Author: PNRJ

The urban-rural divide runs deep

PNRJ cognitive science, public policy , , , , , , , , ,

Feb 5, JDN 2457790

Are urban people worth less than rural people?

That probably sounds like a ridiculous thing to ask; of course not, all people are worth the same (other things equal of course—philanthropists are worth more than serial murderers). But then, if you agree with that, you’re probably an urban person, as I’m sure most of my readers are (and as indeed most people in highly-developed countries are).

A disturbing number of rural people, however, honestly do seem to believe this. They think that our urban lifestyles (whatever they imagine those to be) devalue us as citizens and human beings.

That is the key subtext to understand in the terrifying phenomenon that is Donald Trump. Most of the people who voted for him can’t possibly have thought he was actually trustworthy, and many probably didn’t actually support his policies of bigotry and authoritarianism (though he was very popular among bigots and authoritarians). From speaking with family members and acquaintances who proudly voted for Trump, one thing came through very clearly: This was a gigantic middle finger pointed at cities. They didn’t even really want Trump; they just knew we didn’t, and so they voted for him out of spite as much as anything else. They also have really confused views about free trade, so some of them voted for him because he promised to bring back jobs lost to trade (that weren’t lost to trade, can’t be brought back, and shouldn’t be even if they could). Talk with a Trump voter for a few minutes, and sneers of “latte-sipping liberal” (I don’t even like coffee) and “coastal elite” (I moved here to get educated; I wasn’t born here) are sure to follow.

There has always been some conflict between rural and urban cultures, for as long as there have been urban cultures for rural cultures to be in conflict with. It is found not just in the US, but in most if not all countries around the world. It was relatively calm during the postwar boom in the 20th century, as incomes everywhere (or at least everywhere within highly-developed countries) were improving more or less in lockstep. But the 21st century has brought us much more unequal growth, concentrated on particular groups of people and particular industries. This has brought more resentment. And that divide, above all else, is what brought us Trump; the correlation between population density and voting behavior is enormous.

Of course, “urban” is sometimes a dog-whistle for “Black”; but sometimes I think it actually really means “urban”—and yet there’s still a lot of hatred embedded in it. Indeed, perhaps that’s why the dog-whistle works; a White man from a rural town can sneer at “urban” people and it’s not entirely clear whether he’s being racist or just being anti-urban.

The assumption that rural lifestyles are superior runs so deep in our culture that even in articles by urban people (like this one from the LA Times) supposedly reflecting about how to resolve this divide, there are long paeans to the world of “hard work” and “sacrifice” and “autonomy” of rural life, and mocking “urban elites” for their “disproportionate” (by which you can only mean almost proportionate) power over government.

Well, guess what? If you want to live in a rural area, go live in a rural area. Don’t pine for it. Don’t tell me how great farm life is. If you want to live on a farm, go live on a farm. I have nothing against it; we need farmers, after all. I just want you to shut up about how great it is, especially if you’re not going to actually do it. Pining for someone else’s lifestyle when you could easily take on that lifestyle if you really wanted it just shows that you think the grass is greener on the other side.

Because the truth is, farm living isn’t so great for most people. The world’s poorest people are almost all farmers. 70% of people below the UN poverty line live in rural areas, even as more and more of the world’s population moves into cities. If you use a broader poverty measure, as many as 85% of the world’s poor live in rural areas.

The kind of “autonomy” that means defending your home with a shotgun is normally what we would call anarchy—it’s a society that has no governance, no security. (Of course, in the US that’s pure illusion; crime rates in general are low and falling, and lower in rural areas than urban areas. But in some parts of the world, that anarchy is very real.) One of the central goals of global economic development is to get people away from subsistence farming into far more efficient manufacturing and service jobs.

At least in the US, farm life is a lot better than it used to be, now that agricultural technology has improved so that one farmer can now do the work of hundreds. Despite increased population and increased food consumption per person, the number of farmers in the US is now the smallest it has been since before the Civil War. The share of employment devoted to agriculture has fallen from over 80% in 1800 to under 2% today. Even just since the 1960s labor productivity of US farms has more than tripled.

