Terrible but not likely, likely but not terrible

May 17 JDN 2458985

The human brain is a remarkably awkward machine. It’s really quite bad at organizing data, relying on associations rather than formal categories.

It is particularly bad at negation. For instance, if I tell you that right now, no matter what, you must not think about a yellow submarine, the first thing you will do is think about a yellow submarine. (You may even get the Beatles song stuck in your head, especially now that I’ve mentioned it.) A computer would never make such a grievous error.

The human brain is also quite bad at separation. Daniel Dennett coined a word “deepity” for a particular kind of deep-sounding but ultimately trivial aphorism that seems to be quite common, which relies upon this feature of the brain. A deepity has at least two possible readings: On one reading, it is true, but utterly trivial. On another, it would be profound if true, but it simply isn’t true. But if you experience both at once, your brain is triggered for both “true” and “profound” and yields “profound truth”. The example he likes to use is “Love is just a word”. Well, yes, “love” is in fact just a word, but who cares? Yeah, words are words. But love, the underlying concept it describes, is not just a word—though if it were that would change a lot.

One thing I’ve come to realize about my own anxiety is that it involves a wide variety of different scenarios I imagine in my mind, and broadly speaking these can be sorted into two categories: Those that are likely but not terrible, and those that are terrible but not likely.

In the former category we have things like taking an extra year to finish my dissertation; the mean time to completion for a PhD is over 8 years, so finishing in 6 instead of 5 can hardly be considered catastrophic.

In the latter category we have things like dying from COVID-19. Yes, I’m a male with type A blood and asthma living in a high-risk county; but I’m also a young, healthy nonsmoker living under lockdown. Even without knowing the true fatality rate of the virus, my chances of actually dying from it are surely less than 1%.

But when both of those scenarios are running through my brain at the same time, the first triggers a reaction for “likely” and the second triggers a reaction for “terrible”, and I get this feeling that something terrible is actually likely to happen. And indeed if my probability of dying were as high as my probability of needing a 6th year to finish my PhD, that would be catastrophic.

I suppose it’s a bit strange that the opposite doesn’t happen: I never seem to get the improbability of dying attached to the mildness of needing an extra year. The confusion never seems to trigger “neither terrible nor likely”. Or perhaps it does, and my brain immediately disregards that as not worthy of consideration? It makes a certain sort of sense: An event that is neither probable nor severe doesn’t seem to merit much anxiety.

I suspect that many other people’s brains work the same way, eliding distinctions between different outcomes and ending up with a sort of maximal product of probability and severity.
The solution to this is not an easy one: It requires deliberate effort and extensive practice, and benefits greatly from formal training by a therapist. Counter-intuitively, you need to actually focus more on the scenarios that cause you anxiety, and accept the anxiety that such focus triggers in you. I find that it helps to actually write down the details of each scenario as vividly as possible, and review what I have written later. After doing this enough times, you can build up a greater separation in your mind, and more clearly categorize—this one is likely but not terrible, that one is terrible but not likely. It isn’t a cure, but it definitely helps me a great deal. Perhaps it could help you.

Darkest Before the Dawn: Bayesian Impostor Syndrome

Jan 12 JDN 2458860

At the time of writing, I have just returned from my second Allied Social Sciences Association Annual Meeting, the AEA’s annual conference (or AEA and friends, I suppose, since there several other, much smaller economics and finance associations are represented as well). This one was in San Diego, which made it considerably cheaper for me to attend than last year’s. Alas, next year’s conference will be in Chicago. At least flights to Chicago tend to be cheap because it’s a major hub.

My biggest accomplishment of the conference was getting some face-time and career advice from Colin Camerer, the Caltech economist who literally wrote the book on behavioral game theory. Otherwise I would call the conference successful, but not spectacular. Some of the talks were much better than others; I think I liked the one by Emmanuel Saez best, and I also really liked the one on procrastination by Matthew Gibson. I was mildly disappointed by Ben Bernanke’s keynote address; maybe I would have found it more compelling if I were more focused on macroeconomics.

But while sitting through one of the less-interesting seminars I had a clever little idea, which may help explain why Impostor Syndrome seems to occur so frequently even among highly competent, intelligent people. This post is going to be more technical than most, so be warned: Here There Be Bayes. If you fear yon algebra and wish to skip it, I have marked below a good place for you to jump back in.

Suppose there are two types of people, high talent H and low talent L. (In reality there is of course a wide range of talents, so I could assign a distribution over that range, but it would complicate the model without really changing the conclusions.) You don’t know which one you are; all you know is a prior probability h that you are high-talent. It doesn’t matter too much what h is, but for concreteness let’s say h = 0.50; you’ve got to be in the top 50% to be considered “high-talent”.

You are engaged in some sort of activity that comes with a high risk of failure. Many creative endeavors fit this pattern: Perhaps you are a musician looking for a producer, an actor looking for a gig, an author trying to secure an agent, or a scientist trying to publish in a journal. Or maybe you’re a high school student applying to college, or a unemployed worker submitting job applications.

If you are high-talent, you’re more likely to succeed—but still very likely to fail. And even low-talent people don’t always fail; sometimes you just get lucky. Let’s say the probability of success if you are high-talent is p, and if you are low-talent, the probability of success is q. The precise value depends on the domain; but perhaps p = 0.10 and q = 0.02.

Finally, let’s suppose you are highly rational, a good and proper Bayesian. You update all your probabilities based on your observations, precisely as you should.

How will you feel about your talent, after a series of failures?

More precisely, what posterior probability will you assign to being a high-talent individual, after a series of n+k attempts, of which k met with success and n met with failure?

Since failure is likely even if you are high-talent, you shouldn’t update your probability too much on a failurebut each failure should, in fact, lead to revising your probability downward.

Conversely, since success is rare, it should cause you to revise your probability upward—and, as will become important, your revisions upon success should be much larger than your revisions upon failure.

We begin as any good Bayesian does, with Bayes’ Law:

P[H|(~S)^n (S)^k] = P[(~S)^n (S)^k|H] P[H] / P[(~S)^n (S)^k]

In words, this reads: The posterior probability of being high-talent, given that you have observed k successes and n failures, is equal to the probability of observing such an outcome, given that you are high-talent, times the prior probability of being high-skill, divided by the prior probability of observing such an outcome.

