# When maximizing utility doesn’t

Jun 4 JDN 2460100

Expected utility theory behaves quite strangely when you consider questions involving mortality.

Nick Beckstead and Teruji Thomas recently published a paper on this: All well-defined utility functions are either reckless in that they make you take crazy risks, or timid in that they tell you not to take even very small risks. It’s starting to make me wonder if utility theory is even the right way to make decisions after all.

Consider a game of Russian roulette where the prize is $1 million. The revolver has 6 chambers, 3 with a bullet. So that’s a 1/2 chance of$1 million, and a 1/2 chance of dying. Should you play?

I think it’s probably a bad idea to play. But the prize does matter; if it were $100 million, or$1 billion, maybe you should play after all. And if it were $10,000, you clearly shouldn’t. And lest you think that there is no chance of dying you should be willing to accept for any amount of money, consider this: Do you drive a car? Do you cross the street? Do you do anything that could ever have any risk of shortening your lifespan in exchange for some other gain? I don’t see how you could live a remotely normal life without doing so. It might be a very small risk, but it’s still there. This raises the question: Suppose we have some utility function over wealth; ln(x) is a quite plausible one. What utility should we assign to dying? The fact that the prize matters means that we can’t assign death a utility of negative infinity. It must be some finite value. But suppose we choose some value, -V, (so V is positive), for the utility of dying. Then we can find some amount of money that will make you willing to play: ln(x) = V, x = e^(V). Now, suppose that you have the chance to play this game over and over again. Your marginal utility of wealth will change each time you win, so we may need to increase the prize to keep you playing; but we could do that. The prizes could keep scaling up as needed to make you willing to play. So then, you will keep playing, over and over—and then, sooner or later, you’ll die. So, at each step you maximized utility—but at the end, you didn’t get any utility. Well, at that point your heirs will be rich, right? So maybe you’re actually okay with that. Maybe there is some amount of money ($1 billion?) that you’d be willing to die in order to ensure your heirs have.

But what if you don’t have any heirs? Or, what if we consider making such a decision as a civilization? What if death means not only the destruction of you, but also the destruction of everything you care about?

As a civilization, are there choices before us that would result in some chance of a glorious, wonderful future, but also some chance of total annihilation? I think it’s pretty clear that there are. Nuclear technology, biotechnology, artificial intelligence. For about the last century, humanity has been at a unique epoch: We are being forced to make this kind of existential decision, to face this kind of existential risk.

It’s not that we were immune to being wiped out before; an asteroid could have taken us out at any time (as happened to the dinosaurs), and a volcanic eruption nearly did. But this is the first time in humanity’s existence that we have had the power to destroy ourselves. This is the first time we have a decision to make about it.

One possible answer would be to say we should never be willing to take any kind of existential risk. Unlike the case of an individual, when we speaking about an entire civilization, it no longer seems obvious that we shouldn’t set the utility of death at negative infinity. But if we really did this, it would require shutting down whole industries—definitely halting all research in AI and biotechnology, probably disarming all nuclear weapons and destroying all their blueprints, and quite possibly even shutting down the coal and oil industries. It would be an utterly radical change, and it would require bearing great costs.

On the other hand, if we should decide that it is sometimes worth the risk, we will need to know when it is worth the risk. We currently don’t know that.

Even worse, we will need some mechanism for ensuring that we don’t take the risk when it isn’t worth it. And we have nothing like such a mechanism. In fact, most of our process of research in AI and biotechnology is widely dispersed, with no central governing authority and regulations that are inconsistent between countries. I think it’s quite apparent that right now, there are research projects going on somewhere in the world that aren’t worth the existential risk they pose for humanity—but the people doing them are convinced that they are worth it because they so greatly advance their national interest—or simply because they could be so very profitable.

In other words, humanity finally has the power to make a decision about our survival, and we’re not doing it. We aren’t making a decision at all. We’re letting that responsibility fall upon more or less randomly-chosen individuals in government and corporate labs around the world. We may be careening toward an abyss, and we don’t even know who has the steering wheel.

# Reckoning costs in money distorts them

May 7 JDN 2460072

Consider for a moment what it means when an economic news article reports “rising labor costs”. What are they actually saying?

They’re saying that wages are rising—perhaps in some industry, perhaps in the economy as a whole. But this is not a cost. It’s a price. As I’ve written about before, the two are fundamentally distinct.

The cost of labor is measured in effort, toil, and time. It’s the pain of having to work instead of whatever else you’d like to do with your time.

The price of labor is a monetary amount, which is delivered in a transaction.

This may seem perfectly obvious, but it has important and oft-neglected implications. A cost, one paid, is gone. That value has been destroyed. We hope that it was worth it for some benefit we gained. A price, when paid, is simply transferred: One person had that money before, now someone else has it. Nothing was gained or lost.

So in fact when reports say that “labor costs have risen”, what they are really saying is that income is being transferred from owners to workers without any change in real value taking place. They are framing as a loss what is fundamentally a zero-sum redistribution.

In fact, it is disturbingly common to see a fundamentally good redistribution of income framed in the press as a bad outcome because of its expression as “costs”; the “cost” of chocolate is feared to go up if we insist upon enforcing bans on forced labor—when in fact it is only the price that goes up, and the cost actually goes down: chocolate would no longer include complicity in an atrocity. The real suffering of making chocolate would be thereby reduced, not increased. Even when they aren’t literally enslaved, those workers are astonishingly poor, and giving them even a few more cents per hour would make a real difference in their lives. But God forbid we pay a few cents more for a candy bar!

If labor costs were to rise, that would mean that work had suddenly gotten harder, or more painful; or else, that some outside circumstance had made it more difficult to work. Having a child increases your labor costs—you now have the opportunity cost of not caring for the child. COVID increased the cost of labor, by making it suddenly dangerous just to go outside in public. That could also increase prices—you may demand a higher wage, and people do seem to have demanded higher wages after COVID. But these are two separate effects, and you can have one without the other. In fact, women typically see wage stagnation or even reduction after having kids (but men largely don’t), despite their real opportunity cost of labor having obviously greatly increased.

On an individual level, it’s not such a big mistake to equate price and cost. If you are buying something, its cost to you basically just is its price, plus a little bit of transaction cost for actually finding and buying it. But on a societal level, it makes an enormous difference. It distorts our policy priorities and can even lead to actively trying to suppress things that are beneficial—such as rising wages.

This false equivalence between price and costs seems to be at least as common among economists as it is among laypeople. Economists will often justify it on the grounds that in an ideal perfect competitive market the two would be in some sense equated. But of course we don’t live in that ideal perfect market, and even if we did, they would only beproportional at the margin, not fundamentally equal across the board. It would still be obviously wrong to characterize the total value or cost of work by the price paid for it; only the last unit of effort would be priced so that marginal value equals price equals marginal cost. The first 39 hours of your work would cost you less than what you were paid, and produce more than you were paid; only that 40th hour would set the three equal.