But the reason that some 80% of Americans have chosen to live in cities—and yes, I can clearly say “chosen”, because cities are more expensive and therefore urban living is a voluntary activity. Most people who live in the city right now could move to the country if we really wanted to. We choose not to, because we know our life would be worse if we did.

Indeed, I dare say that a lot of the hatred of city-dwellers has got to be envy. Our (median) incomes are higher and our (mean) lifespans are longer. Fewer of our children are in poverty. Life is better here—we know it, and deep down, they know it too.

We also have better Internet access, unsurprisingly—though rural areas are only a few years behind, and the technology improves so rapidly that twice as many rural homes in the US have Internet access than urban homes did in 1998.

Now, a rational solution to this problem would be either to improve the lives of people in rural areas or else move everyone to urban areas—and both of those things have been happening, not only in the US but around the world. But in order to do that, you need to be willing to change things. You have to give up the illusion that farm life is some wonderful thing we should all be emulating, rather than the necessary toil that humanity was forced to go through for centuries until civilization could advance beyond it. You have to be willing to replace farmers with robots, so that people who would have been farmers can go do something better with their lives. You need to give up the illusion that there is something noble or honorable about hard labor on a farm—indeed, you need to give up the illusion that there is anything noble or honorable about hard work in general. Work is not a benefit; work is a cost. Work is what we do because we have to—and when we no longer have to do it, we should stop. Wanting to escape toil and suffering doesn’t make you lazy or selfish—it makes you rational.

We could surely be more welcoming—but cities are obviously more welcoming to newcomers than rural areas are. Our housing is too expensive, but that’s in part because so many people want to live here—supply hasn’t been able to keep up with demand.

I may seem to be presenting this issue as one-sided; don’t urban people devalue rural people too? Sometimes. Insults like “hick” and “yokel” and “redneck” do of course exist. But I’ve never heard anyone from a city seriously argue that people who live in rural areas should have votes that systematically count for less than those of people who live in cities—yet the reverse is literally what people are saying when they defend the Electoral College. If you honestly think that the Electoral College deserves to exist in anything like its present form, you must believe that some Americans are worth more than others, and the people who are worth more are almost all in rural areas while the people who are worth less are almost all in urban areas.

No, National Review, the Electoral College doesn’t “save” America from California’s imperial power; it gives imperial power to a handful of swing states. The only reason California would be more important than any other state is that more Americans live here. Indeed, a lot of Republicans in California are disenfranchised, because they know that their votes will never overcome the overwhelming Democratic majority for the state as a whole and the system is winner-takes-all. Indeed, about 30% of California votes Republican (well, not in the last election, because that was Trump—Orange County went Democrat for the first time in decades), so the number of disenfranchised Republicans alone in California is larger than the population of Michigan, which in turn is larger than the population of Wyoming, North Dakota, South Dakota, Montana, Nebraska, West Virginia, and Kansas combined. Indeed, there are more people in California than there are in Canada. So yeah, I’m thinking maybe we should get a lot of votes?

But it’s easy for you to drum up fear over “imperial rule” by California in particular, because we’re so liberal—and so urban, indeed an astonishing 95% urban, the most of any US state (or frankly probably any major regional entity on the planet Earth! To beat that you have to be something like Singapore, which literally just is a single city).

In fact, while insults thrown at urban people get thrown at basically all of us regardless of what we do, most of the insults that are thrown at rural people are mainly thrown at uneducated rural people. (And statistically, while many people in rural areas are educated and many people in urban areas are not, there’s definitely a positive correlation between urbanization and education.) It’s still unfair in many ways, not least because education isn’t entirely a choice, not in a society where tuition at an average private university costs more than the median individual income. Many of the people we mock as being stupid were really just born poor. It may not be their fault, but they can’t believe that the Earth is only 10,000 years old and not have some substantial failings in their education. I still don’t think mockery is the right answer; it’s really kicking them while they’re down. But clearly there is something wrong with our society when 40% of people believe something so obviously ludicrous—and those beliefs are very much concentrated in the same Southern states that have the most rural populations. “They think we’re ignorant just because we believe that God made the Earth 6,000 years ago!” I mean… yes? I’m gonna have to own up to that one, I guess. I do in fact think that people who believe things that were disproven centuries ago are ignorant.