We can compute the probabilities on the right-hand side using the binomial distribution:

P[H] = h

P[(~S)^n (S)^k|H] = (n+k C k) p^k (1-p)^n

P[(~S)^n (S)^k] = (n+k C k) p^k (1-p)^n h + (n+k C k) q^k (1-q)^n (1-h)

Plugging all this back in and canceling like terms yields:

P[H|(~S)^n (S)^k] = 1/(1 + [1-h/h] [q/p]^k [(1-q)/(1-p)]^n)

This turns out to be particularly convenient in log-odds form:

L[X] = ln [ P(X)/P(~X) ]

L[(~S)^n) (S)^k|H] = ln [h/(1-h)] + k ln [p/q] + n ln [(1-p)/(1-q)]

Since p > q, ln[p/q] is a positive number, while ln[(1-p)/(1-q)] is a negative number. This corresponds to the fact that you will increase your posterior when you observe a success (k increases by 1) and decrease your posterior when you observe a failure (n increases by 1).

But when p and q are small, it turns out that ln[p/q] is much larger in magnitude than ln[(1-p)/(1-q)]. For the numbers I gave above, p = 0.10 and q = 0.02, ln[p/q] = 1.609 while ln[(1-p)/(1-q)] = -0.085. You will therefore update substantially more upon a success than on a failure.

Yet successes are rare! This means that any given success will most likely be first preceded by a sequence of failures. This results in what I will call the darkest-before-dawn effect: Your opinion of your own talent will tend to be at its very worst in the moments just preceding a major success.

I’ve graphed the results of a few simulations illustrating this: On the X-axis is the number of overall attempts made thus far, and on the Y-axis is the posterior probability of being high-talent. The simulated individual undergoes randomized successes and failures with the probabilities I chose above.

Bayesian_Impostor_full

There are 10 simulations on that one graph, which may make it a bit confusing. So let’s focus in on two runs in particular, which turned out to be run 6 and run 10:

[If you skipped over the math, here’s a good place to come back. Welcome!]

Bayesian_Impostor_focus

Run 6 is a lucky little devil. They had an immediate success, followed by another success in their fourth attempt. As a result, they quickly update their posterior to conclude that they are almost certainly a high-talent individual, and even after a string of failures beyond that they never lose faith.

Run 10, on the other hand, probably has Impostor Syndrome. Failure after failure after failure slowly eroded their self-esteem, leading them to conclude that they are probably a low-talent individual. And then, suddenly, a miracle occurs: On their 20th attempt, at last they succeed, and their whole outlook changes; perhaps they are high-talent after all.

Note that all the simulations are of high-talent individuals. Run 6 and run 10 are equally competent. Ex ante, the probability of success for run 6 and run 10 was exactly the same. Moreover, both individuals are completely rational, in the sense that they are doing perfect Bayesian updating.

And yet, if you compare their self-evaluations after the 19th attempt, they could hardly look more different: Run 6 is 85% sure that they are high-talent, even though they’ve been in a slump for the last 13 attempts. Run 10, on the other hand, is 83% sure that they are low-talent, because they’ve never succeeded at all.

It is darkest just before the dawn: Run 10’s self-evaluation is at its very lowest right before they finally have a success, at which point their self-esteem surges upward, almost to baseline. With just one more success, their opinion of themselves would in fact converge to the same as Run 6’s.

This may explain, at least in part, why Impostor Syndrome is so common. When successes are few and far between—even for the very best and brightest—then a string of failures is the most likely outcome for almost everyone, and it can be difficult to tell whether you are so bright after all. Failure after failure will slowly erode your self-esteem (and should, in some sense; you’re being a good Bayesian!). You’ll observe a few lucky individuals who get their big break right away, and it will only reinforce your fear that you’re not cut out for this (whatever this is) after all.

Of course, this model is far too simple: People don’t just come in “talented” and “untalented” varieties, but have a wide range of skills that lie on a continuum. There are degrees of success and failure as well: You could get published in some obscure field journal hardly anybody reads, or in the top journal in your discipline. You could get into the University of Northwestern Ohio, or into Harvard. And people face different barriers to success that may have nothing to do with talent—perhaps why marginalized people such as women, racial minorities, LGBT people, and people with disabilities tend to have the highest rates of Impostor Syndrome. But I think the overall pattern is right: People feel like impostors when they’ve experienced a long string of failures, even when that is likely to occur for everyone.

What can be done with this information? Well, it leads me to three pieces of advice:

1. When success is rare, find other evidence. If truly “succeeding” (whatever that means in your case) is unlikely on any given attempt, don’t try to evaluate your own competence based on that extremely noisy signal. Instead, look for other sources of data: Do you seem to have the kinds of skills that people who succeed in your endeavors have—preferably based on the most objective measures you can find? Do others who know you or your work have a high opinion of your abilities and your potential? This, perhaps is the greatest mistake we make when falling prey to Impostor Syndrome: We imagine that we have somehow “fooled” people into thinking we are competent, rather than realizing that other people’s opinions of us are actually evidence that we are in fact competent. Use this evidence. Update your posterior on that.

2. Don’t over-update your posterior on failures—and don’t under-update on successes. Very few living humans (if any) are true and proper Bayesians. We use a variety of heuristics when judging probability, most notably the representative and availability heuristics. These will cause you to over-respond to failures, because this string of failures makes you “look like” the kind of person who would continue to fail (representative), and you can’t conjure to mind any clear examples of success (availability). Keeping this in mind, your update upon experiencing failure should be small, probably as small as you can make it. Conversely, when you do actually succeed, even in a small way, don’t dismiss it. Don’t look for reasons why it was just luck—it’s always luck, at least in part, for everyone. Try to update your self-evaluation more when you succeed, precisely because success is rare for everyone.

