optimization

What behavioral economics needs

pnrj cognitive science, core principles, critique of neoclassical economics, heuristics and biases, mathematical models, science and academia , , , , , , , , , , , , , ,

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.

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

pnrj cognitive science, core principles, critique of neoclassical economics, ethics, heuristics and biases , , , , , , ,

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 optimizer—to 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 satisficer—they 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.

Good enough is perfect, perfect is bad

pnrj book reviews, cognitive science, core principles, critique of neoclassical economics, personal , , , , , , , , , ,

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.

How do we measure happiness?

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JDN 2457028 EST 20:33.

No, really, I’m asking. I strongly encourage my readers to offer in the comments any ideas they have about the measurement of happiness in the real world; this has been a stumbling block in one of my ongoing research projects.

In one sense the measurement of happiness—or more formally utility—is absolutely fundamental to economics; in another it’s something most economists are astonishingly afraid of even trying to do.

The basic question of economics has nothing to do with money, and is really only incidentally related to “scarce resources” or “the production of goods” (though many textbooks will define economics in this way—apparently implying that a post-scarcity economy is not an economy). The basic question of economics is really this: How do we make people happy?

This must always be the goal in any economic decision, and if we lose sight of that fact we can make some truly awful decisions. Other goals may work sometimes, but they inevitably fail: If you conceive of the goal as “maximize GDP”, then you’ll try to do any policy that will increase the amount of production, even if that production comes at the expense of stress, injury, disease, or pollution. (And doesn’t that sound awfully familiar, particularly here in the US? 40% of Americans report their jobs as “very stressful” or “extremely stressful”.) If you were to conceive of the goal as “maximize the amount of money”, you’d print money as fast as possible and end up with hyperinflation and total economic collapse ala Zimbabwe. If you were to conceive of the goal as “maximize human life”, you’d support methods of increasing population to the point where we had a hundred billion people whose lives were barely worth living. Even if you were to conceive of the goal as “save as many lives as possible”, you’d find yourself investing in whatever would extend lifespan even if it meant enormous pain and suffering—which is a major problem in end-of-life care around the world. No, there is one goal and one goal only: Maximize happiness.

I suppose technically it should be “maximize utility”, but those are in fact basically the same thing as long as “happiness” is broadly conceived as eudaimonia—the joy of a life well-lived—and not a narrow concept of just adding up pleasure and subtracting out pain. The goal is not to maximize the quantity of dopamine and endorphins in your brain; the goal is to achieve a world where people are safe from danger, free to express themselves, with friends and family who love them, who participate in a world that is just and peaceful. We do not want merely the illusion of these things—we want to actually have them. So let me be clear that this is what I mean when I say “maximize happiness”.

The challenge, therefore, is how we figure out if we are doing that. Things like money and GDP are easy to measure; but how do you measure happiness?
Early economists like Adam Smith and John Stuart Mill tried to deal with this question, and while they were not very successful I think they deserve credit for recognizing its importance and trying to resolve it. But sometime around the rise of modern neoclassical economics, economists gave up on the project and instead sought a narrower task, to measure preferences.

This is often called technically ordinal utility, as opposed to cardinal utility; but this terminology obscures the fundamental distinction. Cardinal utility is actual utility; ordinal utility is just preferences.

(The notion that cardinal utility is defined “up to a linear transformation” is really an eminently trivial observation, and it shows just how little physics the physics-envious economists really understand. All we’re talking about here is units of measurement—the same distance is 10.0 inches or 25.4 centimeters, so is distance only defined “up to a linear transformation”? It’s sometimes argued that there is no clear zero—like Fahrenheit and Celsius—but actually it’s pretty clear to me that there is: Zero utility is not existing. So there you go, now you have Kelvin.)

Preferences are a bit easier to measure than happiness, but not by as much as most economists seem to think. If you imagine a small number of options, you can just put them in order from most to least preferred and there you go; and we could imagine asking someone to do that, or—the technique of revealed preference—use the choices they make to infer their preferences by assuming that when given the choice of X and Y, choosing X means you prefer X to Y.

Like much of neoclassical theory, this sounds good in principle and utterly collapses when applied to the real world. Above all: How many options do you have? It’s not easy to say, but the number is definitely huge—and both of those facts pose serious problems for a theory of preferences.

The fact that it’s not easy to say means that we don’t have a well-defined set of choices; even if Y is theoretically on the table, people might not realize it, or they might not see that it’s better even though it actually is. Much of our cognitive effort in any decision is actually spent narrowing the decision space—when deciding who to date or where to go to college or even what groceries to buy, simply generating a list of viable options involves a great deal of effort and extremely complex computation. If you have a true utility function, you can satisfice—choosing the first option that is above a certain threshold—or engage in constrained optimization—choosing whether to continue searching or accept your current choice based on how good it is. Under preference theory, there is no such “how good it is” and no such thresholds. You either search forever or choose a cutoff arbitrarily.