So really this issue is one-sided. We who live in cities are being systematically degraded and disenfranchised, and when we challenge that system we are accused of being selfish or elitist or worse. We are told that our lifestyles are inferior and shameful, and when we speak out about the positive qualities of our lives—our education, our acceptance of diversity, our flexibility in the face of change—we are again accused of elitism and condescension.

We could simply stew in that resentment. But we can do better. We can reach out to people in rural areas, show them not just that our lives are better—as I said, they already know this—but that they can have these lives too. And we can make policy so that this really can happen for people. Envy doesn’t automatically lead to resentment; that only happens when combined with a lack of mobility. The way urban people pine for the countryside is baffling, since we could go there any time; but the way that country people long for the city is perfectly understandable, as our lives really are better but our rent is too high for them to afford. We need to bring that rent down, not just for the people already living in cities, but also for the people who want to but can’t.

And of course we don’t want to move everyone to cities, either. Many people won’t want to live in cities, and we need a certain population of farmers to make our food after all. We can work to improve infrastructure in rural areas—particularly when it comes to hospitals, which are a basic necessity that is increasingly underfunded. We shouldn’t stop using cost-effectiveness calculations, but we need to compare against the right things. If that hospital isn’t worth building, it should be because there’s another, better hospital we could make for the same amount or cheaper—not because we think that this town doesn’t deserve to have a hospital. We can expand our public transit systems over a wider area, and improve their transit speeds so that people can more easily travel to the city from further away.

We should seriously face up to the costs that free trade has imposed upon many rural areas. We can’t give up on free trade—but that doesn’t mean we need to keep our trade policy exactly as it is. We can do more to ensure that multinational corporations don’t have overwhelming bargaining power against workers and small businesses. We can establish a tax system that would redistribute more of the gains from free trade to the people and places most hurt by the transition. Right now, poor people in the US are often the most fiercely opposed to redistribution of wealth, because somehow they perceive that wealth will be redistributed from them when it would in fact be redistributed to them. They are in a scarcity mindset, their whole worldview shaped by the fact that they struggle to get by. They see every change as a threat, every stranger as an enemy.

Somehow we need to fight that mindset, get them to see that there are many positive changes that can be made, many things that we can achieve together that none of us could achieve along.

Why do so many Americans think that crime is increasing?

PNRJ cognitive science, public policy , , , , , ,

Jan 29, JDN 2457783

Since the 1990s, crime in United States has been decreasing, and yet in every poll since then most Americans report that they believe that crime is increasing.

It’s not a small decrease either. The US murder rate is down to the lowest it has been in a century. There are now a smaller absolute number (by 34 log points) of violent crimes per year in the US than there were 20 years ago, despite a significant increase in total population (19 log points—and the magic of log points is that, yes, the rate has decreased by precisely 53 log points).

It isn’t geographically uniform, of course; some states have improved much more than others, and a few states (such as New Mexico) have actually gotten worse.

The 1990s were a peak of violent crime, so one might say that we are just regressing to the mean. (Even that would be enough to make it baffling that people think crime is increasing.) But in fact overall crime in the US is now the lowest it has been since the 1970s, and still decreasing.

Indeed, this decrease has been underestimated, because we are now much better about reporting and investigating crimes than we used to be (which may also be part of why they are decreasing, come to think of it). If you compare against surveys of people who say they have been personally victimized, we’re looking at a decline in violent crime rates of two thirds—109 log points.

