uncertainty

The radical uncertainty of life

pnrj core principles, financial advice, futurism , , ,

Jul 31 JDN 2459792

It’s a question you get a lot in job interviews, and sometimes from elsewhere as well: “Where do you see yourself in ten years?”

I never quite know how to answer such a question, because the future is so full of uncertainty.

Ten years from now:

I could be a tenured professor, or have left academia entirely. I could be teaching here at Edinburgh, or at an even more prestigious university, or at a tiny, obscure school. I could be working in private industry, or unemployed. I could be working as a full-time freelance writer.

I could have published nothing new, or have published a few things, or have won a Fields Medal. (It’s especially unlikely to have won a Nobel by then, but it’s a bit less unlikely that I might have done work that would one day lead to one.)

I could be still living in the United Kingdom, or back in the United States, or in some other country entirely.

I could be healthier than I am now, or permanently disabled. I could even be dead, from a variety of diseases, or a car accident, or a gunshot wound.

I could have adopted three children, or none. I could be divorced. My spouse could be dead.

It could even all be moot because the Russian war in Ukraine—or some other act of Russian aggression—has escalated into a nuclear Third World War.

These are the relatively likely scenarios.

I’m not saying I’m going to win a Fields Medal—but I am the sort of person who wins Fields Medals, surely far more likely than any randomly selected individual. I’m not saying we’re going to have WW3, but we’re definitely closer to it than we’ve been since the end of the Cold War.

There are plenty of other, unlikely scenarios that still remain possible:

I could be working in finance, or engineering, or medicine. I could be living on a farm. I could be President of the United States. I could have won a multi-million-dollar lottery and retired to a life of luxury and philanthropy. Those seem rather unlikely for me personally—but they are all true of someone, somewhere.

I could be living on a space station, or a Lunar base. I could be cybernetically enhanced. 2032 seems early for such things—but it didn’t to folks writing in the 1980s, so who knows? (Maybe it will even happen so gradually we won’t notice: Is a glucose-monitoring implant a cybernetic enhancement? It doesn’t seem so unlikely I might one day have one of those.)

None of us really knows what the future is going to hold. We could say what we want, or what we expect is the most likely, but more often than not, the world will surprise us.

What does this mean for our lives now? Should we give up trying to make plans, since the future is so unpredictable? Should we “eat, drink, and be merry, for tomorrow we die”?

I think the key is to realize that there is a kind of planning that’s still useful even if you can’t predict what will happen—and that is to plan to be flexible and resilient.

You can keep your eyes open for opportunities, rather than trying too hard to hold onto what you already have. Rather than trying in vain to keep everything the same, you can accept that your life is going to change and try to direct that change in better directions.

Rather than planning on staying in the same career for your whole life—which hardly anyone in our generation does—you should expect to change careers, and be working on building a wide range of transferable skills and a broad network of friends and colleagues. Maybe sooner or later you’ll find the right place to settle down, but it could be awhile.

You may not know where you’ll be living or working in ten years, but odds are pretty good that it’ll still be useful for you to have some money saved up, so you should probably save some money. If we end up in a post-scarcity utopia, you won’t need it, but you also won’t care. If we end up in a post-apocalyptic hellscape, it really won’t matter one way or the other. And those two extremes are about what would need to happen for you not to be able to make use of savings.

And where should you put that saved money? Stocks, bonds, cryptocurrency? Well, crypto would give you a chance at spectacular gains—but a much larger chance of spectacular losses. Bonds are very safe, but also don’t grow very much. So, as I’ve said before, you probably want to buy stocks. Yes, you could end up better off by choosing something else; but you have to play the odds, and stocks give you the best odds.

You will have setbacks at some point, either small or large. Everyone does. You can’t plan for what they will be, but you can plan to have resources available to deal with them.

Hey, maybe you should even buy life insurance, just in case you really do die tomorrow. You probably won’t—but somebody will, and doesn’t know it yet.

Fake skepticism

pnrj cognitive science, heuristics and biases , , , , , , , , ,

Jun 3 JDN 2458273

“You trust the mainstream media?” “Wake up, sheeple!” “Don’t listen to what so-called scientists say; do your own research!”