Even if we could decide how many options there are in any given choice, in order for this to form a complete guide for human behavior we would need an enormous amount of information. Suppose there are 10 different items I could have or not have; then there are 10! = 3.6 million possible preference orderings. If there were 100 items, there would be 100! = 9e157 possible orderings. It won’t do simply to decide on each item whether I’d like to have it or not. Some things are complements: I prefer to have shoes, but I probably prefer to have $100 and no shoes at all rather than $50 and just a left shoe. Other things are substitutes: I generally prefer eating either a bowl of spaghetti or a pizza, rather than both at the same time. No, the combinations matter, and that means that we have an exponentially increasing decision space every time we add a new option. If there really is no more structure to preferences than this, we have an absurd computational task to make even the most basic decisions.

This is in fact most likely why we have happiness in the first place. Happiness did not emerge from a vacuum; it evolved by natural selection. Why make an organism have feelings? Why make it care about things? Wouldn’t it be easier to just hard-code a list of decisions it should make? No, on the contrary, it would be exponentially more complex. Utility exists precisely because it is more efficient for an organism to like or dislike things by certain amounts rather than trying to define arbitrary preference orderings. Adding a new item means assigning it an emotional value and then slotting it in, instead of comparing it to every single other possibility.

To illustrate this: I like Coke more than I like Pepsi. (Let the flame wars begin?) I also like getting massages more than I like being stabbed. (I imagine less controversy on this point.) But the difference in my mind between massages and stabbings is an awful lot larger than the difference between Coke and Pepsi. Yet according to preference theory (“ordinal utility”), that difference is not meaningful; instead I have to say that I prefer the pair “drink Pepsi and get a massage” to the pair “drink Coke and get stabbed”. There’s no such thing as “a little better” or “a lot worse”; there is only what I prefer over what I do not prefer, and since these can be assigned arbitrarily there is an impossible computational task before me to make even the most basic decisions.

Real utility also allows you to make decisions under risk, to decide when it’s worth taking a chance. Is a 50% chance of $100 worth giving up a guaranteed $50? Probably. Is a 50% chance of $10 million worth giving up a guaranteed $5 million? Not for me. Maybe for Bill Gates. How do I make that decision? It’s not about what I prefer—I do in fact prefer $10 million to $5 million. It’s about how much difference there is in terms of my real happiness—$5 million is almost as good as $10 million, but $100 is a lot better than $50. My marginal utility of wealth—as I discussed in my post on progressive taxation—is a lot steeper at $50 than it is at $5 million. There’s actually a way to use revealed preferences under risk to estimate true (“cardinal”) utility, developed by Von Neumann and Morgenstern. In fact they proved a remarkably strong theorem: If you don’t have a cardinal utility function that you’re maximizing, you can’t make rational decisions under risk. (In fact many of our risk decisions clearly aren’t rational, because we aren’t actually maximizing an expected utility; what we’re actually doing is something more like cumulative prospect theory, the leading cognitive economic theory of risk decisions. We overrespond to extreme but improbable events—like lightning strikes and terrorist attacks—and underrespond to moderate but probable events—like heart attacks and car crashes. We play the lottery but still buy health insurance. We fear Ebola—which has never killed a single American—but not influenza—which kills 10,000 Americans every year.)

A lot of economists would argue that it’s “unscientific”—Kenneth Arrow said “impossible”—to assign this sort of cardinal distance between our choices. But assigning distances between preferences is something we do all the time. Amazon.com lets us vote on a 5-star scale, and very few people send in error reports saying that cardinal utility is meaningless and only preference orderings exist. In 2000 I would have said “I like Gore best, Nader is almost as good, and Bush is pretty awful; but of course they’re all a lot better than the Fascist Party.” If we had simply been able to express those feelings on the 2000 ballot according to a range vote, either Nader would have won and the United States would now have a three-party system (and possibly a nationalized banking system!), or Gore would have won and we would be a decade ahead of where we currently are in preventing and mitigating global warming. Either one of these things would benefit millions of people.