Just since 2008 violent crime has decreased by 26% (30 log points)—but of course we all know that Obama is “soft on crime” because he thinks cops shouldn’t be allowed to just shoot Black kids for no reason.

And yet, over 60% of Americans believe that overall crime in the US has increased in the last 10 years (though only 38% think it has increased in their own community!). These figures are actually down from 2010, when 66% thought crime was increasing nationally and 49% thought it was increasing in their local area.

The proportion of people who think crime is increasing does seem to decrease as crime rates decrease—but it still remains alarmingly high. If people were half as rational as most economists seem to believe, the proportion of people who think crime is increasing should drop to basically zero whenever crime rates decrease, since that’s a really basic fact about the world that you can just go look up on the Web in a couple of minutes. There’s no deep ambiguity, not even much “rational ignorance” given the low cost of getting correct answers. People just don’t bother to check, or don’t feel they need to.
What’s going on? How can crime fall to half what it was 20 years ago and yet almost two-thirds of people think it’s actually increasing?

Well, one hint is that news coverage of crime doesn’t follow the same pattern as actual crime.

News coverage in general is a terrible source of information, not simply because news organizations can be biased, make glaring mistakes, and sometimes outright lie—but actually for a much more fundamental reason: Even a perfect news channel, qua news channel, would report what is surprising—and what is surprising is, by definition, improbable. (Indeed, there is a formal mathematical concept in probability theory called surprisal that is simply the logarithm of 1 over the probability.) Even assuming that news coverage reports only the truth, the probability of seeing something on the news isn’t proportional to the probability of the event occurring—it’s more likely proportional to the entropy, which is probability times surprisal.

Now, if humans were optimal information processing engines, that would be just fine, actually; reporting events proportional to their entropy is actually a very efficient mechanism for delivering information (optimal, under certain types of constraints), provided that you can then process the information back into probabilities afterward.

But of course, humans aren’t optimal information processing engines. We don’t recompute the probabilities from the given entropy; instead we use the availability heuristic, by which we simply use the number of times we can think of something happening as our estimate of the probability of that event occurring. If you see more murders on TV news than you used you, you assume that murders must be more common than they used to be. (And when I put it like that, it really doesn’t sound so unreasonable, does it? Intuitively the availability heuristic seems to make sense—which is part of why it’s so insidious.)

Another likely reason for the discrepancy between perception and reality is nostalgia. People almost always have a more positive view of the past than it deserves, particularly when referring to their own childhoods. Indeed, I’m quite certain that a major reason why people think the world was much better when they were kids was that their parents didn’t tell them what was going on. And of course I’m fine with that; you don’t need to burden 4-year-olds with stories of war and poverty and terrorism. I just wish people would realize that they were being protected from the harsh reality of the world, instead of thinking that their little bubble of childhood innocence was a genuinely much safer world than the one we live in today.

Then take that nostalgia and combine it with the availability heuristic and the wall-to-wall TV news coverage of anything bad that happens—and almost nothing good that happens, certainly not if it’s actually important. I’ve seen bizarre fluff pieces about puppies, but never anything about how world hunger is plummeting or air quality is dramatically improved or cars are much safer. That’s the one thing I will say about financial news; at least they report it when unemployment is down and the stock market is up. (Though most Americans, especially most Republicans, still seem really confused on those points as well….) They will attribute it to anything from sunspots to the will of Neptune, but at least they do report good news when it happens. It’s no wonder that people are always convinced that the world is getting more dangerous even as it gets safer and safer.

The real question is what we do about it—how do we get people to understand even these basic facts about the world? I still believe in democracy, but when I see just how painfully ignorant so many people are of such basic facts, I understand why some people don’t. The point of democracy is to represent everyone’s interests—but we also end up representing everyone’s beliefs, and sometimes people’s beliefs just don’t line up with reality. The only way forward I can see is to find a way to make people’s beliefs better align with reality… but even that isn’t so much a strategy as an objective. What do I say to someone who thinks that crime is increasing, beyond showing them the FBI data that clearly indicates otherwise? When someone is willing to override all evidence with what they feel in their heart to be true, what are the rest of us supposed to do?