Once you account for all the various market distortions in the world, there’s no particular relationship between what something costs—in terms of real effort and suffering—and its price—in monetary terms. Things can be expensive and easy, or cheap and awful. In fact, they often seem to be; for some reason, there seems to be a pattern where the most terrible, miserable jobs (e.g. coal mining) actually pay the leastand the easiest, most pleasant jobs (e.g. stock trading) pay the most. Some jobs that benefit society pay well (e.g. doctors) and others pay terribly or not at all (e.g. climate activists). Some actions that harm the world get punished (e.g. armed robbery) and others get rewarded with riches (e.g. oil drilling). In the real world, whether a job is good or bad and whether it is paid well or poorly seem to be almost unrelated.

In fact, sometimes they seem even negatively related, where we often feel tempted to “sell out” and do something destructive in order to get higher pay. This is likely due to Berkson’s paradox: If people are willing to do jobs if they are either high-paying or beneficial to humanity, then we should expect that, on average, most of the high-paying jobs people do won’t be beneficial to humanity. Even if there were inherently no correlation or a small positive one, people’s refusal to do harmful low-paying work removes those jobs from our sample and results in a negative correlation in what remains.

I think that the best solution, ultimately, is to stop reckoning costs in money entirely. We should reckon them in happiness.

This is of course much more difficult than simply using prices; it’s not easy to say exactly how many QALY are sacrificed in the extraction of cocoa beans or the drilling of offshore oil wells. But if we actually did find a way to count them, I strongly suspect we’d find that it was far more than we ought to be willing to pay.

A very rough approximation, surely flawed but at least a start, would be to simply convert all payments into proportions of their recipient’s income: For full-time wages, this would result in basically everyone being counted the same, as 1 hour of work if you work 40 hours per week, 50 weeks per year is precisely 0.05% of your annual income. So we could say that whatever is equivalent to your hourly wage constitutes 50 microQALY.

This automatically implies that every time a rich person pays a poor person, QALY increase, while every time a poor person pays a rich person, QALY decrease. This is not an error in the calculation. It is a fact of the universe. We ignore it only at out own peril. All wealth redistributed downward is a benefit, while all wealth redistributed upward is a harm. That benefit may cause some other harm, or that harm may be compensated by some other benefit; but they are still there.