These kinds of statements have become quite ubiquitous lately (though perhaps the attitudes were always there, and we only began to hear them because of the Internet and social media), and are often used to defend the most extreme and bizarre conspiracy theories, from moon-landing denial to flat Earth. The amazing thing about these kinds of statements is that they can be used to defend literally anything, as long as you can find some source with less than 100% credibility that disagrees with it. (And what source has 100% credibility?)

And that, I think, should tell you something. An argument that can prove anything is an argument that proves nothing.

Reversed stupidity is not intelligence. The fact that the mainstream media, or the government, or the pharmaceutical industry, or the oil industry, or even gangsters, fanatics, or terrorists believes something does not make it less likely to be true.

In fact, the vast majority of beliefs held by basically everyone—including the most fanatical extremists—are true. I could list such consensus true beliefs for hours: “The sky is blue.” “2+2=4.” “Ice is colder than fire.”

Even if a belief is characteristic of a specifically evil or corrupt organization, that does not necessarily make it false (though it usually is evidence of falsehood in a Bayesian sense). If only terrible people belief X, then maybe you shouldn’t believe X. But if both good and bad people believe X, the fact that bad people believe X really shouldn’t matter to you.

People who use this kind of argument often present themselves as being “skeptics”. They imagine that they have seen through the veil of deception that blinds others.

In fact, quite the opposite is the case: This is fake skepticism. These people are not uniquely skeptical; they are uniquely credulous. If you think the Earth is flat because you don’t trust the mainstream scientific community, that means you do trust someone far less credible than the mainstream scientific community.

Real skepticism is difficult. It requires concerted effort and investigation, and typically takes years. To really seriously challenge the expert consensus in a field, you need to become an expert in that field. Ideally, you should get a graduate degree in that field and actually start publishing your heterodox views. Failing that, you should at least be spending hundreds or thousands of hours doing independent research. If you are unwilling or unable to do that, you are not qualified to assess the validity of the expert consensus.

This does not mean the expert consensus is always right—remarkably often, it isn’t. But it means you aren’t allowed to say it’s wrong, because you don’t know enough to assess that.

This is not elitism. This is not an argument from authority. This is a basic respect for the effort and knowledge that experts spend their lives acquiring.

People don’t like being told that they are not as smart as other people—even though, with any variation at all, that’s got to be true for a certain proportion of people. But I’m not even saying experts are smarter than you. I’m saying they know more about their particular field of expertise.

Do you walk up to construction workers on the street and critique how they lay concrete? When you step on an airplane, do you explain to the captain how to read an altimeter? When you hire a plumber, do you insist on using the snake yourself?

Probably not. And why not? Because you know these people have training; they do this for a living. Yeah, well, scientists do this for a living too—and our training is much longer. To be a plumber, you need a high school diploma and an apprenticeship that usually lasts about four years. To be a scientist, you need a PhD, which means four years of college plus an additional five or six years of graduate school.

To be clear, I’m not saying you should listen to experts speaking outside their expertise. Some of the most idiotic, arrogant things ever said by human beings have been said by physicists opining on biology or economists ranting about politics. Even within a field, some people have such narrow expertise that you can’t really trust them even on things that seem related—like macroeconomists with idiotic views on trade, or ecologists who clearly don’t understand evolution.

This is also why one of the great challenges of being a good interdisciplinary scientist is actually obtaining enough expertise in both fields you’re working in; it isn’t literally twice the work (since there is overlap—or you wouldn’t be doing it—and you do specialize in particular interdisciplinary subfields), but it’s definitely more work, and there are definitely a lot of people on each side of the fence who may never take you seriously no matter what you do.

How do you tell who to trust? This is why I keep coming back to the matter of expert consensus. The world is much too complicated for anyone, much less everyone, to understand it all. We must be willing to trust the work of others. The best way we have found to decide which work is trustworthy is by the norms and institutions of the scientific community itself. Since 97% of climatologists say that climate change is caused by humans, they’re probably right. Since 99% of biologists believe humans evolved by natural selection, that’s probably what happened. Since 87% of economists oppose tariffs, tariffs probably aren’t a good idea.