In defense of slacktivism

PNRJ cognitive science, ethics, public policy, Uncategorized , , , , , , , , ,

Jan 22, JDN 2457776

It’s one of those awkward portmanteaus that people often make to try to express a concept in fewer syllables, while also implicitly saying that the phenomenon is specific enough to deserve its own word: “Slacktivism”, made of “slacker” and “activism”, not unlike “mansplain” is made of “man” and “explain” or “edutainment” was made of “education” and “entertainment”—or indeed “gerrymander” was made of “Elbridge Gerry” and “salamander”. The term seems to be particularly popular on Huffington Post, which has a whole category on slacktivism. There is a particular subcategory of slacktivism that is ironically against other slacktivism, which has been dubbed “snarktivism”.

It’s almost always used as a pejorative; very few people self-identify as “slacktivists” (though once I get through this post, you may see why I’m considering it myself). “Slacktivism” is activism that “isn’t real” somehow, activism that “doesn’t count”.

Of course, that raises the question: What “counts” as legitimate activism? Is it only protest marches and sit-ins? Then very few people have ever been or will ever be activists. Surely donations should count, at least? Those have a direct, measurable impact. What about calling your Congressman, or letter-writing campaigns? These have been staples of activism for decades.
If the term “slacktivism” means anything at all, it seems to point to activities surrounding raising awareness, where the goal is not to enact a particular policy or support a particular NGO but to simply get as much public attention to a topic as possible. It seems to be particularly targeted at blogging and social media—and that’s important, for reasons I’ll get to shortly. If you gather a group of people in your community and give a speech about LGBT rights, you’re an activist. If you send out the exact same speech on Facebook, you’re a slacktivist.

One of the arguments against “slacktivism” is that it can be used to funnel resources at the wrong things; this blog post makes a good point that the Kony 2012 campaign doesn’t appear to have actually accomplished anything except profits for the filmmakers behind it. (Then again: A blog post against slacktivism? Are you sure you’re not doing right now the thing you think you are against?) But is this problem unique to slacktivism, or is it a more general phenomenon that people simply aren’t all that informed about how to have the most impact? There are an awful lot of inefficient charities out there, and in fact the most important waste of charitable funds involves people giving to their local churches. Fortunately, this is changing, as people become more secularized; churches used to account for over half of US donations, and now they only account for less than a third. (Naturally, Christian organizations are pulling out their hair over this.) The 60 million Americans who voted for Trump made a horrible mistake and will cause enormous global damage; but they weren’t slacktivists, were they?

Studies do suggest that traditionally “slacktivist” activities like Facebook likes aren’t a very strong predictor of future, larger actions, and more private modes of support (like donations and calling your Congressman) tend to be stronger predictors. But so what? In order for slacktivism to be a bad thing, they would have to be a negative predictor. They would have to substitute for more effective activism, and there’s no evidence that this happens.

In fact, there’s even some evidence that slacktivism has a positive effect (normally I wouldn’t cite Fox News, but I think in this case we should expect a bias in the opposite direction, and you can read the full Georgetown study if you want):

A study from Georgetown University in November entitled “Dynamics of Cause Engagement” looked how Americans learned about and interacted with causes and other social issues, and discovered some surprising findings on Slacktivism.

While the traditional forms of activism like donating money or volunteering far outpaces slacktivism, those who engage in social issues online are twice as likely as their traditional counterparts to volunteer and participate in events. In other words, slacktivists often graduate to full-blown activism.

At worst, most slacktivists are doing nothing for positive social change, and that’s what the vast majority of people have been doing for the entirety of human history. We can bemoan this fact, but that won’t change it. Most people are simply too uniformed to know what’s going on in the world, and too broke and too busy to do anything about it.

Indeed, slacktivism may be the one thing they can do—which is why I think it’s worth defending.