3. Don’t lose hope. The next one really could be your big break. While astronomically baffling (no, it’s darkest at midnight, in between dusk and dawn!), “it is always darkest before the dawn” really does apply here. You are likely to feel the worst about yourself at the very point where you are about to finally succeed. The lowest self-esteem you ever feel will be just before you finally achieve a major success. Of course, you can’t know if the next one will be it—or if it will take five, or ten, or twenty more tries. And yes, each new failure will hurt a little bit more, make you doubt yourself a little bit more. But if you are properly grounded by what others think of your talents, you can stand firm, until that one glorious day comes and you finally make it.

Now, if I could only manage to take my own advice….

Pascal’s Mugging

Nov 10 JDN 2458798

In the Singularitarian community there is a paradox known as “Pascal’s Mugging”. The name is an intentional reference to Pascal’s Wager (and the link is quite apt, for reasons I’ll discuss in a later post.)

There are a few different versions of the argument; Yudkowsky’s original argument in which he came up with the name “Pascal’s Mugging” relies upon the concept of the universe as a simulation and an understanding of esoteric mathematical notation. So here is a more intuitive version:

A strange man in a dark hood comes up to you on the street. “Give me five dollars,” he says, “or I will destroy an entire planet filled with ten billion innocent people. I cannot prove to you that I have this power, but how much is an innocent life worth to you? Even if it is as little as $5,000, are you really willing to bet on ten trillion to one odds that I am lying?”

Do you give him the five dollars? I suspect that you do not. Indeed, I suspect that you’d be less likely to give him the five dollars than if he had merely said he was homeless and asked for five dollars to help pay for food. (Also, you may have objected that you value innocent lives, even faraway strangers you’ll never meet, at more than $5,000 each—but if that’s the case, you should probably be donating more, because the world’s best charities can save a live for about $3,000.)

But therein lies the paradox: Are you really willing to bet on ten trillion to one odds?

This argument gives me much the same feeling as the Ontological Argument; as Russell said of the latter, “it is much easier to be persuaded that ontological arguments are no good than it is to say exactly what is wrong with them.” It wasn’t until I read this post on GiveWell that I could really formulate the answer clearly enough to explain it.

The apparent force of Pascal’s Mugging comes from the idea of expected utility: Even if the probability of an event is very small, if it has a sufficiently great impact, the expected utility can still be large.

The problem with this argument is that extraordinary claims require extraordinary evidence. If a man held a gun to your head and said he’d shoot you if you didn’t give him five dollars, you’d give him five dollars. This is a plausible claim and he has provided ample evidence. If he were instead wearing a bomb vest (or even just really puffy clothing that could conceal a bomb vest), and he threatened to blow up a building unless you gave him five dollars, you’d probably do the same. This is less plausible (what kind of terrorist only demands five dollars?), but it’s not worth taking the chance.

But when he claims to have a Death Star parked in orbit of some distant planet, primed to make another Alderaan, you are right to be extremely skeptical. And if he claims to be a being from beyond our universe, primed to destroy so many lives that we couldn’t even write the number down with all the atoms in our universe (which was actually Yudkowsky’s original argument), to say that you are extremely skeptical seems a grievous understatement.

That GiveWell post provides a way to make this intuition mathematically precise in terms of Bayesian logic. If you have a normal prior with mean 0 and standard deviation 1, and you are presented with a likelihood with mean X and standard deviation X, what should you make your posterior distribution?

Normal priors are quite convenient; they conjugate nicely. The precision (inverse variance) of the posterior distribution is the sum of the two precisions, and the mean is a weighted average of the two means, weighted by their precision.

So the posterior variance is 1/(1 + 1/X^2).

The posterior mean is 1/(1+1/X^2)*(0) + (1/X^2)/(1+1/X^2)*(X) = X/(X^2+1).

That is, the mean of the posterior distribution is just barely higher than zero—and in fact, it is decreasing in X, if X > 1.

For those who don’t speak Bayesian: If someone says he’s going to have an effect of magnitude X, you should be less likely to believe him the larger that X is. And indeed this is precisely what our intuition said before: If he says he’s going to kill one person, believe him. If he says he’s going to destroy a planet, don’t believe him, unless he provides some really extraordinary evidence.

What sort of extraordinary evidence? To his credit, Yudkowsky imagined the sort of evidence that might actually be convincing:

If a poorly-dressed street person offers to save 10(10^100) lives (googolplex lives) for $5 using their Matrix Lord powers, and you claim to assign this scenario less than 10-(10^100) probability, then apparently you should continue to believe absolutely that their offer is bogus even after they snap their fingers and cause a giant silhouette of themselves to appear in the sky.

This post he called “Pascal’s Muggle”, after the term from the Harry Potter series, since some of the solutions that had been proposed for dealing with Pascal’s Mugging had resulted in a situation almost as absurd, in which the mugger could exhibit powers beyond our imagining and yet nevertheless we’d never have sufficient evidence to believe him.

So, let me go on record as saying this: Yes, if someone snaps his fingers and causes the sky to rip open and reveal a silhouette of himself, I’ll do whatever that person says. The odds are still higher that I’m dreaming or hallucinating than that this is really a being from beyond our universe, but if I’m dreaming, it makes no difference, and if someone can make me hallucinate that vividly he can probably cajole the money out of me in other ways. And there might be just enough chance that this could be real that I’m willing to give up that five bucks.

These seem like really strange thought experiments, because they are. But like many good thought experiments, they can provide us with some important insights. In this case, I think they are telling us something about the way human reasoning can fail when faced with impacts beyond our normal experience: We are in danger of both over-estimating and under-estimating their effects, because our brains aren’t equipped to deal with magnitudes and probabilities on that scale. This has made me realize something rather important about both Singularitarianism and religion, but I’ll save that for next week’s post.

Revealed preference: Does the fact that I did it mean I preferred it?

Post 312 Oct 27 JDN 2458784

One of the most basic axioms of neoclassical economics is revealed preference: Because we cannot observe preferences directly, we infer them from actions. Whatever you chose must be what you preferred.

Stated so badly, this is obviously not true: We often make decisions that we later come to regret. We may choose under duress, or confusion; we may lack necessary information. We change our minds.

