variables all contributing directly or possibly indirectly to the education outcomes we see and imagine.
Counterfactuals

Counterfactuals

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I have written a lot lately about the incredible human ability to imagine worlds that don’t exist. An important way that we understand the world is by imagining what would happen if we did something that we have not yet done or if we imagine what would have happened had we done something different in the past. We are able to use our experiences about the world and our intuition on causality to imagine a different state of affairs from what currently exists. Innovation, scientific advancements, and social cooperation all depend on our ability to imagine different worlds and intuit causal chains between our current world and the imagined reality we desire.
In The Book of Why Jude Pearl writes, “counterfactuals are an essential part of how humans learn about the world and how our actions affect it. While we can never walk down both the paths that diverge in a wood, in a great many cases we can know, with some degree of confidence, what lies down each.”
A criticism of modern science and statistics is the reliance on randomized controlled trials and the fact that we cannot run an RCT on many of the things we study. We cannot run RCTs on our planet to determine the role of meteor impacts or lightning strikes on the emergence of life. We cannot run RCTs on the toxicity of snake venoms in human subjects. We cannot run RCTs on giving stimulus checks  to Americans during the COVID-19 Pandemic. Due to physical limitations and ethical considerations, RCTs are not always possible. Nevertheless, we can still study the world and use counterfactuals to think about the role of specific interventions.
If we forced ourselves to only accept knowledge based on RCTs then we would not be able to study the areas I mentioned above. We cannot go down both paths in randomized experiments with those choices. We either ethically cannot administer an RCT or we are stuck with the way history played out. We can, however, employ counterfactuals, imagining different worlds in our heads to think about what would have happened had we gone down another path. In this process we might make errors, but we can continually learn and improve our mental models. We can study what did happen, think about what we can observe based on causal structures, and better understand what would have happened had we done something different. This is how much of human progress has moved forward, without RCTs and with counterfactuals, imagining how the world could be different, how people, places, societies, and molecules could have reacted differently with different actions and conditions.
Dose-Response Curves

Dose-Response Curves

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One limitation of linear regression models, explains Judea Pearl in his book The Book of Why is that they are unable to accurately model interactions or relationships that don’t follow linear relationships. This lesson was hammered into my head by a statistics professor at the University of Nevada, Reno when discussing binomial variables. For variables where there are only two possible options, such as yes or no, a linear regression model doesn’t work. When the Challenger Shuttle’s O-ring failed, it was because the team had run a linear regression model to determine a binomial variable, the O-ring fails or it’s integrity holds. However, there are other situations where a linear regression becomes problematic.
 
 
In the book, Pearl writes, “linear models cannot represent dose-response curves that are not straight lines. They cannot represent threshold effects, such as a drug that has increasing effects up to a certain dosage and then no further effect.”
 
 
Linear relationship models become problematic when the effect of a variable is not constant over dosage. In the field of study that I was trained in, political science, this isn’t a big deal. In my field, simply demonstrating that there is a mostly consistent connection between ratings of trust in public institutions and receipt of GI benefits, for example, is usually sufficient. However, in fields like medicine or nuclear physics, it is important to recognize that a linear regression model might be ill suited to the actual reality of the variable.
 
 
A drug that is ineffective at small doses, becomes effective at moderate doses, but quickly becomes deadly at high doses shouldn’t be modeled with a linear regression model. This type of drug is one that the general public needs to be especially careful with, since so many individuals approach medicine with a “if some is good then more is better” mindset. Within physics, as was seen in the Challenger example, the outcomes can also be a matter of life. If a particular rubber for tires holds its strength but fails at a given threshold, if a rubber seal fails at a low temperature, or if a nuclear cooling pool will flash boil at a certain heat, then linear regression models will be inadequate for making predictions about the true nature of variables.
 
 
This is an important thing for us to think about when we consider the way that science is used in general discussion. We should recognize that people assume a linear relationship based on an experimental study, and we should look for binomial variables or potential non-linear relationships when thinking about a study and its conclusions. Improving our thinking about linear regression and dose-response curves can help us be smarter when it comes to things that matter like global pandemics and even more general discussions about what we think the government should or should not do.