Can we be certain that the consensus is right? No. There is precious little in this universe that we can be certain about. But as in any game of chance, you need to play the best odds, and my money will always be on the scientific consensus.

Why are humans so bad with probability?

pnrj cognitive science, critique of neoclassical economics, statistics , , , , , , , , , , , ,

Apr 29 JDN 2458238

In previous posts on deviations from expected utility and cumulative prospect theory, I’ve detailed some of the myriad ways in which human beings deviate from optimal rational behavior when it comes to probability.

This post is going to be a bit different: Yes, we behave irrationally when it comes to probability. Why?

Why aren’t we optimal expected utility maximizers?
This question is not as simple as it sounds. Some of the ways that human beings deviate from neoclassical behavior are simply because neoclassical theory requires levels of knowledge and intelligence far beyond what human beings are capable of; basically anything requiring “perfect information” qualifies, as does any game theory prediction that involves solving extensive-form games with infinite strategy spaces by backward induction. (Don’t feel bad if you have no idea what that means; that’s kind of my point. Solving infinite extensive-form games by backward induction is an unsolved problem in game theory; just this past week I saw a new paper presented that offered a partial potential solution—and yet we expect people to do it optimally every time?)

I’m also not going to include questions of fundamental uncertainty, like “Will Apple stock rise or fall tomorrow?” or “Will the US go to war with North Korea in the next ten years?” where it isn’t even clear how we would assign a probability. (Though I will get back to them, for reasons that will become clear.)

No, let’s just look at the absolute simplest cases, where the probabilities are all well-defined and completely transparent: Lotteries and casino games. Why are we so bad at that?

Lotteries are not a computationally complex problem. You figure out how much the prize is worth to you, multiply it by the probability of winning—which is clearly spelled out for you—and compare that to how much the ticket price is worth to you. The most challenging part lies in specifying your marginal utility of wealth—the “how much it’s worth to you” part—but that’s something you basically had to do anyway, to make any kind of trade-offs on how to spend your time and money. Maybe you didn’t need to compute it quite so precisely over that particular range of parameters, but you need at least some idea how much $1 versus $10,000 is worth to you in order to get by in a market economy.

Casino games are a bit more complicated, but not much, and most of the work has been done for you; you can look on the Internet and find tables of probability calculations for poker, blackjack, roulette, craps and more. Memorizing all those probabilities might take some doing, but human memory is astonishingly capacious, and part of being an expert card player, especially in blackjack, seems to involve memorizing a lot of those probabilities.

Furthermore, by any plausible expected utility calculation, lotteries and casino games are a bad deal. Unless you’re an expert poker player or blackjack card-counter, your expected income from playing at a casino is always negative—and the casino set it up that way on purpose.

Why, then, can lotteries and casinos stay in business? Why are we so bad at such a simple problem?

Clearly we are using some sort of heuristic judgment in order to save computing power, and the people who make lotteries and casinos have designed formal models that can exploit those heuristics to pump money from us. (Shame on them, really; I don’t fully understand why this sort of thing is legal.)

In another previous post I proposed what I call “categorical prospect theory”, which I think is a decently accurate description of the heuristics people use when assessing probability (though I’ve not yet had the chance to test it experimentally).

But why use this particular heuristic? Indeed, why use a heuristic at all for such a simple problem?

I think it’s helpful to keep in mind that these simple problems are weird; they are absolutely not the sort of thing a tribe of hunter-gatherers is likely to encounter on the savannah. It doesn’t make sense for our brains to be optimized to solve poker or roulette.

The sort of problems that our ancestors encountered—indeed, the sort of problems that we encounter, most of the time—were not problems of calculable probability risk; they were problems of fundamental uncertainty. And they were frequently matters of life or death (which is why we’d expect them to be highly evolutionarily optimized): “Was that sound a lion, or just the wind?” “Is this mushroom safe to eat?” “Is that meat spoiled?”