This would also put some things in perspective. When HSBC was fined £70 million for its crimes, that can be compared against its £1.5 billion in net income; if it were an individual, it would have been hurt about 50 milliQALY, which is about what I would feel if I lost $2000. Of course, it’s not a person, and it’s not clear exactly how this loss was passed through to employees or shareholders; but that should give us at least some sense of how small that loss was for them. They probably felt it… a little. When Trump was ordered to pay a$1.3 million settlement, based on his $2.5 billion net wealth (corresponding to roughly$125 million in annual investment income), that cost him about 10 milliQALY; for me that would be about $500. At the other extreme, if someone goes from making$1 per day to making 1.50 per day, that’s a 50% increase in their income—500 milliQALY per year. For those who have no income at all, this becomes even trickier; for them I think we should probably use their annual consumption, since everyone needs to eat and that costs something, though likely not very much. Or we could try to measure their happiness directly, trying to determine how much it hurts to not eat enough and work all day in sweltering heat. Properly shifting this whole cultural norm will take a long time. For now, I leave you with this: Any time you see a monetary figure, ask yourself: How much is that worth to them?” The world will seem quite different once you get in the habit of that. # What behavioral economics needs Apr 16 JDN 2460049 The transition from neoclassical to behavioral economics has been a vital step forward in science. But lately we seem to have reached a plateau, with no major advances in the paradigm in quite some time. It could be that there is work already being done which will, in hindsight, turn out to be significant enough to make that next step forward. But my fear is that we are getting bogged down by our own methodological limitations. Neoclassical economics shared with us its obsession with mathematical sophistication. To some extent this was inevitable; in order to impress neoclassical economists enough to convert some of them, we had to use fancy math. We had to show that we could do it their way in order to convince them why we shouldn’t—otherwise, they’d just have dismissed us the way they had dismissed psychologists for decades, as too “fuzzy-headed” to do the “hard work” of putting everything into equations. But the truth is, putting everything into equations was never the right approach. Because human beings clearly don’t think in equations. Once we write down a utility function and get ready to take its derivative and set it equal to zero, we have already distanced ourselves from how human thought actually works. When dealing with a simple physical system, like an atom, equations make sense. Nobody thinks that the electron knows the equation and is following it intentionally. That equation simply describes how the forces of the universe operate, and the electron is subject to those forces. But human beings do actually know things and do things intentionally. And while an equation could be useful for analyzing human behavior in the aggregate—I’m certainly not objecting to statistical analysis—it really never made sense to say that people make their decisions by optimizing the value of some function. Most people barely even know what a function is, much less remember calculus well enough to optimize one. Yet right now, behavioral economics is still all based in that utility-maximization paradigm. We don’t use the same simplistic utility functions as neoclassical economists; we make them more sophisticated and realistic. Yet in that very sophistication we make things more complicated, more difficult—and thus in at least that respect, even further removed from how actual human thought must operate. The worst offender here is surely Prospect Theory. I recognize that Prospect Theory predicts human behavior better than conventional expected utility theory; nevertheless, it makes absolutely no sense to suppose that human beings actually do some kind of probability-weighting calculation in their heads when they make judgments. Most of my students—who are well-trained in mathematics and economics—can’t even do that probability-weighting calculation on paper, with a calculator, on an exam. (There’s also absolutely no reason to do it! All it does it make your decisions worse!) This is a totally unrealistic model of human thought. This is not to say that human beings are stupid. We are still smarter than any other entity in the known universe—computers are rapidly catching up, but they haven’t caught up yet. It is just that whatever makes us smart must not be easily expressible as an equation that maximizes a function. Our thoughts are bundles of heuristics, each of which may be individually quite simple, but all of which together make us capable of not only intelligence, but something computers still sorely, pathetically lack: wisdom. Computers optimize functions better than we ever will, but we still make better decisions than they do. I think that what behavioral economics needs now is a new unifying theory of these heuristics, which accounts for not only how they work, but how we select which one to use in a given situation, and perhaps even where they come from in the first place. This new theory will of course be complex; there’s a lot of things to explain, and human behavior is a very complex phenomenon. But it shouldn’t be—mustn’t be—reliant on sophisticated advanced mathematics, because most people can’t do advanced mathematics (almost by construction—we would call it something different otherwise). If your model assumes that people are taking derivatives in their heads, your model is already broken. 90% of the world’s people can’t take a derivative. I guess it could be that our cognitive processes in some sense operate as if they are optimizing some function. This is commonly posited for the human motor system, for instance; clearly baseball players aren’t actually solving differential equations when they throw and catch balls, but the trajectories that balls follow do in fact obey such equations, and the reliability with which baseball players can catch and throw suggests that they are in some sense acting as if they can solve them. But I think that a careful analysis of even this classic example reveals some deeper insights that should call this whole notion into question. How do baseball players actually do what they do? They don’t seem to be calculating at all—in fact, if you asked them to try to calculate while they were playing, it would destroy their ability to play. They learn. They engage in practiced motions, acquire skills, and notice patterns. I don’t think there is anywhere in their brains that is actually doing anything like solving a differential equation. It’s all a process of throwing and catching, throwing and catching, over and over again, watching and remembering and subtly adjusting. One thing that is particularly interesting to me about that process is that is astonishingly flexible. It doesn’t really seem to matter what physical process you are interacting with; as long as it is sufficiently orderly, such a method will allow you to predict and ultimately control that process. You don’t need to know anything about differential equations in order to learn in this way—and, indeed, I really can’t emphasize this enough, baseball players typically don’t. In fact, learning is so flexible that it can even perform better than calculation. The usual differential equations most people would think to use to predict the throw of a ball would assume ballistic motion in a vacuum, which absolutely not what a curveball is. In order to throw a curveball, the ball must interact with the air, and it must be launched with spin; curving a baseball relies very heavily on the Magnus Effect. I think it’s probably possible to construct an equation that would fully predict the motion of a curveball, but it would be a tremendously complicated one, and might not even have an exact closed-form solution. In fact, I think it would require solving the Navier-Stokes equations, for which there is an outstanding Millennium Prize. Since the viscosity of air is very low, maybe you could get away with approximating using the Euler fluid equations. To be fair, a learning process that is adapting to a system that obeys an equation will yield results that become an ever-closer approximation of that equation. And it is in that sense that a baseball player can be said to be acting as if solving a differential equation. But this relies heavily on the system in question being one that obeys an equation—and when it comes to economic systems, is that even true? What if the reason we can’t find a simple set of equations that accurately describe the economy (as opposed to equations of ever-escalating complexity that still utterly fail to describe the economy) is that there isn’t one? What if the reason we can’t find the utility function people are maximizing is that they aren’t maximizing anything? What behavioral economics needs now is a new approach, something less constrained by the norms of neoclassical economics and more aligned with psychology and cognitive science. We should be modeling human beings based on how they actually think, not some weird mathematical construct that bears no resemblance to human reasoning but is designed to impress people who are obsessed with math. I’m of course not the first person to have suggested this. I probably won’t be the last, or even the one who most gets listened to. But I hope that I might get at least a few more people to listen to it, because I have gone through the mathematical gauntlet and earned my bona fides. It is too easy to dismiss this kind of reasoning from people who don’t actually understand advanced mathematics. But I do understand differential equations—and I’m telling you, that’s not how people think. # Implications of stochastic overload Apr 2 JDN 2460037 A couple weeks ago I presented my stochastic overload model, which posits a neurological mechanism for the Yerkes-Dodson effect: Stress increases sympathetic activation, and this increases performance, up to the point where it starts to risk causing neural pathways to overload and shut down. This week I thought I’d try to get into some of the implications of this model, how it might be applied to make predictions or guide policy. One thing I often struggle with when it comes to applying theory is what actual benefits we get from a quantitative mathematical model as opposed to simply a basic qualitative idea. In many ways I think these benefits are overrated; people seem to think that putting something into an equation automatically makes it true and useful. I am sometimes tempted to try to take advantage of this, to put things into equations even though I know there is no good reason to put them into equations, simply because so many people seem to find equations so persuasive for some reason. (Studies have even shown that, particularly in disciplines that don’t use a lot of math, inserting a totally irrelevant equation into a paper makes it more likely to be accepted.) The basic implications of the Yerkes-Dodson effect are already widely known, and utterly ignored in our society. We know that excessive stress is harmful to health and performance, and yet our entire economy seems to be based around maximizing the amount of stress that workers experience. I actually think neoclassical economics bears a lot of the blame for this, as neoclassical economists are constantly talking about “increasing work incentives”—which is to say, making work life more and more stressful. (And let me remind you that there has never been any shortage of people willing to work in my lifetime, except possibly briefly during the COVID pandemic. The shortage has always been employers willing to hire them.) I don’t know if my model can do anything to change that. Maybe by putting it into an equation I can make people pay more attention to it, precisely because equations have this weird persuasive power over most people. As far as scientific benefits, I think that the chief advantage of a mathematical model lies in its ability to make quantitative predictions. It’s one thing to say that performance increases with low levels of stress then decreases with high levels; but it would be a lot more useful if we could actually precisely quantify how much stress is optimal for a given person and how they are likely to perform at different levels of stress. Unfortunately, the stochastic overload model can only make detailed predictions if you have fully specified the probability distribution of innate activation, which requires a lot of free parameters. This is especially problematic if you don’t even know what type of distribution to use, which we really don’t; I picked three classes of distribution because they were plausible and tractable, not because I had any particular evidence for them. Also, we don’t even have standard units of measurement for stress; we have a vague notion of what more or less stressed looks like, but we don’t have the sort of quantitative measure that could be plugged into a mathematical model. Probably the best units to use would be something like blood cortisol levels, but then we’d need to go measure those all the time, which raises its own issues. And maybe people don’t even respond to cortisol in the same ways? But at least we could measure your baseline cortisol for awhile to get a prior distribution, and then see how different incentives increase your cortisol levels; and then the model should give relatively precise predictions about how this will affect your overall performance. (This is a very neuroeconomic approach.) So, for now, I’m not really sure how useful the stochastic overload model is. This is honestly something I feel about a lot of the theoretical ideas I have come up with; they often seem too abstract to be usefully applicable to anything. Maybe that’s how all theory begins, and applications only appear later? But that doesn’t seem to be how people expect me to talk about it whenever I have to present my work or submit it for publication. They seem to want to know what it’s good for, right now, and I never have a good answer to give them. Do other researchers have such answers? Do they simply pretend to? Along similar lines, I recently had one of my students ask about a theory paper I wrote on international conflict for my dissertation, and after sending him a copy, I re-read the paper. There are so many pages of equations, and while I am confident that the mathematical logic is valid,I honestly don’t know if most of them are really useful for anything. (I don’t think I really believe that GDP is produced by a Cobb-Douglas production function, and we don’t even really know how to measure capital precisely enough to say.) The central insight of the paper, which I think is really important but other people don’t seem to care about, is a qualitative one: International treaties and norms provide an equilibrium selection mechanism in iterated games. The realists are right that this is cheap talk. The liberals are right that it works. Because when there are many equilibria, cheap talk works. I know that in truth, science proceeds in tiny steps, building a wall brick by brick, never sure exactly how many bricks it will take to finish the edifice. It’s impossible to see whether your work will be an irrelevant footnote or the linchpin for a major discovery. But that isn’t how the institutions of science are set up. That isn’t how the incentives of academia work. You’re not supposed to say that this may or may not be correct and is probably some small incremental progress the ultimate impact of which no one can possibly foresee. You’re supposed to sell your work—justify how it’s definitely true and why it’s important and how it has impact. You’re supposed to convince other people why they should care about it and not all the dozens of other probably equally-valid projects being done by other researchers. I don’t know how to do that, and it is agonizing to even try. It feels like lying. It feels like betraying my identity. Being good at selling isn’t just orthogonal to doing good science—I think it’s opposite. I think the better you are at selling your work, the worse you are at cultivating the intellectual humility necessary to do good science. If you think you know all the answers, you’re just bad at admitting when you don’t know things. It feels like in order to succeed in academia, I have to act like an unscientific charlatan. Honestly, why do we even need to convince you that our work is more important than someone else’s? Are there only so many science points to go around? Maybe the whole problem is this scarcity mindset. Yes, grant funding is limited; but why does publishing my work prevent you from publishing someone else’s? Why do you have to reject 95% of the papers that get sent to you? Don’t tell me you’re limited by space; the journals are digital and searchable and nobody reads the whole thing anyway. Editorial time isn’t infinite, but most of the work has already been done by the time you get a paper back from peer review. Of course, I know the real reason: Excluding people is the main source of prestige. # The role of innate activation in stochastic overload Mar 26 JDN 2460030 Two posts ago I introduced my stochastic overload model, which offers an explanation for the Yerkes-Dodson effect by positing that additional stress increases sympathetic activation, which is useful up until the point where it starts risking an overload that forces systems to shut down and rest. The central equation of the model is actually quite simple, expressed either as an expectation or as an integral: Y = E[x + s | x + s < 1] P[x + s < 1] Y = \int_{0}^{1-s} (x+s) dF(x) The amount of output produced is the expected value of innate activation plus stress activation, times the probability that there is no overload. Increased stress raises this expectation value (the incentive effect), but also increases the probability of overload (the overload effect). The model relies upon assuming that the brain starts with some innate level of activation that is partially random. Exactly what sort of Yerkes-Dodson curve you get from this model depends very much on what distribution this innate activation takes. I’ve so far solved it for three types of distribution. The simplest is a uniform distribution, where within a certain range, any level of activation is equally probable. The probability density function looks like this: Assume the distribution has support between a and b, where a < b. When b+s < 1, then overload is impossible, and only the incentive effect occurs; productivity increases linearly with stress. The expected output is simply the expected value of a uniform distribution from a+s to b+s, which is: E[x + s] = (a+b)/2+s Then, once b+s > 1, overload risk begins to increase. In this range, the probability of avoiding overload is: P[x + s < 1] = F(1-s) = (1-s-a)/(b-a) (Note that at b+s=1, this is exactly 1.) The expected value of x+s in this range is: E[x + s | x + s < 1] = (1-s)(1+s)/(2(b-a)) Multiplying these two together: Y = [(1-s)(1+s)(1-s-a)]/[2(b-a)^2] Here is what that looks like for a=0, b=1/2: It does have the right qualitative features: increasing, then decreasing. But its sure looks weird, doesn’t it? It has this strange kinked shape. So let’s consider some other distributions. The next one I was able to solve it for is an exponential distribution, where the most probable activation is zero, and then higher activation always has lower probability than lower activation in an exponential decay: For this it was actually easiest to do the integral directly (I did it by integrating by parts, but I’m sure you don’t care about all the mathematical steps): Y = \int_{0}^{1-s} (x+s) dF(x) Y = (1/λ+s) – (1/ λ + 1)e^(-λ(1-s)) The parameter λdecides how steeply your activation probability decays. Someone with low λ is relatively highly activated all the time, while someone with high λ is usually not highly activated; this seems like it might be related to the personality trait neuroticism. Here are graphs of what the resulting Yerkes-Dodson curve looks like for several different values of λ: λ = 0.5: λ = 1: λ = 2: λ = 4: λ = 8: The λ = 0.5 person has high activation a lot of the time. They are actually fairly productive even without stress, but stress quickly overwhelms them. The λ = 8 person has low activation most of the time. They are not very productive without stress, but can also bear relatively high amounts of stress without overloading. (The low-λ people also have overall lower peak productivity in this model, but that might not be true in reality, if λ is inversely correlated with some other attributes that are related to productivity.) Neither uniform nor exponential has the nice bell-curve shape for innate activation we might have hoped for. There is another class of distributions, beta distributions, which do have this shape, and they are sort of tractable—you need something called an incomplete beta function, which isn’t an elementary function but it’s useful enough that most statistical packages include it. Beta distributions have two parameters, α and β. They look like this: Beta distributions are quite useful in Bayesian statistics; if you’re trying to estimate the probability of a random event that either succeeds or fails with a fixed probability (a Bernoulli process), and so far you have observed a successes and b failures, your best guess of its probability at each trial is a beta distribution with α = a+1 and β = b+1. For beta distributions with parameters α and β, the result comes out to (I is that incomplete beta function I mentioned earlier): Y = I(1-s, α+1, β) + I(1-s, α, β) For whole number values of α andβ, the incomplete beta function can be computed by hand (though it is more work the larger they are); here’s an example with α = β = 2. The innate activation probability looks like this: And the result comes out like this: Y = 2(1-s)^3 – 3/2(1-s)^4 + 3s(1-s)^2 – 2s(1-s)^3 This person has pretty high innate activation most of the time, so stress very quickly overwhelms them. If I had chosen a much higher β, I could change that, making them less likely to be innately so activated. These are the cases I’ve found to be relatively tractable so far. They all have the right qualitative pattern: Increasing stress increases productivity for awhile, then begins decreasing it once overload risk becomes too high. They also show a general pattern where people who are innately highly activated (neurotic?) are much more likely to overload and thus much more sensitive to stress. # What happens when a bank fails Mar 19 JDN 2460023 As of March 9, Silicon Valley Bank (SVB) has failed and officially been put into receivership under the FDIC. A bank that held209 billion in assets has suddenly become insolvent.

