revealed preference

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

pnrj critique of neoclassical economics, heuristics and biases , , , , , , ,

Post 312 Oct 27 JDN 2458784

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

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

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

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

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

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

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

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

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

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

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

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

Bigotry is more powerful than the market

pnrj cognitive science, core principles, critique of neoclassical economics, current events, ethics, heuristics and biases, inequality, market failure, public policy , , , , , , , , , , , , , , , , , , , , , , ,

Nov 20, JDN 2457683

If there’s one message we can take from the election of Donald Trump, it is that bigotry remains a powerful force in our society. A lot of autoflagellating liberals have been trying to explain how this election result really reflects our failure to help people displaced by technology and globalization (despite the fact that personal income and local unemployment had negligible correlation with voting for Trump), or Hillary Clinton’s “bad campaign” that nonetheless managed the same proportion of Democrat turnout that re-elected her husband in 1996.

No, overwhelmingly, the strongest predictor of voting for Trump was being White, and living in an area where most people are White. (Well, actually, that’s if you exclude authoritarianism as an explanatory variable—but really I think that’s part of what we’re trying to explain.) Trump voters were actually concentrated in areas less affected by immigration and globalization. Indeed, there is evidence that these people aren’t racist because they have anxiety about the economy—they are anxious about the economy because they are racist. How does that work? Obama. They can’t believe that the economy is doing well when a Black man is in charge. So all the statistics and even personal experiences mean nothing to them. They know in their hearts that unemployment is rising, even as the BLS data clearly shows it’s falling.

The wide prevalence and enormous power of bigotry should be obvious. But economists rarely talk about it, and I think I know why: Their models say it shouldn’t exist. The free market is supposed to automatically eliminate all forms of bigotry, because they are inefficient.

The argument for why this is supposed to happen actually makes a great deal of sense: If a company has the choice of hiring a White man or a Black woman to do the same job, but they know that the market wage for Black women is lower than the market wage for White men (which it most certainly is), and they will do the same quality and quantity of work, why wouldn’t they hire the Black woman? And indeed, if human beings were rational profit-maximizers, this is probably how they would think.

More recently some neoclassical models have been developed to try to “explain” this behavior, but always without daring to give up the precious assumption of perfect rationality. So instead we get the two leading neoclassical theories of discrimination, which are statistical discrimination and taste-based discrimination.

Statistical discrimination is the idea that under asymmetric information (and we surely have that), features such as race and gender can act as signals of quality because they are correlated with actual quality for various reasons (usually left unspecified), so it is not irrational after all to choose based upon them, since they’re the best you have.

Taste-based discrimination is the idea that people are rationally maximizing preferences that simply aren’t oriented toward maximizing profit or well-being. Instead, they have this extra term in their utility function that says they should also treat White men better than women or Black people. It’s just this extra thing they have.

A small number of studies have been done trying to discern which of these is at work.
The correct answer, of course, is neither.

Statistical discrimination, at least, could be part of what’s going on. Knowing that Black people are less likely to be highly educated than Asians (as they definitely are) might actually be useful information in some circumstances… then again, you list your degree on your resume, don’t you? Knowing that women are more likely to drop out of the workforce after having a child could rationally (if coldly) affect your assessment of future productivity. But shouldn’t the fact that women CEOs outperform men CEOs be incentivizing shareholders to elect women CEOs? Yet that doesn’t seem to happen. Also, in general, people seem to be pretty bad at statistics.

The bigger problem with statistical discrimination as a theory is that it’s really only part of a theory. It explains why not all of the discrimination has to be irrational, but some of it still does. You need to explain why there are these huge disparities between groups in the first place, and statistical discrimination is unable to do that. In order for the statistics to differ this much, you need a past history of discrimination that wasn’t purely statistical.

Taste-based discrimination, on the other hand, is not a theory at all. It’s special pleading. Rather than admit that people are failing to rationally maximize their utility, we just redefine their utility so that whatever they happen to be doing now “maximizes” it.

This is really what makes the Axiom of Revealed Preference so insidious; if you really take it seriously, it says that whatever you do, must by definition be what you preferred. You can’t possibly be irrational, you can’t possibly be making mistakes of judgment, because by definition whatever you did must be what you wanted. Maybe you enjoy bashing your head into a wall, who am I to judge?

I mean, on some level taste-based discrimination is what’s happening; people think that the world is a better place if they put women and Black people in their place. So in that sense, they are trying to “maximize” some “utility function”. (By the way, most human beings behave in ways that are provably inconsistent with maximizing any well-defined utility function—the Allais Paradox is a classic example.) But the whole framework of calling it “taste-based” is a way of running away from the real explanation. If it’s just “taste”, well, it’s an unexplainable brute fact of the universe, and we just need to accept it. If people are happier being racist, what can you do, eh?

So I think it’s high time to start calling it what it is. This is not a question of taste. This is a question of tribal instinct. This is the product of millions of years of evolution optimizing the human brain to act in the perceived interest of whatever it defines as its “tribe”. It could be yourself, your family, your village, your town, your religion, your nation, your race, your gender, or even the whole of humanity or beyond into all sentient beings. But whatever it is, the fundamental tribe is the one thing you care most about. It is what you would sacrifice anything else for.