In fact, many of the uncertainties most important to our ancestors are still important today: “Will these new strangers be friendly, or dangerous?” “Is that person attracted to me, or am I just projecting my own feelings?” “Can I trust you to keep your promise?” These sorts of social uncertainties are even deeper; it’s not clear that any finite being could ever totally resolve its uncertainty surrounding the behavior of other beings with the same level of intelligence, as the cognitive arms race continues indefinitely. The better I understand you, the better you understand me—and if you’re trying to deceive me, as I get better at detecting deception, you’ll get better at deceiving.

Personally, I think that it was precisely this sort of feedback loop that resulting in human beings getting such ridiculously huge brains in the first place. Chimpanzees are pretty good at dealing with the natural environment, maybe even better than we are; but even young children can outsmart them in social tasks any day. And once you start evolving for social cognition, it’s very hard to stop; basically you need to be constrained by something very fundamental, like, say, maximum caloric intake or the shape of the birth canal. Where chimpanzees look like their brains were what we call an “interior solution”, where evolution optimized toward a particular balance between cost and benefit, human brains look more like a “corner solution”, where the evolutionary pressure was entirely in one direction until we hit up against a hard constraint. That’s exactly what one would expect to happen if we were caught in a cognitive arms race.

What sort of heuristic makes sense for dealing with fundamental uncertainty—as opposed to precisely calculable probability? Well, you don’t want to compute a utility function and multiply by it, because that adds all sorts of extra computation and you have no idea what probability to assign. But you’ve got to do something like that in some sense, because that really is the optimal way to respond.

So here’s a heuristic you might try: Separate events into some broad categories based on how frequently they seem to occur, and what sort of response would be necessary.

Some things, like the sun rising each morning, seem to always happen. So you should act as if those things are going to happen pretty much always, because they do happen… pretty much always.

Other things, like rain, seem to happen frequently but not always. So you should look for signs that those things might happen, and prepare for them when the signs point in that direction.

Still other things, like being attacked by lions, happen very rarely, but are a really big deal when they do. You can’t go around expecting those to happen all the time, that would be crazy; but you need to be vigilant, and if you see any sign that they might be happening, even if you’re pretty sure they’re not, you may need to respond as if they were actually happening, just in case. The cost of a false positive is much lower than the cost of a false negative.

And still other things, like people sprouting wings and flying, never seem to happen. So you should act as if those things are never going to happen, and you don’t have to worry about them.

This heuristic is quite simple to apply once set up: It can simply slot in memories of when things did and didn’t happen in order to decide which category they go in—i.e. availability heuristic. If you can remember a lot of examples of “almost never”, maybe you should move it to “unlikely” instead. If you get a really big number of examples, you might even want to move it all the way to “likely”.

Another large advantage of this heuristic is that by combining utility and probability into one metric—we might call it “importance”, though Bayesian econometricians might complain about that—we can save on memory space and computing power. I don’t need to separately compute a utility and a probability; I just need to figure out how much effort I should put into dealing with this situation. A high probability of a small cost and a low probability of a large cost may be equally worth my time.

How might these heuristics go wrong? Well, if your environment changes sufficiently, the probabilities could shift and what seemed certain no longer is. For most of human history, “people walking on the Moon” would seem about as plausible as sprouting wings and flying away, and yet it has happened. Being attacked by lions is now exceedingly rare except in very specific places, but we still harbor a certain awe and fear before lions. And of course availability heuristic can be greatly distorted by mass media, which makes people feel like terrorist attacks and nuclear meltdowns are common and deaths by car accidents and influenza are rare—when exactly the opposite is true.

How many categories should you set, and what frequencies should they be associated with? This part I’m still struggling with, and it’s an important piece of the puzzle I will need before I can take this theory to experiment. There is probably a trade-off between more categories giving you more precision in tailoring your optimal behavior, but costing more cognitive resources to maintain. Is the optimal number 3? 4? 7? 10? I really don’t know. Even I could specify the number of categories, I’d still need to figure out precisely what categories to assign.

Nuclear power is safe. Why don’t people like it?

pnrj ethics, heuristics and biases, public policy , , , , , , , , , , , , , , , , , , , , ,

Sep 24, JDN 2457656

This post will have two parts, corresponding to each sentence. First, I hope to convince you that nuclear power is safe. Second, I’ll try to analyze some of the reasons why people don’t like it and what we might be able to do about that.