This is the second-largest bank failure in US history, after Washington Mutual (WaMu) in 2008. In fact it will probably have more serious consequences than WaMu, for two reasons:

1. WaMu collapsed as part of the Great Recession, so there was already a lot of other things going on and a lot of policy responses already in place.

2. WaMu was mostly a conventional commercial bank that held deposits and loans for consumers, so its assets were largely protected by the FDIC, and thus its bankruptcy didn’t cause contagion the spread out to the rest of the system. (Other banks—shadow banks—did during the crash, but not so much WaMu.) SVB mostly served tech startups, so a whopping 89% of its deposits were not protected by FDIC insurance.

You’ve likely heard of many of the companies that had accounts at SVB: Roku, Roblox, Vimeo, even Vox. Stocks of the US financial industry lost $100 billion in value in two days. The good news is that this will not be catastrophic. It probably won’t even trigger a recession (though the high interest rates we’ve been having lately potentially could drive us over that edge). Because this is commercial banking, it’s done out in the open, with transparency and reasonably good regulation. The FDIC knows what they are doing, and even though they aren’t covering all those deposits directly, they intend to find a buyer for the bank who will, and odds are good that they’ll be able to cover at least 80% of the lost funds. In fact, while this one is exceptionally large, bank failures are not really all that uncommon. There have been nearly 100 failures of banks with assets over$1 billion in the US alone just since the 1970s. The FDIC exists to handle bank failures, and generally does the job well.

Then again, it’s worth asking whether we should really have a banking system in which failures are so routine.

The reason banks fail is kind of a dark open secret: They don’t actually have enough money to cover their deposits.

Banks loan away most of their cash, and rely upon the fact that most of their depositors will not want to withdraw their money at the same time. They are required to keep a certain ratio in reserves, but it’s usually fairly small, like 10%. This is called fractional-reserve banking.

As long as less than 10% of deposits get withdrawn at any given time, this works. But if a bunch of depositors suddenly decide to take out their money, the bank may not have enough to cover it all, and suddenly become insolvent.

In fact, the fear that a bank might become insolvent can actually cause it to become insolvent, in a self-fulfilling prophecy. Once depositors get word that the bank is about to fail, they rush to be the first to get their money out before it disappears. This is a bank run, and it’s basically what happened to SVB.

The FDIC was originally created to prevent or mitigate bank runs. Not only did they provide insurance that reduced the damage in the event of a bank failure; by assuring depositors that their money would be recovered even if the bank failed, they also reduced the chances of a bank run becoming a self-fulfilling prophecy.