And there really do seem to be economists who use it in this bald way: From the fact that a particular outcome occurred in a free market, they will infer that it must be optimally efficient. (“Freshwater” economists who are dubious of any intervention into markets seem to be most guilty of this.) In the most extreme form, this account would have us believe that people who trip and fall do so on purpose.

I doubt anyone believes that particular version—but there do seem to be people who believe that unemployment is the result of people voluntarily choosing not to work, and revealed preference has also led economists down some strange paths when trying to explain what sure looks like irrational behavior—such as “rational addiction” theory, positing that someone can absolutely become addicted to alcohol or heroin and end up ruining their life all based on completely rational, forward-thinking decision planning.

The theory can be adapted to deal with these issues, by specifying that it’s only choices made with full information and all of our faculties intact that count as revealing our preferences.

But when are we ever in such circumstances? When do we ever really have all the information we need in order to make a rational decision? Just what constitutes intact faculties? No one is perfectly rational—so how rational must we be in order for our decisions to count as revealing our preferences?

Revealed preference theory also quickly becomes tautologous: Why do we choose to do things? Because we prefer them. What do we prefer? What we choose to do. Without some independent account of what our preferences are, we can’t really predict behavior this way.

A standard counter-argument to this is that revealed preference theory imposes certain constraints of consistency and transitivity, so it is not utterly vacuous. The problem with this answer is that human beings don’t obey those constraints. The Allais Paradox, the Ellsberg Paradox, the sunk cost fallacy. It’s even possible to use these inconsistencies to create “money pumps” that will cause people to systematically give you money; this has been done in experiments. While real-world violations seem to be small, they’re definitely present. So insofar as your theory is testable, it’s false.

The good news is that we really don’t need revealed preference theory. We already have ways of telling what human beings prefer that are considerably richer than simply observing what they choose in various scenarios. One very simple but surprisingly powerful method is to ask. In general, if you ask people what they want and they have no reason to distrust you, they will in fact tell you what they want.

We also have our own introspection, as well as our knowledge about millions of years of evolutionary history that shaped our brains. We don’t expect a lot of people to prefer suffering, for instance (even masochists, who might be said to ‘prefer pain’, seem to be experiencing that pain rather differently than the rest of us would). We generally expect that people will prefer to stay alive rather than die. Some may prefer chocolate, others vanilla; but few prefer motor oil. Our preferences may vary, but they do follow consistent patterns; they are not utterly arbitrary and inscrutable.

There is a deeper problem that any account of human desires must face, however: Sometimes we are actually wrong about our own desires. Affective forecasting, the prediction of our own future mental states, is astonishingly unreliable. People often wildly overestimate the emotional effects of both positive and negative outcomes. (Interestingly, people with depression tend not to do this—those with severe depression often underestimate the emotional effects of positive outcomes, while those with mild depression seem to be some of the most accurate forecasters, an example of the depressive realism effect.)

There may be no simple solution to this problem. Human existence is complicated; we spend large portions of our lives trying to figure out what it is we really want.
This means that we should not simply trust that whatever it is happens is what everyone—or even necessarily anyone—wants to happen. People make mistakes, even large, systematic, repeated mistakes. Sometimes what happens is just bad, and we should be trying to change it. Indeed, sometimes people need to be protected from their own bad decisions.

The backfire effect has been greatly exaggerated

Sep 8 JDN 2458736

Do a search for “backfire effect” and you’re likely to get a large number of results, many of them from quite credible sources. The Oatmeal did an excellent comic on it. The basic notion is simple: “[…]some individuals when confronted with evidence that conflicts with their beliefs come to hold their original position even more strongly.”

The implications of this effect are terrifying: There’s no point in arguing with anyone about anything controversial, because once someone strongly holds a belief there is nothing you can do to ever change it. Beliefs are fixed and unchanging, stalwart cliffs against the petty tides of evidence and logic.

Fortunately, the backfire effect is not actually real—or if it is, it’s quite rare. Over many years those seemingly-ineffectual tides can erode those cliffs down and turn them into sandy beaches.

The most recent studies with larger samples and better statistical analysis suggest that the typical response to receiving evidence contradicting our beliefs is—lo and behold—to change our beliefs toward that evidence.

To be clear, very few people completely revise their worldview in response to a single argument. Instead, they try to make a few small changes and fit them in as best they can.

But would we really expect otherwise? Worldviews are holistic, interconnected systems. You’ve built up your worldview over many years of education, experience, and acculturation. Even when someone presents you with extremely compelling evidence that your view is wrong, you have to weigh that against everything else you have experienced prior to that point. It’s entirely reasonable—rational, even—for you to try to fit the new evidence in with a minimal overall change to your worldview. If it’s possible to make sense of the available evidence with only a small change in your beliefs, it makes perfect sense for you to do that.

What if your whole worldview is wrong? You might have based your view of the world on a religion that turns out not to be true. You might have been raised into a culture with a fundamentally incorrect concept of morality. What if you really do need a radical revision—what then?

Well, that can happen too. People change religions. They abandon their old cultures and adopt new ones. This is not a frequent occurrence, to be sure—but it does happen. It happens, I would posit, when someone has been bombarded with contrary evidence not once, not a few times, but hundreds or thousands of times, until they can no longer sustain the crumbling fortress of their beliefs against the overwhelming onslaught of argument.

I think the reason that the backfire effect feels true to us is that our life experience is largely that “argument doesn’t work”; we think back to all the times that we have tried to convince to change a belief that was important to them, and we can find so few examples of when it actually worked. But this is setting the bar much too high. You shouldn’t expect to change an entire worldview in a single conversation. Even if your worldview is correct and theirs is not, that one conversation can’t have provided sufficient evidence for them to rationally conclude that. One person could always be mistaken. One piece of evidence could always be misleading. Even a direct experience could be a delusion or a foggy memory.

You shouldn’t be trying to turn a Young-Earth Creationist into an evolutionary biologist, or a climate change denier into a Greenpeace member. You should be trying to make that Creationist question whether the Ussher chronology is really so reliable, or if perhaps the Earth might be a bit older than a 17th century theologian interpreted it to be. You should be getting the climate change denier to question whether scientists really have such a greater vested interest in this than oil company lobbyists. You can’t expect to make them tear down the entire wall—just get them to take out one brick today, and then another brick tomorrow, and perhaps another the day after that.