Depending on how familiar you are with the statistics on nuclear power, the idea that nuclear power is safe may strike you as either a completely ridiculous claim or an egregious understatement. If your primary familiarity with nuclear power safety is via the widely-publicized examples of Chernobyl, Three Mile Island, and more recently Fukushima, you may have the impression that nuclear power carries huge, catastrophic risks. (You may also be confusing nuclear power with nuclear weapons—nuclear weapons are indeed the greatest catastrophic risk on Earth today, but equating the two is like equating automobiles and machine guns because both of them are made of metal and contain lubricant, flammable materials, and springs.)

But in fact nuclear energy is astonishingly safe. Indeed, even those examples aren’t nearly as bad as people have been led to believe. Guess how many people died as a result of Three Mile Island, including estimated increased cancer deaths from radiation exposure?

Zero. There are zero confirmed deaths and the consensus estimate of excess deaths caused by the Three Mile Island incident by all causes combined is zero.

What about Fukushima? Didn’t 10,000 people die there? From the tsunami, yes. But the nuclear accident resulted in zero fatalities. If anything, those 10,000 people were killed by coal—by climate change. They certainly weren’t killed by nuclear.

Chernobyl, on the other hand, did actually kill a lot of people. Chernobyl caused 31 confirmed direct deaths, as well as an estimated 4,000 excess deaths by all causes. On the one hand, that’s more than 9/11; on the other hand, it’s about a month of US car accidents. Imagine if people had the same level of panic and outrage at automobiles after a month of accidents that they did at nuclear power after Chernobyl.

The vast majority of nuclear accidents cause zero fatalities; other than Chernobyl, none have ever caused more than 10. Deepwater Horizon killed 11 people, and yet for some reason Americans did not unite in opposition against ever using oil (or even offshore drilling!) ever again.

In fact, even that isn’t fair to nuclear power, because we’re not including the thousands of lives saved every year by using nuclear instead of coal and oil.

Keep in mind, the WHO estimates 10 to 100 million excess deaths due to climate change over the 21st century. That’s an average of 100,000 to 1 million deaths every year. Nuclear power currently produces about 11% of the world’s energy, so let’s do a back-of-the-envelope calculation for how many lives that’s saving. Assuming that additional climate change would be worse in direct proportion to the additional carbon emissions (which is conservative), and assuming that half that energy would be replaced by coal or oil (also conservative, using Germany’s example), we’re looking at about a 6% increase in deaths due to climate change if all those nuclear power plants were closed. That’s 6,000 to 60,000 lives that nuclear power plants save every year.

I also haven’t included deaths due to pollution—note that nuclear power plants don’t pollute air or water whatsoever, and only produce very small amounts of waste that can be quite safely stored. Air pollution in all its forms is responsible for one in eight deaths worldwide. Let me say that again: One in eight of all deaths in the world is caused by air pollution—so this is on the order of 7 million deaths per year, every year. We burn our way to a biannual Holocaust. Most of this pollution is actually caused by burning wood—fireplaces, wood stoves, and bonfires are terrible for the air—and many countries would actually see a substantial reduction in their toxic pollution if they switched to oil or even coal in favor of wood. But a large part of that pollution is caused by coal, and a nontrivial amount is caused by oil. Coal-burning factories and power plants are responsible for about 1 million deaths per year in China alone. Most of that pollution could be prevented if those power plants were nuclear instead.

Factor all that in, and nuclear power currently saves tens if not hundreds of thousands of lives per year, and expanding it to replace all fossil fuels could save millions more. Indeed, a more precise estimate of the benefits of nuclear power published a few years ago in Environmental Science and Technology is that nuclear power plants have saved some 1.8 million human lives since their invention, putting them on a par with penicillin and the polio vaccine.

So, I hope I’ve convinced you of the first proposition: Nuclear power plants are safe—and not just safe, but heroic, in fact one of the greatest life-saving technologies ever invented. So, why don’t people like them?