Ignorability

Ignorability

Posted on by jabittan
The idea of ignorability helps us in science by playing a role in randomized trials. In the real world, there are too many potential variables to be able to comprehensively predict exactly how a given intervention will play out in every case. We almost always have outliers that have wildly different outcomes compared to what we would have predicted. Quite often some strange factor that could not be controlled or predicted caused the individual case to differ dramatically from the norm.
Thanks to concepts of ignorability, we don’t have to spend too much time worrying about the causal structures that created a single outlier. In The Book of Why Judea Pearl tries his best to provide a definition of ingorability for those who need to assess whether ignorability holds in a given outlier decision. He writes, “the assignment of patients to either treatment or control is ignorable if patients who would have one potential outcome are just as likely to be in the treatment or control group as the patients who would have a different potential outcome.”
What Pearl means is that ignorability applies when there is not a determining factor that makes people with any given outcome more likely to be in a control or treatment group. When people are randomized into control versus treatment, then there is not likely to be a commonality among people in either group that makes them more or less likely to have a given reaction. So a random outlier in one group can be expected to be offset by a random outlier in the other group (not literally a direct opposite, but we shouldn’t see a trend of specific outliers all in either treatment or control).
Ignroability does not apply in situations where there is a self-selection effect for control or treatment. In the world of the COVID-19 Pandemic, this applies in situations like human challenge trials. It is unlikely that people who know they are at risk of bad reactions to a vaccine would self-select into a human challenge trial. This same sort of thing happens with corporate health benefits initiatives, smart phone beta-testers, and general inadvertent errors in scientific studies. Outliers may not be outliers we can ignore if there is a self-selection effect, and the outcomes that we observe may reflect something other than what we are studying, meaning that we can’t apply ignorability in a way that allows us to draw a conclusion specifically on our intervention.
Co-opting Mental Machinery

Co-opting Mental Machinery

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The human mind is great at pattern recognition, but it is not the only brain that can recognize a pattern. Pigeons can recognize patterns for food distribution with button presses, mice can remember mazes and navigate through complex patterns to a reward, and other animals can recognize patterns in hunting, mating, and other activities. What humans do differently is use pattern recognition to determine causal structures by imagining and testing alternative hypotheses. This is a crucial step beyond the pattern recognition of other animals.
In The Book of Why Judea Pearl writes, “It is not too much of a stretch to think that 40,000 years ago, humans co-opted the machinery in their brain that already existed for pattern recognition and started to use it for causal reasoning.” This idea is interesting because it explains our pattern recognition linkage with other animals and helps us think about how brain structures and ways of thinking may have evolved.
In isolation, a brain process is interesting, but not as interesting as when considered alongside similar brain processes. When we look at pattern recognition and its similarities to causal reasoning, we see a jumping off point. We can see how brain processes that helped us in one area opened up new possibilities through development. This helps us think more deeply about the mental abilities that we have.
The ways we think and how our brains work is not static. Different cultural factors, environmental factors, and existing brain processes can all shape how our brains work and evolve individually and as a species.  As Pearl notes, it is likely that many of our brain processes co-opted other mental machinery for new purposes. Very few of what see in human psychology can be well understood in isolation. Asking why and how evolution could have played a role is crucial to understanding who we are now and how we got to this point. Causality is not something that just existed naturally in the brain. It was built by taking other processes and co-opting them for new purposes, and those new purposes have allowed us to do magnificent things like build rockets, play football, and develop clean water systems.
The Representation Problem

The Representation Problem

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In The Book of Why Judea Pearl lays out what computer scientists call the representation problem by writing, “How do humans represent possible worlds in their minds and compute the closest one, when the number of possibilities is far beyond the capacity of the human brain?”
 