The proverb is of uncertain provenance, variously attributed, rarely verified, but it is still my favorite: No single raindrop feels responsible for the flood.

Do not seek to be a flood. Seek only to be a raindrop—for if we all do, the flood will happen sure enough. (There’s a version more specific to our times: So maybe we’re snowflakes. I believe there is a word for a lot of snowflakes together: Avalanche.)

And remember this also: When you argue in public (which includes social media), you aren’t just arguing for the person you’re directly engaged with; you are also arguing for everyone who is there to listen. Even if you can’t get the person you’re arguing with to concede even a single point, maybe there is someone else reading your post who now thinks a little differently because of something you said. In fact, maybe there are many people who think a little differently—the marginal impact of slacktivism can actually be staggeringly large if the audience is big enough.

This can be frustrating, thankless work, for few people will ever thank you for changing their mind, and many will condemn you even for trying. Finding out you were wrong about a deeply-held belief can be painful and humiliating, and most people will attribute that pain and humiliation to the person who called them out for being wrong—rather than placing the blame where it belongs, which is on whatever source or method made you wrong in the first place. Being wrong feels just like being right.

But this is important work, among the most important work that anyone can do. Philosophy, mathematics, science, technology—all of these things depend upon it. Changing people’s minds by evidence and rational argument is literally the foundation of civilization itself. Every real, enduring increment of progress humanity has ever made depends upon this basic process. Perhaps occasionally we have gotten lucky and made the right choice for the wrong reasons; but without the guiding light of reason, there is nothing to stop us from switching back and making the wrong choice again soon enough.

So I guess what I’m saying is: Don’t give up. Keep arguing. Keep presenting evidence. Don’t be afraid that your arguments will backfire—because in fact they probably won’t.

Procrastination is an anxiety symptom

Aug 18 JDN 2458715

Why do we procrastinate? Some people are chronic procrastinators, while others only do it on occasion, but almost everyone procrastinates: We have something important to do, and we should be working on it, but we find ourselves doing anything else we can think of—cleaning is a popular choice—rather than actually getting to work. This continues until we get so close to the deadline that we have no choice but to rush through the work, lest it not get done at all. The result is more stress and lower-quality work. Why would we put ourselves through this?

There are a few different reasons why people may procrastinate. The one that most behavioral economists lean toward is hyperbolic discounting: Because we undervalue the future relative to the present, we set aside unpleasant tasks for later, when it seems they won’t be as bad.

This could be relevant in some cases, particularly for those who chronically procrastinate on a wide variety of tasks, but I find it increasingly unconvincing.

First of all, there’s the fact that many of the things we do while procrastinating are not particularly pleasant. Some people procrastinate by playing games, but even more procrastinate by cleaning house or reorganizing their desks. These aren’t enjoyable activities that you would want to do as soon as possible to maximize the joy.

Second, most people don’t procrastinate consistently on everything. We procrastinate on particular types of tasks—things we consider particularly important, as a matter of fact. I almost never procrastinate in general: I complete tasks early, I plan ahead, I am always (over)prepared. But lately I’ve been procrastinating on three tasks in particular: Revising my second-year paper to submit to journals, writing grant proposals, and finishing my third-year paper. These tasks are all academic, of course; they all involve a great deal of intellectual effort. But above all, they are high stakes. I didn’t procrastinate on homework for classes, but I’m procrastinating on finishing my dissertation.

Another common explanation for procrastination involves self-control: We can’t stop ourselves from doing whatever seems fun at the moment, when we should be getting down to work on what really matters.

This explanation is even worse: There is no apparent correlation between propensity to procrastinate and general impulsiveness—or, if anything, the correlation seems to be negative. The people I know who procrastinate the most consistently are the least impulsive; they tend to ponder and deliberate every decision, even small decisions for which the extra time spent clearly isn’t worth it.

The explanation I find much more convincing is that procrastination isn’t about self-control or time at all. It’s about anxiety. Procrastination is a form of avoidance: We don’t want to face the painful experience, so we stay away from it as long as we can.

This is certainly how procrastination feels for me: It’s not that I can’t stop myself from doing something fun, it’s that I can’t bring myself to face this particular task that is causing me overwhelming stress.

This also explains why it’s always something important that we procrastinate on: It’s precisely things with high stakes that are going to cause a lot of painful feelings. And anxiety itself is deeply linked to the fear of negative evaluation—which is exactly what you’re afraid of when submitting to a journal or applying for a grant. Usually it’s a bit more metaphorical than that, the “evaluation” of being judged by your peers; but here we are literally talking about a written evaluation from a reviewer.

This is why the most effective methods at reducing procrastination all involve reducing your anxiety surrounding the task. In fact, one of the most important is forgiving yourself for prior failings—including past procrastination. Students who were taught to forgive themselves for procrastinating were less likely to procrastinate in the future. If this were a matter of self-control, forgiving yourself should be counterproductive; but in fact it’s probably the most effective intervention.

Unsurprisingly, those with the highest stress level had the highest rates of procrastination (causality could run both ways there); but this is much less true for those who are good at practicing self-compassion. The idea behind self-compassion is very simple: Treat yourself as kindly as you would treat someone you care about.

I am extraordinarily bad at self-compassion. It is probably my greatest weakness. If we were to measure self-compassion by the gap between how kind you are to yourself and how kind you are to others, I would probably have one of the largest gaps in the world. Compassion for others has been a driving force in my life for as long as I can remember, and I put my money where my mouth is, giving at least 8% of my gross income to top-rated international charities every year. But compassion for myself feels inauthentic, even alien; I brutally punish myself for every failure, every moment of weakness. If someone else treated me the way I treat myself, I’d consider them abusive. It’s something I’ve struggled with for many years.