Unfortunately, I suspect that no amount of statistical data by itself will convince those who still feel a deep-seated revulsion to nuclear power. Even many environmentalists, people who could be nuclear energy’s greatest advocates, are often opposed to it. I read all the way through Naomi Klein’s This Changes Everything and never found even a single cogent argument against nuclear power; she simply takes it as obvious that nuclear power is “more of the same line of thinking that got us in this mess”. Perhaps because nuclear power could be enormously profitable for certain corporations (which is true; but then, it’s also true of solar and wind power)? Or because it also fits this narrative of “raping and despoiling the Earth” (sort of, I guess)? She never really does explain; I’m guessing she assumes that her audience will simply share her “gut feeling” intuition that nuclear power is dangerous and untrustworthy. One of the most important inconvenient truths for environmentalists is that nuclear power is not only safe, it is almost certainly our best hope for stopping climate change.

Perhaps all this is less baffling when we recognize that other heroic technologies are often also feared or despised for similarly bizarre reasons—vaccines, for instance.

First of all, human beings fear what we cannot understand, and while the human immune system is certainly immensely complicated, nuclear power is based on quantum mechanics, a realm of scientific knowledge so difficult and esoteric that it is frequently used as the paradigm example of something that is hard to understand. (As Feynman famously said, “I think I can safely say that nobody understands quantum mechanics.”) Nor does it help that popular treatments of quantum physics typically bear about as much resemblance to the actual content of the theory as the X-Men films do to evolutionary biology, and con artists like Deepak Chopra take advantage of this confusion to peddle their quackery.

Nuclear radiation is also particularly terrifying because it is invisible and silent; while a properly-functioning nuclear power plant emits less ionizing radiation than the Capitol Building and eating a banana poses substantially higher radiation risk than talking on a cell phone, nonetheless there is real danger posed by ionizing radiation, and that danger is particularly terrifying because it takes a form that human senses cannot detect. When you are burned by fire or cut by a knife, you know immediately; but gamma rays could be coursing through you right now and you’d feel no different. (Huge quantities of neutrinos are coursing through you, but fear not, for they’re completely harmless.) The symptoms of severe acute radiation poisoning also take a particularly horrific form: After the initial phase of nausea wears off, you can enter a “walking ghost phase”, where your eventual death is almost certain due to your compromised immune and digestive systems, but your current condition is almost normal. This makes the prospect of death by nuclear accident a particularly vivid and horrible image.

Vividness makes ideas more available to our memory; and thus, by the availability heuristic, we automatically infer that it must be more probable than it truly is. You can think of horrific nuclear accidents like Chernobyl, and all the carnage they caused; but all those millions of people choking to death in China don’t make for a compelling TV news segment (or at least, our TV news doesn’t seem to think so). Vividness doesn’t actually seem to make things more persuasive, but it does make them more memorable.

Yet even if we allow for the possibility that death by radiation poisoning is somewhat worse than death by coal pollution (if I had to choose between the two, okay, maybe I’d go with the coal), surely it’s not ten thousand times worse? Surely it’s not worth sacrificing entire cities full of people to coal in order to prevent a handful of deaths by nuclear energy?

Another reason that has been proposed is a sense that we can control risk from other sources, but a nuclear meltdown would be totally outside our control. Perhaps that is the perception, but if you think about it, it really doesn’t make a lot of sense. If there’s a nuclear meltdown, emergency services will report it, and you can evacuate the area. Yes, the radiation moves at the speed of light; but it also dissipates as the inverse square of distance, so if you just move further away you can get a lot safer quite quickly. (Think about the brightness of a lamp in your face versus across a football field. Radiation works the same way.) The damage is also cumulative, so the radiation risk from a meltdown is only going to be serious if you stay close to the reactor for a sustained period of time. Indeed, it’s much easier to avoid nuclear radiation than it is to avoid air pollution; you can’t just stand behind a concrete wall to shield against air pollution, and moving further away isn’t possible if you don’t know where it’s coming from. Control would explain why we fear cars less than airplanes (which is also statistically absurd), but it really can’t explain why nuclear power scares people more than coal and oil.