From an economist’s perspective, there’s something quite odd about how people’s objections to slacktivism are almost always formulated. The rational, sensible objection would be to their small benefits—this isn’t accomplishing enough, you should do something more effective. But in fact, almost all the objections to slacktivism I have ever read focus on their small costs—you’re not a “real activist” because you don’t make sacrifices like I do.

Yet it is a basic principle of economic rationality that, all other things equal, lower cost is better. Indeed, this is one of the few principles of economic rationality that I really do think is unassailable; perfect information is unrealistic and total selfishness makes no sense at all. But cost minimization is really very hard to argue with—why pay more, when you can pay less and get the same benefit?

From an economist’s perspective, the most important thing about an activity is its cost-effectiveness, measured either by net benefit—benefit minus cost—or rate of return—benefit divided by cost. But in both cases, a lower cost is always better; and in fact slacktivism has an astonishing rate of return, precisely because its cost is so small.

Suppose that a campaign of 10 million Facebook likes actually does have a 1% chance of changing a policy in a way that would save 10,000 lives, with a life expectancy of 50 years each. Surely this is conservative, right? I’m only giving it a 1% chance of success, on a policy with a relatively small impact (10,000 lives could be a single clause in an EPA regulatory standard), with a large number of slacktivist participants (10 million is more people than the entire population of Switzerland). Yet because clicking “like” and “share” only costs you maybe 10 seconds, we’re talking about an expected cost of (10 million)(10/86,400/365) = 0.32 QALY for an expected benefit of (10,000)(0.01)(50) = 5000 QALY. That is a rate of return of 1,500,000%—that’s 1.5 million percent.

Let’s compare this to the rate of return on donating to a top charity like UNICEF, Oxfam, the Against Malaria Foundation, or the Schistomoniasis Control Initiative, for which donating about $300 would save the life of 1 child, adding about 50 QALY. That $300 most likely cost you about 0.01 QALY (assuming an annual income of $30,000), so we’re looking at a return of 500,000%. Now, keep in mind that this is a huge rate of return, far beyond what you can ordinarily achieve, that donating $300 to UNICEF is probably one of the best things you could possibly be doing with that money—and yet slacktivism may still exceed it in efficiency. Maybe slacktivism doesn’t sound so bad after all?

Of course, the net benefit of your participation is higher in the case of donation; you yourself contribute 50 QALY instead of only contributing 0.0005 QALY. Ultimately net benefit is what matters; rate of return is a way of estimating what the net benefit would be when comparing different ways of spending the same amount of time or money. But from the figures I just calculated, it begins to seem like maybe the very best thing you could do with your time is clicking “like” and “share” on Facebook posts that will raise awareness of policies of global importance. Now, you have to include all that extra time spent poring through other Facebook posts, and consider that you may not be qualified to assess the most important issues, and there’s a lot of uncertainty involved in what sort of impact you yourself will have… but it’s almost certainly not the worst thing you could be doing with your time, and frankly running these numbers has made me feel a lot better about all the hours I have actually spent doing this sort of thing. It’s a small benefit, yes—but it’s an even smaller cost.

Indeed, the fact that so many people treat low cost as bad, when it is almost by definition good, and the fact that they also target their ire so heavily at blogging and social media, says to me that what they are really trying to accomplish here has nothing to do with actually helping people in the most efficient way possible.

Rather, it’s two things.

The obvious one is generational—it’s yet another chorus in the unending refrain that is “kids these days”. Facebook is new, therefore it is suspicious. Adults have been complaining about their descendants since time immemorial; some of the oldest written works we have are of ancient Babylonians complaining that their kids are lazy and selfish. Either human beings have been getting lazier and more selfish for thousands of years, or, you know, kids are always a bit more lazy and selfish than their parents or at least seem so from afar.

The one that’s more interesting for an economist is signaling. By complaining that other people aren’t paying enough cost for something, what you’re really doing is complaining that they aren’t signaling like you are. The costly signal has been made too cheap, so now it’s no good as a signal anymore.