Really, the wonder is that I don’t procrastinate more; I think it’s because I’m already doing most of the things that people will tell you to do to avoid procrastination, like scheduling specific tasks to specific times and prioritizing a small number of important tasks each day. I even keep track of how I actually use my time (I call it “descriptive scheduling”, as opposed to conventional “normative scheduling”), and use that information to make my future schedules more realistic—thus avoiding or at least mitigating the planning fallacy. But when it’s just too intimidating to even look at the paper I’m supposed to be revising, none of that works.

If you too are struggling with procrastination (and odds of that are quite high), I’m afraid that I don’t have any brilliant advice for you today. I can recommend those scheduling techniques, and they may help; but the ultimate cause of procrastination is not bad scheduling or planning but something much deeper: anxiety about the task itself and being evaluated upon it. Procrastination is not laziness or lack of self-control: It’s an anxiety symptom.

I don’t care what happened in that video

Jan 27 JDN 2458511

Right now there is an ongoing controversy over a viral video of a confrontation between young protesters wearing MAGA hats and an elderly Native American man. Various sources are purporting to show “a fuller picture” and “casting new light” and showing “a different side”. Others are saying it’s exactly as bad as it looks.

I think it probably is as bad as it looks, but the truth is: I don’t care. This is a distraction.

If you think litigating the precise events of this video is important, you are suffering from a severe case of scope neglect. You are looking at a single event between a handful of people when you should be looking at the overall trends of a country of over 300 million people.

First of all: The government shutdown only just ended. There are still going to be a lot of pieces to pick up. That’s what we should be talking about. That’s what we should be posting about. That’s what we should be calling Senators about. This is a national emergency. The longer this lasts, the worse it is going to get. People will die because of this shutdown—from tainted food and polluted water and denied food stamps. Our national security is being jeopardized—particularly with regard to cybersecurity.

The shutdown was also a completely unforced error. Government shutdowns shouldn’t even exist, and now that this one is over, we need to change the budget process so that this can never happen again.

And if you want to talk about the racist, sexist, and authoritarian leanings of Trump supporters, that’s quite important too. But it doesn’t hinge upon one person or one confrontation. I’m sure there are Trump supporters who aren’t racist; and I’m sure there are Obama supporters who are. But the overall statistical trend there is extremely strong.

I understand that most people suffer from severe scope neglect, and we have to live in a world filled with such people; so maybe there’s some symbolic value in finding one particularly egregious case that you can put a face on and share with the world. But if you’re going to do that, there’s two things I’d ask of you:

1. Make absolutely sure that this case is genuine. Nothing will destroy your persuasiveness faster than holding up an ambiguous case as if it were definitive.
2. After you’ve gotten their attention with the single example, show the statistics. There are truths, whole truths, and statistics. If you really want to know something, you use statistics.

The statistics are what this is really about. One person, even a hundred people—that really doesn’t matter. We need to keep our eyes on the millions of people, the directions of entire nations. For a lot of people, looking at numbers is boring; but there are people behind those numbers, and numbers are what tell us what’s really going on in the world.

For example: Trump really does seem to have brought bigotry out in the open. Hate crimes in the US increased for the third year in a row last year.

Then there are his direct policy actions which are human rights violations: The number of children detained at the border has skyrocketed to almost 13,000.

On the other hand, the economy is doing quite well: Unemployment stands at about 4%, and median income is increasing and poverty is decreasing.
Global extreme poverty continues its preciptious decline, but global climate change is getting worse, and already past the point where some serious consequences are going to be unavoidable.

Some indicators are more ambiguous: Corporate profits are near their all-time high, even in inflation-adjusted terms. That could be a sign of an overall good economy—but it also clearly has something to do with redistribution of income toward the wealthy.

Of course, all of those things were true yesterday, and will be true tomorrow. They were true last week, and will be true next week. They don’t lend themselves to a rapid-fire news cycle.

But maybe that means we don’t need a rapid-fire news cycle? Maybe that’s not the best way to understand what’s going on in the world?

What would a new macroeconomics look like?

Dec 9 JDN 2458462

In previous posts I have extensively criticized the current paradigm of macroeconomics. But it’s always easier to tear the old edifice down than to build a better one in its place. So in this post I thought I’d try to be more constructive: What sort of new directions could macroeconomics take?

The most important change we need to make is to abandon the assumption of dynamic optimization. This will be a very hard sell, as most macroeconomists have become convinced that the Lucas Critique means we need to always base everything on the dynamic optimization of a single representative agent. I don’t think this was actually what Lucas meant (though maybe we should ask him; he’s still at Chicago), and I certainly don’t think it is what he should have meant. He had a legitimate point about the way macroeconomics was operating at that time: It was ignoring the feedback loops that occur when we start trying to change policies.

Goodhart’s Law is probably a better formulation: Once you make an indicator into a target, you make it less effective as an indicator. So while inflation does seem to be negatively correlated with unemployment, that doesn’t mean we should try to increase inflation to extreme levels in order to get rid of unemployment; sooner or later the economy is going to adapt and we’ll just have both inflation and unemployment at the same time. (Campbell’s Law provides a specific example that I wish more people in the US understood: Test scores would be a good measure of education if we didn’t use them to target educational resources.)

The reason we must get rid of dynamic optimization is quite simple: No one behaves that way.

It’s often computationally intractable even in our wildly oversimplified models that experts spend years working onnow you’re imagining that everyone does this constantly?

The most fundamental part of almost every DSGE model is the Euler equation; this equation comes directly from the dynamic optimization. It’s supposed to predict how people will choose to spend and save based upon their plans for an infinite sequence of future income and spending—and if this sounds utterly impossible, that’s because it is. Euler equations don’t fit the data at all, and even extreme attempts to save them by adding a proliferation of additional terms have failed. (It reminds me very much of the epicycles that astronomers used to add to the geocentric model of the universe to try to squeeze in weird results like Mars, before they had the heliocentric model.)

We should instead start over: How do people actually choose their spending? Well, first of all, it’s not completely rational. But it’s also not totally random. People spend on necessities before luxuries; they try to live within their means; they shop for bargains. There is a great deal of data from behavioral economics that could be brought to bear on understanding the actual heuristics people use in deciding how to spend and save. There have already been successful policy interventions using this knowledge, like Save More Tomorrow.