Another important factor may be an odd sort of bipartisan consensus: While the Left hates nuclear power because it makes corporations profitable or because it’s unnatural and despoils the Earth or something, the Right hates nuclear power because it requires substantial government involvement and might displace their beloved fossil fuels. (The Right’s deep, deep love of the fossil fuel industry now borders on the pathological. Even now that they are obviously economically inefficient and environmentally disastrous, right-wing parties around the world continue to defend enormous subsidies for oil and coal companies. Corruption and regulatory capture could partly explain this, but only partly. Campaign contributions can’t explain why someone would write a book praising how wonderful fossil fuels are and angrily denouncing anyone who would dare criticize them.) So while the two sides may hate each other in general and disagree on most other issues—including of course climate change itself—they can at least agree that nuclear power is bad and must be stopped.

Where do we go from here, then? I’m not entirely sure. As I said, statistical data by itself clearly won’t be enough. We need to find out what it is that makes people so uniquely terrified of nuclear energy, and we need to find a way to assuage those fears.

And we must do this now. For every day we don’t—every day we postpone the transition to a zero-carbon energy grid—is another thousand people dead.

What do we mean by “risk”?

pnrj critique of neoclassical economics , , , , , , , , , ,

JDN 2457118 EDT 20:50.

In an earlier post I talked about how, empirically, expected utility theory can’t explain the fact that we buy both insurance and lottery tickets, and how, normatively it really doesn’t make a lot of sense to buy lottery tickets precisely because of what expected utility theory says about them.

But today I’d like to talk about one of the major problems with expected utility theory, which I consider one of the major unexplored frontiers of economics: Expected utility theory treats all kinds of risk exactly the same.

In reality there are three kinds of risk: The first is what I’ll call classical risk, which is like the game of roulette; the odds are well-defined and known in advance, and you can play the game a large number of times and average out the results. This is where expected utility theory really shines; if you are dealing with classical risk, expected utility is obviously the way to go and Von Neumann and Morgenstern quite literally proved mathematically that anything else is irrational.

The second is uncertainty, a distinction which was most famously expounded by Frank Knight, an economist at the University of Chicago. (Chicago is a funny place; on the one hand they are a haven for the madness that is Austrian economics; on the other hand they have led the charge in behavioral and cognitive economics. Knight was a perfect fit, because he was a little of both.) Uncertainty is risk under ill-defined or unknown probabilities, where there is no way to play the game twice. Most real-world “risk” is actually uncertainty: Will the People’s Republic of China collapse in the 21st century? How many deaths will global warming cause? Will human beings ever colonize Mars? Is P = NP? None of those questions have known answers, but nor can we clearly assign probabilities either; Either P = NP or not, as a mathematical theorem (or, like the continuum hypothesis, it’s independent of ZFC, the most bizarre possibility of all), and it’s not as if someone is rolling dice to decide how many people global warming will kill. You can think of this in terms of “possible worlds”, though actually most modal theorists would tell you that we can’t even say that P=NP is possible (nor can we say it isn’t possible!) because, as a necessary statement, it can only be possible if it is actually true; this follows from the S5 axiom of modal logic, and you know what, even I am already bored with that sentence. Clearly there is some sense in which P=NP is possible, and if that’s not what modal logic says then so much the worse for modal logic. I am not a modal realist (not to be confused with a moral realist, which I am); I don’t think that possible worlds are real things out there somewhere. I think possibility is ultimately a statement about ignorance, and since we don’t know that P=NP is false then I contend that it is possible that it is true. Put another way, it would not be obviously irrational to place a bet that P=NP will be proved true by 2100; but if we can’t even say that it is possible, how can that be?

Anyway, that’s the mess that uncertainty puts us in, and almost everything is made of uncertainty. Expected utility theory basically falls apart under uncertainty; it doesn’t even know how to give an answer, let alone one that is correct. In reality what we usually end up doing is waving our hands and trying to assign a probability anyway—because we simply don’t know what else to do.

The third one is not one that’s usually talked about, yet I think it’s quite important; I will call it one-shot risk. The probabilities are known or at least reasonably well approximated, but you only get to play the game once. You can also generalize to few-shot risk, where you can play a small number of times, where “small” is defined relative to the probabilities involved; this is a little vaguer, but basically what I have in mind is that even though you can play more than once, you can’t play enough times to realistically expect the rarest outcomes to occur. Expected utility theory almost works on one-shot and few-shot risk, but you have to be very careful about taking it literally.