Indeed, SVB is the exception that proves the rule, as they failed largely because their assets were mainly not FDIC insured.

Fractional-reserve banking effectively allows banks to create money, in the form of credit that they offer to borrowers. That credit gets deposited in other banks, which then go on to loan it out to still others; the result is that there is more money in the system than was ever actually printed by the central bank.

In most economies this commercial bank money is a far larger quantity than the central bank money actually printed by the central bank—often nearly 10 to 1. This ratio is called the money multiplier.

Indeed, it’s not a coincidence that the reserve ratio is 10% and the multiplier is 10; the theoretical maximum multiplier is always the inverse of the reserve ratio, so if you require reserves of 10%, the highest multiplier you can get is 10. Had we required 20% reserves, the multiplier would drop to 5.

Most countries have fractional-reserve banking, and have for centuries; but it’s actually a pretty weird system if you think about it.

Back when we were on the gold standard, fractional-reserve banking was a way of cheating, getting our money supply to be larger than the supply of gold would actually allow.

But now that we are on a pure fiat money system, it’s worth asking what fractional-reserve banking actually accomplishes. If we need more money, the central bank could just print more. Why do we delegate that task to commercial banks?

David Friedman of the Cato Institute had some especially harsh words on this, but honestly I find them hard to disagree with:

Before leaving the subject of fractional reserve systems, I should mention one particularly bizarre variant — a fractional reserve system based on fiat money. I call it bizarre because the essential function of a fractional reserve system is to reduce the resource cost of producing money, by allowing an ounce of reserves to replace, say, five ounces of currency. The resource cost of producing fiat money is zero; more precisely, it costs no more to print a five-dollar bill than a one-dollar bill, so the cost of having a larger number of dollars in circulation is zero. The cost of having more bills in circulation is not zero but small. A fractional reserve system based on fiat money thus economizes on the cost of producing something that costs nothing to produce; it adds the disadvantages of a fractional reserve system to the disadvantages of a fiat system without adding any corresponding advantages. It makes sense only as a discreet way of transferring some of the income that the government receives from producing money to the banking system, and is worth mentioning at all only because it is the system presently in use in this country.

Our banking system evolved gradually over time, and seems to have held onto many features that made more sense in an earlier era. Back when we had arbitrarily tied our central bank money supply to gold, creating a new money supply that was larger may have been a reasonable solution. But today, it just seems to be handing the reins over to private corporations, giving them more profits while forcing the rest of society to bear more risk.

The obvious alternative is full-reserve banking, where banks are simply required to hold 100% of their deposits in reserve and the multiplier drops to 1. This idea has been supported by a number of quite prominent economists, including Milton Friedman.

It’s not just a right-wing idea: The left-wing organization Positive Money is dedicated to advocating for a full-reserve banking system in the UK and EU. (The ECB VP’s criticism of the proposal is utterly baffling to me: it “would not create enough funding for investment and growth.” Um, you do know you can print more money, right? Hm, come to think of it, maybe the ECB doesn’t know that, because they think inflation is literally Hitler. There are legitimate criticisms to be had of Positive Money’s proposal, but “There won’t be enough money under this fiat money system” is a really weird take.)

There’s a relatively simple way to gradually transition from our current system to a full-reserve sytem: Simply increase the reserve ratio over time, and print more central bank money to keep the total money supply constant. If we find that it seems to be causing more problems than it solves, we could stop or reverse the trend.

Krugman has pointed out that this wouldn’t really fix the problems in the banking system, which actually seem to be much worse in the shadow banking sector than in conventional commercial banking. This is clearly right, but it isn’t really an argument against trying to improve conventional banking. I guess if stricter regulations on conventional banking push more money into the shadow banking system, that’s bad; but really that just means we should be imposing stricter regulations on the shadow banking system first (or simultaneously).

We don’t need to accept bank runs as a routine part of the financial system. There are other ways of doing things.

# Optimization is unstable. Maybe that’s why we satisfice.

Feb 26 JDN 2460002

Imagine you have become stranded on a deserted island. You need to find shelter, food, and water, and then perhaps you can start working on a way to get help or escape the island.

Suppose you are programmed to be an optimizerto get the absolute best solution to any problem. At first this may seem to be a boon: You’ll build the best shelter, find the best food, get the best water, find the best way off the island.

But you’ll also expend an enormous amount of effort trying to make it the best. You could spend hours just trying to decide what the best possible shelter would be. You could pass up dozens of viable food sources because you aren’t sure that any of them are the best. And you’ll never get any rest because you’re constantly trying to improve everything.

In principle your optimization could include that: The cost of thinking too hard or searching too long could be one of the things you are optimizing over. But in practice, this sort of bounded optimization is often remarkably intractable.

And what if you forgot about something? You were so busy optimizing your shelter you forgot to treat your wounds. You were so busy seeking out the perfect food source that you didn’t realize you’d been bitten by a venomous snake.

This is not the way to survive. You don’t want to be an optimizer.

No, the person who survives is a satisficerthey make sure that what they have is good enough and then they move on to the next thing. Their shelter is lopsided and ugly. Their food is tasteless and bland. Their water is hard. But they have them.

Once they have shelter and food and water, they will have time and energy to do other things. They will notice the snakebite. They will treat the wound. Once all their needs are met, they will get enough rest.

Empirically, humans are satisficers. We seem to be happier because of it—in fact, the people who are the happiest satisfice the most. And really this shouldn’t be so surprising: Because our ancestral environment wasn’t so different from being stranded on a desert island.

Good enough is perfect. Perfect is bad.

Let’s consider another example. Suppose that you have created a powerful artificial intelligence, an AGI with the capacity to surpass human reasoning. (It hasn’t happened yet—but it probably will someday, and maybe sooner than most people think.)

What do you want that AI’s goals to be?

Okay, ideally maybe they would be something like “Maximize goodness”, where we actually somehow include all the panoply of different factors that go into goodness, like beneficence, harm, fairness, justice, kindness, honesty, and autonomy. Do you have any idea how to do that? Do you even know what your own full moral framework looks like at that level of detail?

Far more likely, the goals you program into the AGI will be much simpler than that. You’ll have something you want it to accomplish, and you’ll tell it to do that well.

Let’s make this concrete and say that you own a paperclip company. You want to make more profits by selling paperclips.

First of all, let me note that this is not an unreasonable thing for you to want. It is not an inherently evil goal for one to have. The world needs paperclips, and it’s perfectly reasonable for you to want to make a profit selling them.

But it’s also not a true ultimate goal: There are a lot of other things that matter in life besides profits and paperclips. Anyone who isn’t a complete psychopath will realize that.

But the AI won’t. Not unless you tell it to. And so if we tell it to optimize, we would need to actually include in its optimization all of the things we genuinely care about—not missing a single one—or else whatever choices it makes are probably not going to be the ones we want. Oops, we forgot to say we need clean air, and now we’re all suffocating. Oops, we forgot to say that puppies don’t like to be melted down into plastic.