The best thing about this is that it should make our models simpler. We’re no longer asking each agent in the model to solve an impossible problem. However people actually make these decisions, we know it can be done, because it is being done. Most people don’t really think that hard, even when they probably should; so the heuristics really can’t be that complicated. My guess is that you can get a good fit—certainly better than an Euler equation—just by assuming that people set a target for how much they’re going to save (which is also probably pretty small for most people), and then spend the rest.

The second most important thing we need to add is inequality. Some people are much richer than others; this is a very important fact about economics that we need to understand. Yet it has taken the economics profession decades to figure this out, and even now I’m only aware of one class of macroeconomic models that seriously involves inequality, the Heterogeneous Agent New Keynesian (HANK) models which didn’t emerge until the last few years (the earliest publication I can find is 2016!). And these models are monsters; they are almost always computationally intractable and have a huge number of parameters to estimate.

Understanding inequality will require more parameters, that much is true. But if we abandon dynamic optimization, we won’t need as many as the HANK models have, and most of the new parameters are actually things we can observe, like the distribution of wages and years of schooling.

Observability of parameters is a big deal. Another problem with the way the Lucas Critique has been used is that we’ve been told we need to be using “deep structural parameters” like the temporal elasticity of substitution and the coefficient of relative risk aversion—but we have no idea what those actually are. We can’t observe them, and all of our attempts to measure them indirectly have yielded inconclusive or even inconsistent results. This is probably because these parameters are based on assumptions about human rationality that are simply not realistic. Most people probably don’t have a well-defined temporal elasticity of substitution, because their day-to-day decisions simply aren’t consistent enough over time for that to make sense. Sometimes they eat salad and exercise; sometimes they loaf on the couch and drink milkshakes. Likewise with risk aversion: many moons ago I wrote about how people will buy both insurance and lottery tickets, which no one with a consistent coefficient of relative risk aversion would ever do.

So if we are interested in deep structural parameters, we need to base those parameters on behavioral experiments so that we can understand actual human behavior. And frankly I don’t think we need deep structural parameters; I think this is a form of greedy reductionism, where we assume that the way to understand something is always to look at smaller pieces. Sometimes the whole is more than the sum of its parts. Economists obviously feel a lot of envy for physics; but they don’t seem to understand that aerodynamics would never have (ahem) gotten off the ground if we had first waited for an exact quantum mechanical solution of the oxygen atom (which we still don’t have, by the way). Macroeconomics may not actually need “microfoundations” in the strong sense that most economists intend; it needs to be consistent with small-scale behavior, but it doesn’t need to be derived from small-scale behavior.

This means that the new paradigm in macroeconomics does not need to be computationally intractable. Using heuristics instead of dynamic optimization and worrying less about microfoundations will make the models simpler; adding inequality need not make them so much more complicated.

Fighting the zero-sum paradigm

Dec 2 JDN 2458455

It should be obvious at this point that there are deep, perhaps even fundamental, divides between the attitudes and beliefs of different political factions. It can be very difficult to even understand, much less sympathize, with the concerns of people who are racist, misogynistic, homophobic, xenophobic, and authoritarian.
But at the end of the day we still have to live in the same country as these people, so we’d better try to understand how they think. And maybe, just maybe, that understanding will help us to change them.

There is one fundamental belief system that I believe underlies almost all forms of extremism. Right now right-wing extremism is the major threat to global democracy, but left-wing extremism subscribes to the same core paradigm (consistent with Horseshoe Theory).

I think the best term for this is the zero-sum paradigm. The idea is quite simple: There is a certain amount of valuable “stuff” (money, goods, land, status, happiness) in the world, and the only political question is who gets how much.

Thus, any improvement in anyone’s life must, necessarily, come at someone else’s expense. If I become richer, you become poorer. If I become stronger, you become weaker. Any improvement in my standard of living is a threat to your status.

If this belief were true, it would justify, or at least rationalize, all sorts of destructive behavior: Any harm I can inflict upon someone else will yield a benefit for me, by some fundamental conservation law of the universe.

Viewed in this light, beliefs like patriarchy and White supremacy suddenly become much more comprehensible: Why would you want to spend so much effort hurting women and Black people? Because, by the fundamental law of zero-sum, any harm to women is a benefit to men, and any harm to Black people is a benefit to White people. The world is made of “teams”, and you are fighting for your own against all the others.

And I can even see why such an attitude is seductive: It’s simple and easy to understand. And there are many circumstances where it can be approximately true.
When you are bargaining with your boss over a wage, one dollar more for you is one dollar less for your boss.
When your factory outsources production to China, one more job for China is one less job for you.

When we vote for President, one more vote for the Democrats is one less vote for the Republicans.

But of course the world is not actually zero-sum. Both you and your boss would be worse off if your job were to disappear; they need your work and you need their money. For every job that is outsourced to China, another job is created in the United States. And democracy itself is such a profound public good that it basically overwhelms all others.

In fact, it is precisely when a system is running well that the zero-sum paradigm becomes closest to true. In the space of all possible allocations, it is the efficient ones that behave in something like a zero-sum way, because when the system is efficient, we are already producing as much as we can.

This may be part of why populist extremism always seems to assert itself during periods of global prosperity, as in the 1920s and today: It is precisely when the world is running at its full capacity that it feels most like someone else’s gain must come at your loss.

Yet if we live according to the zero-sum paradigm, we will rapidly destroy the prosperity that made that paradigm seem plausible. A trade war between the US and China would put millions out of work in both countries. A real war with conventional weapons would kill millions. A nuclear war would kill billions.

This is what we must convey: We must show people just how good things are right now.

This is not an easy task; when people want to believe the world is falling apart, they can very easily find excuses to do so. You can point to the statistics showing a global decline in homicide, but one dramatic shooting on the TV news will wipe that all away. You can show the worldwide rise in real incomes across the board, but that won’t console someone who just lost their job and blames outsourcing or immigrants.

Indeed, many people will be offended by the attempt—the mere suggestion that the world is actually in very good shape and overall getting better will be perceived as an attempt to deny or dismiss the problems and injustices that still exist.