And what we learned on November 9 this year is that an awful lot of Americans define their tribe in very narrow terms. Nationalistic and xenophobic at best, racist and misogynistic at worst.

But I suppose this really isn’t so surprising, if you look at the history of our nation and the world. Segregation was not outlawed in US schools until 1955, and there are women who voted in this election who were born before American women got the right to vote in 1920. The nationalistic backlash against sending jobs to China (which was one of the chief ways that we reduced global poverty to its lowest level ever, by the way) really shouldn’t seem so strange when we remember that over 100,000 Japanese-Americans were literally forcibly relocated into camps as recently as 1942. The fact that so many White Americans seem all right with the biases against Black people in our justice system may not seem so strange when we recall that systemic lynching of Black people in the US didn’t end until the 1960s.

The wonder, in fact, is that we have made as much progress as we have. Tribal instinct is not a strange aberration of human behavior; it is our evolutionary default setting.

Indeed, perhaps it is unreasonable of me to ask humanity to change its ways so fast! We had millions of years to learn how to live the wrong way, and I’m giving you only a few centuries to learn the right way?

The problem, of course, is that the pace of technological change leaves us with no choice. It might be better if we could wait a thousand years for people to gradually adjust to globalization and become cosmopolitan; but climate change won’t wait a hundred, and nuclear weapons won’t wait at all. We are thrust into a world that is changing very fast indeed, and I understand that it is hard to keep up; but there is no way to turn back that tide of change.

Yet “turn back the tide” does seem to be part of the core message of the Trump voter, once you get past the racial slurs and sexist slogans. People are afraid of what the world is becoming. They feel that it is leaving them behind. Coal miners fret that we are leaving them behind by cutting coal consumption. Factory workers fear that we are leaving them behind by moving the factory to China or inventing robots to do the work in half the time for half the price.

And truth be told, they are not wrong about this. We are leaving them behind. Because we have to. Because coal is polluting our air and destroying our climate, we must stop using it. Moving the factories to China has raised them out of the most dire poverty, and given us a fighting chance toward ending world hunger. Inventing the robots is only the next logical step in the process that has carried humanity forward from the squalor and suffering of primitive life to the security and prosperity of modern society—and it is a step we must take, for the progress of civilization is not yet complete.

They wouldn’t have to let themselves be left behind, if they were willing to accept our help and learn to adapt. That carbon tax that closes your coal mine could also pay for your basic income and your job-matching program. The increased efficiency from the automated factories could provide an abundance of wealth that we could redistribute and share with you.

But this would require them to rethink their view of the world. They would have to accept that climate change is a real threat, and not a hoax created by… uh… never was clear on that point actually… the Chinese maybe? But 45% of Trump supporters don’t believe in climate change (and that’s actually not as bad as I’d have thought). They would have to accept that what they call “socialism” (which really is more precisely described as social democracy, or tax-and-transfer redistribution of wealth) is actually something they themselves need, and will need even more in the future. But despite rising inequality, redistribution of wealth remains fairly unpopular in the US, especially among Republicans.

Above all, it would require them to redefine their tribe, and start listening to—and valuing the lives of—people that they currently do not.

Perhaps we need to redefine our tribe as well; many liberals have argued that we mistakenly—and dangerously—did not include people like Trump voters in our tribe. But to be honest, that rings a little hollow to me: We aren’t the ones threatening to deport people or ban them from entering our borders. We aren’t the ones who want to build a wall (though some have in fact joked about building a wall to separate the West Coast from the rest of the country, I don’t think many people really want to do that). Perhaps we live in a bubble of liberal media? But I make a point of reading outlets like The American Conservative and The National Review for other perspectives (I usually disagree, but I do at least read them); how many Trump voters do you think have ever read the New York Times, let alone Huffington Post? Cosmopolitans almost by definition have the more inclusive tribe, the more open perspective on the world (in fact, do I even need the “almost”?).

Nor do I think we are actually ignoring their interests. We want to help them. We offer to help them. In fact, I want to give these people free money—that’s what a basic income would do, it would take money from people like me and give it to people like them—and they won’t let us, because that’s “socialism”! Rather, we are simply refusing to accept their offered solutions, because those so-called “solutions” are beyond unworkable; they are absurd, immoral and insane. We can’t bring back the coal mining jobs, unless we want Florida underwater in 50 years. We can’t reinstate the trade tariffs, unless we want millions of people in China to starve. We can’t tear down all the robots and force factories to use manual labor, unless we want to trigger a national—and then global—economic collapse. We can’t do it their way. So we’re trying to offer them another way, a better way, and they’re refusing to take it. So who here is ignoring the concerns of whom?

Of course, the fact that it’s really their fault doesn’t solve the problem. We do need to take it upon ourselves to do whatever we can, because, regardless of whose fault it is, the world will still suffer if we fail. And that presents us with our most difficult task of all, a task that I fully expect to spend a career trying to do and yet still probably failing: We must understand the human tribal instinct well enough that we can finally begin to change it. We must know enough about how human beings form their mental tribes that we can actually begin to shift those parameters. We must, in other words, cure bigotry—and we must do it now, for we are running out of time.

How do we measure happiness?

pnrj cognitive science, core principles , , , , , , , , , , , , , , , , , , , , , , , ,

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?