The simplest cases to consider are obviously horrific: Tell it to maximize the number of paperclips produced, and it starts tearing the world apart to convert everything to paperclips. (This is the original “paperclipper” concept from Less Wrong.) Tell it to maximize the amount of money you make, and it seizes control of all the world’s central banks and starts printing $9 quintillion for itself. (Why that amount? I’m assuming it uses 64-bit signed integers, and 2^63 is over 9 quintillion. If it uses long ints, we’re even more doomed.) No, inflation-adjusting won’t fix that; even hyperinflation typically still results in more real seigniorage for the central banks doing the printing (which is, you know, why they do it). The AI won’t ever be able to own more than all the world’s real GDP—but it will be able to own that if it prints enough and we can’t stop it. But even if we try to come up with some more sophisticated optimization for it to perform (what I’m really talking about here is specifying its utility function), it becomes vital for us to include everything we genuinely care about: Anything we forget to include will be treated as a resource to be consumed in the service of maximizing everything else. Consider instead what would happen if we programmed the AI to satisfice. The goal would be something like, “Produce at least 400,000 paperclips at a price of at most$0.002 per paperclip.”

Given such an instruction, in all likelihood, it would in fact produce exactly 400,000 paperclips at a price of exactly $0.002 per paperclip. And maybe that’s not strictly the best outcome for your company. But if it’s better than what you were previously doing, it will still increase your profits. Moreover, such an instruction is far less likely to result in the end of the world. If the AI has a particular target to meet for its production quota and price limit, the first thing it would probably try is to use your existing machinery. If that’s not good enough, it might start trying to modify the machinery, or acquire new machines, or develop its own techniques for making paperclips. But there are quite strict limits on how creative it is likely to be—because there are quite strict limits on how creative it needs to be. If you were previously producing 200,000 paperclips at$0.004 per paperclip, all it needs to do is double production and halve the cost. That’s a very standard sort of industrial innovation— in computing hardware (admittedly an extreme case), we do this sort of thing every couple of years.

It certainly won’t tear the world apart making paperclips—at most it’ll tear apart enough of the world to make 400,000 paperclips, which is a pretty small chunk of the world, because paperclips aren’t that big. A paperclip weighs about a gram, so you’ve only destroyed about 400 kilos of stuff. (You might even survive the lawsuits!)

Are you leaving money on the table relative to the optimization scenario? Eh, maybe. One, it’s a small price to pay for not ending the world. But two, if 400,000 at $0.002 was too easy, next time try 600,000 at$0.001. Over time, you can gently increase its quotas and tighten its price requirements until your company becomes more and more successful—all without risking the AI going completely rogue and doing something insane and destructive.

Of course this is no guarantee of safety—and I absolutely want us to use every safeguard we possibly can when it comes to advanced AGI. But the simple change from optimizing to satisficing seems to solve the most severe problems immediately and reliably, at very little cost.

Good enough is perfect; perfect is bad.

I see broader implications here for behavioral economics. When all of our models are based on optimization, but human beings overwhelmingly seem to satisfice, maybe it’s time to stop assuming that the models are right and the humans are wrong.

Optimization is perfect if it works—and awful if it doesn’t. Satisficing is always pretty good. Optimization is unstable, while satisficing is robust.

In the real world, that probably means that satisficing is better.

Good enough is perfect; perfect is bad.

# Where is the money going in academia?

Feb 19 JDN 2459995

A quandary for you:

My salary is £41,000.

Annual tuition for a full-time full-fee student in my department is £23,000.

I teach roughly the equivalent of one full-time course (about 1/2 of one and 1/4 of two others; this is typically counted as “teaching 3 courses”, but if I used that figure, it would underestimate the number of faculty needed).

Each student takes about 5 or 6 courses at a time.

Why do I have 200 students?

If you multiply this out, the 200 students I teach, divided by the 6 instructors they have at one time, times the £23,000 they are paying… I should be bringing in over £760,000 for the university. Why am I paid only 5% of that?

Granted, there are other costs a university must bear aside from paying instructors. There are facilities, and administration, and services. And most of my students are not full-fee paying; that £23,000 figure really only applies to international students.

Students from Scotland pay only £1,820, but there aren’t very many of them, and public funding is supposed to make up that difference. Even students from the rest of the UK pay £9,250. And surely the average tuition paid has got to be close to that? Yet if we multiply that out, £9,000 times 200 divided by 6, we’re still looking at £300,000. So I’m still getting only 14%.

Where is the rest going?

This isn’t specific to my university by any means. It seems to be a global phenomenon. The best data on this seems to be from the US.

According to salary.com, the median salary for an adjunct professor in the US is about $63,000. This actually sounds high, given what I’ve heard from other entry-level faculty. But okay, let’s take that as our figure. (My pay is below this average, though how much depends upon the strength of the pound against the dollar. Currently the pound is weak, so quite a bit.) This means that an adjunct professor in the US with 200 students takes in$760,000 but receives $63,000. Where does that other$700,000 go?

If you think that it’s just a matter of paying for buildings, service staff, and other costs of running a university, consider this: It wasn’t always this way.

Since 1970, inflation-adjusted salaries for US academic faculty at public universities have risen a paltry 3.1%. In other words, basically not at all.

This is considerably slower than the growth of real median household income, which has risen almost 40% in that same time.

Over the same interval, nominal tuition has risen by over 2000%; adjusted for inflation, this is a still-staggering increase of 250%.

In other words, over the last 50 years, college has gotten three times as expensive, but faculty are still paid basically the same. Where is all this extra money going?

Part of the explanation is that public funding for colleges has fallen over time, and higher tuition partly makes up the difference. But private school tuition has risen just as fast, and their faculty salaries haven’t kept up either.

In their annual budget report, the University of Edinburgh proudly declares that their income increased by 9% last year. Let me assure you, my salary did not. (In fact, inflation-adjusted, my salary went down.) And their EBITDA—earnings before interest, taxes, depreciation, and amortization—was £168 million. Of that, £92 million was lost to interest and depreciation, but they don’t pay taxes at all, so their real net income was about £76 million. In the report, they include price changes of their endowment and pension funds to try to make this number look smaller, ending up with only £37 million, but that’s basically fiction; these are just stock market price drops, and they will bounce back.

Using similar financial alchemy, they’ve been trying to cut our pensions lately, because they say they “are too expensive” (because the stock market went down—nevermind that it’ll bounce back in a year or two). Fortunately, the unions are fighting this pretty hard. I wish they’d also fight harder to make them put people like me on the tenure track.

Had that £76 million been distributed evenly between all 5,000 of us faculty, we’d each get an extra £15,600.

Well, then, that solves part of the mystery in perhaps the most obvious, corrupt way possible: They’re literally just hoarding it.

And Edinburgh is far from the worst offender here. No, that would be Harvard, who are sitting on over $50 billion in assets. Since they have 21,000 students, that is over$2 million per student. With even a moderate return on its endowment, Harvard wouldn’t need to charge tuition at all.

But even then, raising my salary to £56,000 wouldn’t explain why I need to teach 200 students. Even that is still only 19% of the £300,000 those students are bringing in. But hey, then at least the primary service for which those students are here for might actually account for one-fifth of what they’re paying!