 
In the Marvel Movie Infinity War, Dr. Strange looks forward in time to see all the possible outcomes of a coming conflict. He looks at 14,000,605 possible futures. But did Dr. Strange really look at all the possible futures out there? 14 million is a convenient big number to include in a movie, but how many possible outcomes are there for your commute home? How many people could change your commute in just the tiniest way? Is it really a different outcome if you hit a bug while driving, if you were stopped at 3 red lights and not 4, or if you had to stop at a crosswalk for a pedestrian? The details and differences in the possible worlds of our commute home can range from the miniscule to the enormous (the difference between you rolling your window down versus a meteor landing in the road in front of you). Certainly with all things considered there are more than 14 million possible futures for your drive home.
 
 
Somehow, we are able to live our lives and make decent predictions of the future despite the enormity of possible worlds that exist ahead of us. Somehow we can represent possible worlds in our minds and determine what future world is the closest one to the reality we will experience. This ability allows us to plan for retirement, have kids, go to the movies, and cook dinner. If we could not do this, we could not drive down the street, could not walk to a neighbors house, and couldn’t navigate a complex social world. But none of us are sitting in a green glow with our head spinning in circles like Dr. Strange as we try to view all the possible worlds in front of us. What is happening in our mind to do this complex math?
 
 
Pearl argues that we solve this representation problem not through magical foresight, but through an intuitive understanding of causal structures. We can’t predict exactly what the stock market is going to do, whether a natural disaster is in our future, or precisely how another person will react to something we say, but we can get a pretty good handle on each of these areas thanks to causal reasoning.
 
 
We can throw out possible futures that have no causal structures related to the reality we inhabit.  You don’t have to think of a world where Snorlax is blocking your way home, because your brain recognizes there is no causal plausibility of a Pokémon character sleeping in the road. Our brain easily discards the absurd possible futures and simultaneous recognizes the causal pathways that could have major impacts on how we will live. This approach gradually narrows down the possibilities to a level where we can make decisions and work with a level of information that our brain (or computers) can reasonably decipher. We also know, without having to do the math, that rolling our window down or hitting a bug is not likely to start a causal pathway that materially changes the outcome of our commute home. The same goes for being stopped at a few more red lights or even stopping to pick up a burrito. Those possibilities exist, but they don’t materially change our lives and so our brain can discard them from the calculation. This is the kind of work our brains our doing, Pearl would argue, to solve the representation problem.

Objective Reality, Rationality, & Shared Worlds - Joe Abittan

Objective Reality, Rationality, & Shared Worlds

Posted on by jabittan
The idea of an objective reality has been under attack for a while, and I have even been part of the team attacking that objective reality. We know that we have a limited ability to sense and experience the world around us. We know that bats, sharks, and bees experience phenomena that we are blind to. We can’t know that the color red that I experience is exactly like the color red that you experience. Given our lack of sense, the fact that physical stimuli are translated into electrical brain impulses, and that there appears to be plenty of subjectivity in how we experience the same thing, an objective reality doesn’t really seem possible. We seemingly all live within a world created by many subjective measures within our own brains.
But is this idea really accurate? I recently completed Steven Pinker’s book Enlightenment Now in which he argues that reason depends on objectivity and that our efforts toward rationality and reason demonstrate that there is some form of objectivity toward which we are continually working. The very act of attempting to think rationally about our world and how we understand the universe demonstrates that we are striving to understand some sort of objective commonality. A quote from The Book of Why by Judea Pearl seems to support Pinker’s assertion. Pearl writes:
“We experience the same world and share the same mental model of its causal structure. … Our shared mental models bind us together into communities. We can therefore judge closeness not by some metaphysical notion of similarity but by how much we must take apart and perturb our shared model before it satisfies a given hypothetical condition that is contrary to fact.”
Pearl wrote this paragraph while discussing the human ability to imagine alternative possibilities (specifically writing about the sentence Joe’s headache would have gone away if he had taken aspirin). The sentence acknowledges a reality (Joe has a headache) and proposes a different reality that doesn’t actually exist (Joe no longer has a headache because he took aspirin). It is this ability to envision different worlds which forms the basis of our causal interpretations of the world, but it also reveals a shared world in which we live and from which we can imagine different possible worlds. It hints at an objective reality shared among individuals and distinct from unreal and imagined, plausible worlds.
Reason and rationality demonstrate that there seems to be an objective reality in which we are situated and in which we experience the world. There are undoubtedly subjective aspects of that world, but we nevertheless are able to share a world in which we can imagine other possible worlds and consider those alternative worlds as closer or further from the world in which we live. Doing this over and over again, among billions of people, helps us define the actual objective reality which constitutes the world we share and from which we have subjective experiences. It is from this world that we can discuss what is subjective, what causes one phenomenon or another, and from which we can imagine alternative realities based on certain interventions. If there was no objective reality for us to all share, then we would never be able to distinguish alternative worlds and compare them as more or less close to the world we share and exist within.
Alternative, Nonexistent Worlds - Judea Pearl - The Book of Why - Joe Abittan