I encounter this especially from the left: Simply pointing out the objective fact that the wealth gap between White and Black households is slowly closing is often taken as a claim that racism no longer exists or doesn’t matter. Congratulating the meteoric rise in women’s empowerment around the world is often paradoxically viewed as dismissing feminism instead of lauding it.

I think the best case against progress can be made with regard to global climate change: Carbon emissions are not falling nearly fast enough, and the world is getting closer to the brink of truly catastrophic ecological damage. Yet even here the zero-sum paradigm is clearly holding us back; workers in fossil-fuel industries think that the only way to reduce carbon emissions is to make their families suffer, but that’s simply not true. We can make them better off too.

Talking about injustice feels righteous. Talking about progress doesn’t. Yet I think what the world needs most right now—the one thing that might actually pull us back from the brink of fascism or even war—is people talking about progress.

If people think that the world is full of failure and suffering and injustice, they will want to tear down the whole system and start over with something else. In a world that is largely democratic, that very likely means switching to authoritarianism. If people think that this is as bad as it gets, they will be willing to accept or even instigate violence in order to change to almost anything else.

But if people realize that in fact the world is full of success and prosperity and progress, that things are right now quite literally better in almost every way for almost every person in almost every country than they were a hundred—or even fifty—years ago, they will not be so eager to tear the system down and start anew. Centrism is often mocked (partly because it is confused with false equivalence), but in a world where life is improving this quickly for this many people, “stay the course” sounds awfully attractive to me.
That doesn’t mean we should ignore the real problems and injustices that still exist, of course. There is still a great deal of progress left to be made.  But I believe we are more likely to make progress if we acknowledge and seek to continue the progress we have already made, than if we allow ourselves to fall into despair as if that progress did not exist.

If you really want grad students to have better mental health, remove all the high-stakes checkpoints

Post 260: Oct 14 JDN 2458406

A study was recently published in Nature Biotechnology showing clear evidence of a mental health crisis among graduate students (no, I don’t know why they picked the biotechnology imprint—I guess it wasn’t good enough for Nature proper?). This is only the most recent of several studies showing exceptionally high rates of mental health issues among graduate students.

I’ve seen universities do a lot of public hand-wringing and lip service about this issue—but I haven’t seen any that were seriously willing to do what it takes to actually solve the problem.

I think this fact became clearest to me when I was required to fill out an official “Individual Development Plan” form as a prerequisite for my advancement to candidacy, which included one question about “What are you doing to support your own mental health and work/life balance?”

The irony here is absolutely excruciating, because advancement to candidacy has been overwhelmingly my leading source of mental health stress for at least the last six months. And it is only one of several different high-stakes checkpoints that grad students are expected to complete, always threatened with defunding or outright expulsion from the graduate program if the checkpoint is not met by a certain arbitrary deadline.

The first of these was the qualifying exams. Then comes advancement to candidacy. Then I have to complete and defend a second-year paper, then a third-year paper. Finally I have to complete and defend a dissertation, and then go onto the job market and go through a gauntlet of applications and interviews. I can’t think of any other time in my life when I was under this much academic and career pressure this consistently—even finishing high school and applying to college wasn’t like this.

If universities really wanted to improve my mental health, they would find a way to get rid of all that.

Granted, a single university does not have total control over all this: There are coordination problems between universities regarding qualifying exams, advancement, and dissertation requirements. One university that unilaterally tried to remove all these would rapidly lose prestige, as it would not be regarded as “rigorous” to reduce the pressure on your grad students. But that itself is precisely the problem—we have equated “rigor” with pressuring grad students until they are on the verge of emotional collapse. Universities don’t seem to know how to make graduate school difficult in the ways that would actually encourage excellence in research and teaching; they simply know how to make it difficult in ways that destroy their students psychologically.

The job market is even more complicated; in the current funding environment, it would be prohibitively expensive to open up enough faculty positions to actually accept even half of all graduating PhDs to tenure-track jobs. Probably the best answer here is to refocus graduate programs on supporting employment outside academia, recognizing both that PhD-level skills are valuable in many workplaces and that not every grad student really wants to become a professor.

But there are clearly ways that universities could mitigate these effects, and they don’t seem genuinely interested in doing so. They could remove the advancement exam, for example; you could simply advance to candidacy as a formality when your advisor decides you are ready, never needing to actually perform a high-stakes presentation before a committee—because what the hell does that accomplish anyway? Speaking of advisors, they could have a formalized matching process that starts with interviewing several different professors and being matched to the one that best fits your goals and interests, instead of expecting you to reach out on your own and hope for the best. They could have you write a dissertation, but not perform a “dissertation defense”—because, again, what can they possibly learn from forcing you to present in a high-stakes environment that they couldn’t have learned from reading your paper and talking with you about it over several months?

They could adjust or even remove funding deadlines—especially for international students. Here at UCI at least, once you are accepted to the program, you are ostensibly guaranteed funding for as long as you maintain reasonable academic progress—but then they define “reasonable progress” in such a way that you have to form an advancement committee, fill out forms, write a paper, and present before a committee all by a certain date or your funding is in jeopardy. Residents of California (which includes all US students who successfully established residency after a full year) are given more time if we need it—but international students aren’t. How is that fair?

The unwillingness of universities to take such actions clearly shows that their commitment to improving students’ mental health is paper-thin. They are only willing to help their students improve their work-life balance as long as it doesn’t require changing anything about the graduate program. They will provide us with counseling services and free yoga classes, but they won’t seriously reduce the pressure they put on us at every step of the way.
I understand that universities are concerned about protecting their prestige, but I ask them this: Does this really improve the quality of your research or teaching output? Do you actually graduate better students by selecting only the ones who can survive being emotionally crushed? Do all these arbitrary high-stakes performances actually result in greater advancement of human knowledge?

Or is it perhaps that you yourselves were put through such hazing rituals years ago, and now your cognitive dissonance won’t let you admit that it was all for naught? “This must be worth doing, or else they wouldn’t have put me through so much suffering!” Are you trying to transfer your own psychological pain onto your students, lest you be forced to face it yourself?