Now let’s considers administrators. Median salary for a university administrator in the US is about $138,000—twice what adjunct professors make. Since 1970, that same time interval when faculty salaries were rising a pitiful 3% and tuition was rising a staggering 250%, how much did chancellors’ salaries increase? Over 60%. Of course, the number of administrators is not fixed. You might imagine that with technology allowing us to automate a lot of administrative tasks, the number of administrators could be reduced over time. If that’s what you thought happened, you would be very, very wrong. The number of university administrators in the US has more than doubled since the 1980s. This is far faster growth than the number of students—and quite frankly, why should the number of administrators even grow with the number of students? There is a clear economy of scale here, yet it doesn’t seem to matter. Combine those two facts: 60% higher pay times twice as many administrators means that universities now spend at least 3 times as much on administration as they did 50 years ago. (Why, that’s just about the proportional increase in tuition! Coincidence? I think not.) Edinburgh isn’t even so bad in this regard. They have 6,000 administrative staff versus 5,000 faculty. If that already sounds crazy—more admins than instructors?—consider that the University of Michigan has 7,000 faculty but 19,000 administrators. Michigan is hardly exceptional in this regard: Illinois UC has 2,500 faculty but nearly 8,000 administrators, while Ohio State has 7,300 faculty and 27,000 administrators. UCLA is even worse, with only 4,000 faculty but 26,000 administrators—a ratio of 6 to 1. It’s not the UC system in general, though: My (other?) alma mater of UC Irvine somehow supports 5,600 faculty with only 6,400 administrators. Yes, that’s right; compared to UCLA, UCI has 40% more faculty but 76% fewer administrators. (As far as students? UCLA has 47,000 while UCI has 36,000.) At last, I think we’ve solved the mystery! Where is all the money in academia going? Administrators. They keep hiring more and more of them, and paying them higher and higher salaries. Meanwhile, they stop hiring tenure-track faculty and replace them with adjuncts that they can get away with paying less. And then, whatever they manage to save that way, they just squirrel away into the endowment. A common right-wing talking point is that more institutions should be “run like a business”. Well, universities seem to have taken that to heart. Overpay your managers, underpay your actual workers, and pocket the savings. # Good enough is perfect, perfect is bad Jan 8 JDN 2459953 Not too long ago, I read the book How to Keep House While Drowning by KC Davis, which I highly recommend. It offers a great deal of useful and practical advice, especially for someone neurodivergent and depressed living through an interminable pandemic (which I am, but honestly, odds are, you may be too). And to say it is a quick and easy read is actually an unfair understatement; it is explicitly designed to be readable in short bursts by people with ADHD, and it has a level of accessibility that most other books don’t even aspire to and I honestly hadn’t realized was possible. (The extreme contrast between this and academic papers is particularly apparent to me.) One piece of advice that really stuck with me was this: Good enough is perfect. At first, it sounded like nonsense; no, perfect is perfect, good enough is just good enough. But in fact there is a deep sense in which it is absolutely true. Indeed, let me make it a bit stronger: Good enough is perfect; perfect is bad. I doubt Davis thought of it in these terms, but this is a concise, elegant statement of the principles of bounded rationality. Sometimes it can be optimal not to optimize. Suppose that you are trying to optimize something, but you have limited computational resources in which to do so. This is actually not a lot for you to suppose—it’s literally true of basically everyone basically every moment of every day. But let’s make it a bit more concrete, and say that you need to find the solution to the following math problem: “What is the product of 2419 times 1137?” (Pretend you don’t have a calculator, as it would trivialize the exercise. I thought about using a problem you couldn’t do with a standard calculator, but I realized that would also make it much weirder and more obscure for my readers.) Now, suppose that there are some quick, simple ways to get reasonably close to the correct answer, and some slow, difficult ways to actually get the answer precisely. In this particular problem, the former is to approximate: What’s 2500 times 1000? 2,500,000. So it’s probably about 2,500,000. Or we could approximate a bit more closely: Say 2400 times 1100, that’s about 100 times 100 times 24 times 11, which is 2 times 12 times 11 (times 10,000), which is 2 times (110 plus 22), which is 2 times 132 (times 10,000), which is 2,640,000. Or, we could actually go through all the steps to do the full multiplication (remember I’m assuming you have no calculator), multiply, carry the 1s, add all four sums, re-check everything and probably fix it because you messed up somewhere; and then eventually you will get: 2,750,403. So, our really fast method was only off by about 10%. Our moderately-fast method was only off by 4%. And both of them were a lot faster than getting the exact answer by hand. Which of these methods you’d actually want to use depends on the context and the tools at hand. If you had a calculator, sure, get the exact answer. Even if you didn’t, but you were balancing the budget for a corporation, I’m pretty sure they’d care about that extra$110,403. (Then again, they might not care about the $403 or at least the$3.) But just as an intellectual exercise, you really didn’t need to do anything; the optimal choice may have been to take my word for it. Or, if you were at all curious, you might be better off choosing the quick approximation rather than the precise answer. Since nothing of any real significance hinged on getting that answer, it may be simply a waste of your time to bother finding it.

This is of course a contrived example. But it’s not so far from many choices we make in real life.

Yes, if you are making a big choice—which job to take, what city to move to, whether to get married, which car or house to buy—you should get a precise answer. In fact, I make spreadsheets with formal utility calculations whenever I make a big choice, and I haven’t regretted it yet. (Did I really make a spreadsheet for getting married? You’re damn right I did; there were a lot of big financial decisions to make there—taxes, insurance, the wedding itself! I didn’t decide whom to marry that way, of course; but we always had the option of staying unmarried.)

But most of the choices we make from day to day are small choices: What should I have for lunch today? Should I vacuum the carpet now? What time should I go to bed? In the aggregate they may all add up to important things—but each one of them really won’t matter that much. If you were to construct a formal model to optimize your decision of everything to do each day, you’d spend your whole day doing nothing but constructing formal models. Perfect is bad.

In fact, even for big decisions, you can’t really get a perfect answer. There are just too many unknowns. Sometimes you can spend more effort gathering additional information—but that’s costly too, and sometimes the information you would most want simply isn’t available. (You can look up the weather in a city, visit it, ask people about it—but you can’t really know what it’s like to live there until you do.) Even those spreadsheet models I use to make big decisions contain error bars and robustness checks, and if, even after investing a lot of effort trying to get precise results, I still find two or more choices just can’t be clearly distinguished to within a good margin of error, I go with my gut. And that seems to have been the best choice for me to make. Good enough is perfect.

I think that being gifted as a child trained me to be dangerously perfectionist as an adult. (Many of you may find this familiar.) When it came to solving math problems, or answering quizzes, perfection really was an attainable goal a lot of the time.

As I got older and progressed further in my education, maybe getting every answer right was no longer feasible; but I still could get the best possible grade, and did, in most of my undergraduate classes and all of my graduate classes. To be clear, I’m not trying to brag here; if anything, I’m a little embarrassed. What it mainly shows is that I had learned the wrong priorities. In fact, one of the main reasons why I didn’t get a 4.0 average in undergrad is that I spent a lot more time back then writing novels and nonfiction books, which to this day I still consider my most important accomplishments and grieve that I’ve not (yet?) been able to get them commercially published. I did my best work when I wasn’t trying to be perfect. Good enough is perfect; perfect is bad.

Now here I am on the other side of the academic system, trying to carve out a career, and suddenly, there is no perfection. When my exam is being graded by someone else, there is a way to get the most points. When I’m the one grading the exams, there is no “correct answer” anymore. There is no one scoring me to see if I did the grading the “right way”—and so, no way to be sure I did it right.