Alternative, Nonexistent Worlds

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Judea Pearl’s The Book of Why hinges on a unique ability that human animals have. Our ability to imagine alternative, nonexistent worlds is what has set us on new pathways and allowed us to dominate the planet. We can think of what would happen if we acted in a certain manner, used a tool in a new way, or if two objects collided together. We can visualize future outcomes of our actions and of the actions of other bodies and predict what can be done to create desired future outcomes.
In the book he writes, “our ability to conceive of alternative, nonexistent worlds separated us from our protohuman ancestors and indeed from any other creature on the planet. Every other creature can see what is. Our gift, which may sometimes be a curse, is that we can see what might have been.”
Pearl argues that our ability to see different possibilities, to imagine new worlds, and to be able to predict actions and behaviors that would realize that imagined world is not something we should ignore. He argues that this ability allows us to move beyond correlations, beyond statistical regressions, and into a world where our causal thinking helps drive our advancement toward the worlds we want.
It is important to note that he is not advocating for holding a belief and setting out to prove it with data and science, but rather than we use data and science combined with our ability to think causally to better understand the world. We do not have to be stuck in a state where we understand statistical techniques but deny plausible causal pathways. We can identify and define causal pathways, even if we cannot fully define causal mechanisms. Our ability to reason through alternative, nonexistent worlds is what allows us to think causally and apply this causal reasoning to statistical relationships. Doing so, Pearl argues, will save lives, help propel technological innovation, and will push science to new frontiers to improve life on our planet.
Causal Illusions

Causal Illusions

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In The Book of Why Judea Pearl writes, “our brains are not wired to do probability problems, but they are wired to do causal problems. And this causal wiring produces systematic probabilistic mistakes, like optical illusions.” This can create problems for us when no causal link exists and when data correlate without any causal connections between outcomes. According to Pearl, our causal thinking, “neglects to account for the process by which observations are selected.” We don’t always realize that we are taking a sample, that our sample could be biased, and that structural factors independent of the phenomenon we are trying to observe could greatly impact the observations we actually make.
Pearl continues, “We live our lives as if the common cause principle were true. Whenever we see patterns, we look for a causal explanation. In fact, we hunger for an explanation, in terms of stable mechanisms that lie outside the data.” When we see a correlation our brains instantly start looking for a causal mechanism that can explain the correlation and the data we see. We don’t often look at the data itself to ask if there was some type of process in the data collection that lead to the outcomes we observed. Instead, we assume the data is correct and  that the data reflects an outside, real-world phenomenon. This is the cause of many causal illusions that Pearl describes in the book. Our minds are wired for causal thinking, and we will invent causality when we see patterns, even if there truly isn’t a causal structure linking the patterns we see.
It is in this spirit that we attribute negative personality traits to people who cut us off on the freeway. We assume they don’t like us, that they are terrible people, or that they are rushing to the hospital with a sick child so that our being cut off has a satisfying causal explanation. When a particular type of car stands out and we start seeing that car everywhere, we misattribute our increased attention to the type of car and assume that there really are more of those cars on the road now. We assume that people find them more reliable or more appealing and that people purposely bought those cars as a causal mechanism to explain why we now see them everywhere. In both of these cases we are creating causal pathways in our mind that in reality are little more than causal illusions, but we want to find a cause to everything and we don’t always realize that we are doing so.