This is extremely important because of another thing that Arrow said was “impossible”—namely, “Arrow’s Impossibility Theorem”. It should be called Arrow’s Range Voting Theorem, because simply by restricting preferences to a well-defined utility and allowing people to make range votes according to that utility, we can fulfill all the requirements that are supposedly “impossible”. The theorem doesn’t say—as it is commonly paraphrased—that there is no fair voting system; it says that range voting is the only fair voting system. A better claim is that there is no perfect voting system, which is true if you mean that there is no way to vote strategically that doesn’t accurately reflect your true beliefs. The Myerson-Satterthwaithe Theorem is then the proper theorem to use; if you could design a voting system that would force you to reveal your beliefs, you could design a market auction that would force you to reveal your optimal price. But the least expressive way to vote in a range vote is to pick your favorite and give them 100% while giving everyone else 0%—which is identical to our current plurality vote system. The worst-case scenario in range voting is our current system.

But the fact that utility exists and matters, unfortunately doesn’t tell us how to measure it. The current state-of-the-art in economics is what’s called “willingness-to-pay”, where we arrange (or observe) decisions people make involving money and try to assign dollar values to each of their choices. This is how you get disturbing calculations like “the lives lost due to air pollution are worth $10.2 billion.”

Why are these calculations disturbing? Because they have the whole thing backwards—people aren’t valuable because they are worth money; money is valuable because it helps people. It’s also really bizarre because it has to be adjusted for inflation. Finally—and this is the point that far too few people appreciate—the value of a dollar is not constant across people. Because different people have different marginal utilities of wealth, something that I would only be willing to pay $1000 for, Bill Gates might be willing to pay $1 million for—and a child in Africa might only be willing to pay $10, because that is all he has to spend. This makes the “willingness-to-pay” a basically meaningless concept independent of whose wealth we are spending.

Utility, on the other hand, might differ between people—but, at least in principle, it can still be added up between them on the same scale. The problem is that “in principle” part: How do we actually measure it?

So far, the best I’ve come up with is to borrow from public health policy and use the QALY, or quality-adjusted life year. By asking people macabre questions like “What is the maximum number of years of your life you would give up to not have a severe migraine every day?” (I’d say about 20—that’s where I feel ambivalent. At 10 I definitely would; at 30 I definitely wouldn’t.) or “What chance of total paralysis would you take in order to avoid being paralyzed from the waist down?” (I’d say about 20%.) we assign utility values: 80 years of migraines is worth giving up 20 years to avoid, so chronic migraine is a quality of life factor of 0.75. Total paralysis is 5 times as bad as paralysis from the waist down, so if waist-down paralysis is a quality of life factor of 0.90 then total paralysis is 0.50.

You can probably already see that there are lots of problems: What if people don’t agree? What if due to framing effects the same person gives different answers to slightly different phrasing? Some conditions will directly bias our judgments—depression being the obvious example. How many years of your life would you give up to not be depressed? Suicide means some people say all of them. How well do we really know our preferences on these sorts of decisions, given that most of them are decisions we will never have to make? It’s difficult enough to make the actual decisions in our lives, let alone hypothetical decisions we’ve never encountered.

Another problem is often suggested as well: How do we apply this methodology outside questions of health? Does it really make sense to ask you how many years of your life drinking Coke or driving your car is worth?
Well, actually… it better, because you make that sort of decision all the time. You drive instead of staying home, because you value where you’re going more than the risk of dying in a car accident. You drive instead of walking because getting there on time is worth that additional risk as well. You eat foods you know aren’t good for you because you think the taste is worth the cost. Indeed, most of us aren’t making most of these decisions very well—maybe you shouldn’t actually drive or drink that Coke. But in order to know that, we need to know how many years of your life a Coke is worth.

As a very rough estimate, I figure you can convert from willingness-to-pay to QALY by dividing by your annual consumption spending Say you spend annually about $20,000—pretty typical for a First World individual. Then $1 is worth about 50 microQALY, or about 26 quality-adjusted life-minutes. Now suppose you are in Third World poverty; your consumption might be only $200 a year, so $1 becomes worth 5 milliQALY, or 1.8 quality-adjusted life-days. The very richest individuals might spend as much as $10 million on consumption, so $1 to them is only worth 100 nanoQALY, or 3 quality-adjusted life-seconds.

That’s an extremely rough estimate, of course; it assumes you are in perfect health, all your time is equally valuable and all your purchasing decisions are optimized by purchasing at marginal utility. Don’t take it too literally; based on the above estimate, an hour to you is worth about $2.30, so it would be worth your while to work for even $3 an hour. Here’s a simple correction we should probably make: if only a third of your time is really usable for work, you should expect at least $6.90 an hour—and hey, that’s a little less than the US minimum wage. So I think we’re in the right order of magnitude, but the details have a long way to go.

So let’s hear it, readers: How do you think we can best measure happiness?