Actually, here at Edinburgh, there are other instructors who moderate grades and often require me to revise them, which feels a bit like “getting it wrong”; but it’s really more like we had different ideas of what the grade curve should look like (not to mention US versus UK grading norms). There is no longer an objectively correct answer the way there is for, say, the derivative of x^3, the capital of France, or the definition of comparative advantage. (Or, one question I got wrong on an undergrad exam because I had zoned out of that lecture to write a book on my laptop: Whether cocaine is a dopamine reuptake inhibitor. It is. And the fact that I still remember that because I got it wrong over a decade ago tells you a lot about me.)

And then when it comes to research, it’s even worse: What even constitutes “good” research, let alone “perfect” research? What would be most scientifically rigorous isn’t what journals would be most likely to publish—and without much bigger grants, I can afford neither. I find myself longing for the research paper that will be so spectacular that top journals have to publish it, removing all risk of rejection and failure—in other words, perfect.

Yet such a paper plainly does not exist. Even if I were to do something that would win me a Nobel or a Fields Medal (this is, shall we say, unlikely), it probably wouldn’t be recognized as such immediately—a typical Nobel isn’t awarded until 20 or 30 years after the work that spawned it, and while Fields Medals are faster, they’re by no means instant or guaranteed. In fact, a lot of ground-breaking, paradigm-shifting research was originally relegated to minor journals because the top journals considered it too radical to publish.

Or I could try to do something trendy—feed into DSGE or GTFO—and try to get published that way. But I know my heart wouldn’t be in it, and so I’d be miserable the whole time. In fact, because it is neither my passion nor my expertise, I probably wouldn’t even do as good a job as someone who really buys into the core assumptions. I already have trouble speaking frequentist sometimes: Are we allowed to say “almost significant” for p = 0.06? Maximizing the likelihood is still kosher, right? Just so long as I don’t impose a prior? But speaking DSGE fluently and sincerely? I’d have an easier time speaking in Latin.

What I know—on some level at least—I ought to be doing is finding the research that I think is most worthwhile, given the resources I have available, and then getting it published wherever I can. Or, in fact, I should probably constrain a little by what I know about journals: I should do the most worthwhile research that is feasible for me and has a serious chance of getting published in a peer-reviewed journal. It’s sad that those two things aren’t the same, but they clearly aren’t. This constraint binds, and its Lagrange multiplier is measured in humanity’s future.

But one thing is very clear: By trying to find the perfect paper, I have floundered and, for the last year and a half, not written any papers at all. The right choice would surely have been to write something.

Because good enough is perfect, and perfect is bad.

# Inequality-adjusted GDP and median income

Dec 11 JDN 2459925

There are many problems with GDP as a measure of a nation’s prosperity. For one, GDP ignores natural resources and ecological degradation; so a tree is only counted in GDP once it is cut down. For another, it doesn’t value unpaid work, so caring for a child only increases GDP if you are a paid nanny rather than the child’s parents.

But one of the most obvious problems is the use of an average to evaluate overall prosperity, without considering the level of inequality.

Consider two countries. In Alphania, everyone has an income of about $50,000. In Betavia, 99% of people have an income of$1,000 and 1% have an income of $10 million. What is the per-capita GDP of each country? Alphania’s is$50,000 of course; but Betavia’s is $100,990. Does it really make sense to say that Betavia is a more prosperous country? Maybe it has more wealth overall, but its huge inequality means that it is really not at a high level of development. It honestly sounds like an awful place to live. A much more sensible measure would be something like median income: How much does a typical person have? In Alphania this is still$50,000; but in Betavia it is only $1,000. Yet even this leaves out most of the actual distribution; by definition a median is only determined by what is the 50th percentile. We could vary all other incomes a great deal without changing the median. A better measure would be some sort of inequality-adjusted per-capita GDP, which rescales GDP based on the level of inequality in a country. But we would need a good way of making that adjustment. I contend that the most sensible way would be to adopt some kind of model of marginal utility of income, and then figure out what income would correspond to the overall average level of utility. In other words, average over the level of happiness that people in a country get from their income, and then figure out what level of income would correspond to that level of happiness. If we magically gave everyone the same amount of money, how much would they need to get in order for the average happiness in the country to remain the same? This is clearly going to be less than the average level of income, because marginal utility of income is decreasing; a dollar is not worth as much in real terms to a rich person as it is to a poor person. So if we could somehow redistribute all income evenly while keeping the average the same, that would actually increase overall happiness (though, for many reasons, we can’t simply do that). For example, suppose that utility of income is logarithmic: U = ln(I). This means that the marginal utility of an additional dollar is inversely proportional to how many dollars you already have: U'(I) = 1/I. It also means that a 1% gain or loss in your income feels about the same regardless of how much income you have: ln((1+r)Y) = ln(Y) + ln(1+r). This seems like a quite reasonable, maybe even a bit conservative, assumption; I suspect that losing 1% of your income actually hurts more when you are poor than when you are rich. Then the inequality adjusted GDP Y is a value such that ln(Y) is equal to the overall average level of utility: E[U] = ln(Y), so Y = exp(E[U]). This sounds like a very difficult thing to calculate. But fortunately, the distribution of actual income seems to quite closely follow a log-normal distribution. This means that when we take the logarithm of income to get utility, we just get back a very nice, convenient normal distribution! In fact, it turns out that for a log-normal distribution, the following holds: exp(E[ln(Y)]) = median(Y) The income which corresponds to the average utility turns out to simply be the median income! We went looking for a better measure than median income, and ended up finding out that median income was the right measure all along. This wouldn’t hold for most other distributions; and since real-world economies don’t perfectly follow a log-normal distribution, a more precise estimate would need to be adjusted accordingly. But the approximation is quite good for most countries we have good data on, so even for the ones we don’t, median income is likely a very good estimate. The ranking of countries by median income isn’t radically different from the ranking by per-capita GDP; rich countries are still rich and poor countries are still poor. But it is different enough to matter. Luxembourg is in 1st place on both lists. Scandinavian countries and the US are in the top 10 in both cases. So it’s fair to say that #ScandinaviaIsBetter for real, and the US really is so rich that our higher inequality doesn’t make our median income lower than the rest of the First World. But some countries are quite different. Ireland looks quite good in per-capita GDP, but quite bad in median income. This is because a lot of the GDP in Ireland is actually profits by corporations that are only nominally headquartered in Ireland and don’t actually employ very many people there. The comparison between the US, the UK, and Canada seems particularly instructive. If you look at per-capita GDP PPP, the US looks much richer at$75,000 compared to Canada’s $57,800 (a difference of 29% or 26 log points). But if you look at median personal income, they are nearly equal:$19,300 in the US and $18,600 in Canada (3.7% or 3.7 log points). On the other hand, in per-capita GDP PPP, the UK looks close to Canada at$55,800 (3.6% or 3.6 lp); but in median income it is dramatically worse, at only \$14,800 (26% or 23 lp). So Canada and the UK have similar overall levels of wealth, but life for a typical Canadian is much better than life for a typical Briton because of the higher inequality in Britain. And the US has more wealth than Canada, but it doesn’t meaningfully improve the lifestyle of a typical American relative to a typical Canadian.