I think an example make things clearer: Playing the lottery is a few-shot risk. You can play the lottery multiple times, yes; potentially hundreds of times in fact. But hundreds of times is nothing compared to the 1 in 400 million chance you have of actually winning. You know that probability; it can be computed exactly from the rules of the game. But nonetheless expected utility theory runs into some serious problems here.

If we were playing a classical risk game, expected utility would obviously be right. So for example if you know that you will live one billion years, and you are offered the chance to play a game (somehow compensating for the mind-boggling levels of inflation, economic growth, transhuman transcendence, and/or total extinction that will occur during that vast expanse of time) in which at each year you can either have a guaranteed $40,000 of inflation-adjusted income or a 99.999,999,75% chance of $39,999 of inflation-adjusted income and a 0.000,000,25% chance of $100 million in inflation-adjusted income—which will disappear at the end of the year, along with everything you bought with it, so that each year you start afresh. Should you take the second option? Absolutely not, and expected utility theory explains why; that one or two years where you’ll experience 8 QALY per year isn’t worth dropping from 4.602056 QALY per year to 4.602049 QALY per year for the other nine hundred and ninety-eight million years. (Can you even fathom how long that is? From here, one billion years is all the way back to the Mesoproterozoic Era, which we think is when single-celled organisms first began to reproduce sexually. The gain is to be Mitt Romney for a year or two; the loss is the value of a dollar each year over and over again for the entire time that has elapsed since the existence of gamete meiosis.) I think it goes without saying that this whole situation is almost unimaginably bizarre. Yet that is implicitly what we’re assuming when we use expected utility theory to assess whether you should buy lottery tickets.

The real situation is more like this: There’s one world you can end up in, and almost certainly will, in which you buy lottery tickets every year and end up with an income of $39,999 instead of $40,000. There is another world, so unlikely as to be barely worth considering, yet not totally impossible, in which you get $100 million and you are completely set for life and able to live however you want for the rest of your life. Averaging over those two worlds is a really weird thing to do; what do we even mean by doing that? You don’t experience one world 0.000,000,25% as much as the other (whereas in the billion-year scenario, that is exactly what you do); you only experience one world or the other.

In fact, it’s worse than this, because if a classical risk game is such that you can play it as many times as you want as quickly as you want, we don’t even need expected utility theory—expected money theory will do. If you can play a game where you have a 50% chance of winning $200,000 and a 50% chance of losing $50,000, which you can play up to once an hour for the next 48 hours, and you will be extended any credit necessary to cover any losses, you’d be insane not to play; your 99.9% confidence level of wealth at the end of the two days is from $850,000 to $6,180,000. While you may lose money for awhile, it is vanishingly unlikely that you will end up losing more than you gain.

Yet if you are offered the chance to play this game only once, you probably should not take it, and the reason why then comes back to expected utility. If you have good access to credit you might consider it, because going $50,000 into debt is bad but not unbearably so (I did, going to college) and gaining $200,000 might actually be enough better to justify the risk. Then the effect can be averaged over your lifetime; let’s say you make $50,000 per year over 40 years. Losing $50,000 means making your average income $48,750, while gaining $200,000 means making your average income $55,000; so your QALY per year go from a guaranteed 4.70 to a 50% chance of 4.69 and a 50% chance of 4.74; that raises your expected utility from 4.70 to 4.715.

But if you don’t have good access to credit and your income for this year is $50,000, then losing $50,000 means losing everything you have and living in poverty or even starving to death. The benefits of raising your income by $200,000 this year aren’t nearly great enough to take that chance. Your expected utility goes from 4.70 to a 50% chance of 5.30 and a 50% chance of zero.

So expected utility theory only seems to properly apply if we can play the game enough times that the improbable events are likely to happen a few times, but not so many times that we can be sure our money will approach the average. And that’s assuming we know the odds and we aren’t just stuck with uncertainty.

Unfortunately, I don’t have a good alternative; so far expected utility theory may actually be the best we have. But it remains deeply unsatisfying, and I like to think we’ll one day come up with something better.