“Anyone can click a button!” you say. Yes, and? Isn’t it wonderful that now anyone with a smartphone (and there are more people with access to smartphones than toilets, because #WeLiveInTheFuture) can contribute, at least in some small way, to improving the world? But if anyone can do it, then you can’t signal your status by doing it. If your goal was to make yourself look better, I can see why this would bother you; all these other people doing things that look just as good as what you do! How will you ever distinguish yourself from the riffraff now?

This is also likely what’s going on as people fret that “a college degree’s not worth anything anymore” because so many people are getting them now; well, as a signal, maybe not. But if it’s just a signal, why are we spending so much money on it? Surely we can find a more efficient way to rank people by their intellect. I thought it was supposed to be an education—in which case the meteoric rise in global college enrollments should be cause for celebration. (In reality of course a college degree can serve both roles, and it remains an open question among labor economists as to which effect is stronger and by how much. But the signaling role is almost pure waste from the perspective of social welfare; we should be trying to maximize the proportion of real value added.)

For this reason, I think I’m actually prepared to call myself a slacktivist. I aim for cost-effective awareness-raising; I want to spread the best ideas to the most people for the lowest cost. Why, would you prefer I waste more effort, to signal my own righteousness?

There is no problem of free will, just a lot of really confused people

PNRJ cognitive science, core principles, Uncategorized , , , , , , , , , , , , , , , , , , , ,

Jan 15, JDN 2457769

I was hoping for some sort of news item to use as a segue, but none in particular emerged, so I decided to go on with it anyway. I haven’t done any cognitive science posts in awhile, and this is one I’ve been meaning to write for a long time—actually it’s the sort of thing that even a remarkable number of cognitive scientists frequently get wrong, perhaps because the structure of human personality makes cognitive science inherently difficult.

Do we have free will?

The question has been asked so many times by so many people it is now a whole topic in philosophy. The Stanford Encyclopedia of Philosophy has an entire article on free will. The Information Philosopher has a gateway page “The Problem of Free Will” linking to a variety of subpages. There are even YouTube videos about “the problem of free will”.

The constant arguing back and forth about this would be problematic enough, but what really grates me are the many, many people who write “bold” articles and books about how “free will does not exist”. Examples include Sam Harris and Jerry Coyne, and have been published in everything from Psychology Today to the Chronicle of Higher Education. There’s even a TED talk.

The worst ones are those that follow with “but you should believe in it anyway”. In The Atlantic we have “Free will does not exist. But we’re better off believing in it anyway.” Scientific American offers a similar view, “Scientists say free will probably doesn’t exist, but urge: “Don’t stop believing!””

This is a mind-bogglingly stupid approach. First of all, if you want someone to believe in something, you don’t tell them it doesn’t exist. Second, if something doesn’t exist, that is generally considered a pretty compelling reason not to believe in it. You’d need a really compelling counter-argument, and frankly I’m not even sure the whole idea is logically coherent. How can I believe in something if I know it doesn’t exist? Am I supposed to delude myself somehow?

But the really sad part is that it’s totally unnecessary. There is no problem of free will. There are just an awful lot of really, really confused people. (Fortunately not everyone is confused; there are those, such as Daniel Dennett, who actually understand what’s going on.)

The most important confusion is over what you mean by the phrase “free will”. There are really two core meanings here, and the conflation of them is about 90% of the problem.

1. Moral responsibility: We have “free will” if and only if we are morally responsible for our actions.

2. Noncausality: We have “free will” if and only if our actions are not caused by the laws of nature.

Basically, every debate over “free will” boils down to someone pointing out that noncausality doesn’t exist, and then arguing that this means that moral responsibility doesn’t exist. Then someone comes back and says that moral responsibility does exist, and then infers that this means noncausality must exist. Or someone points out that noncausality doesn’t exist, and then they realize how horrible it would be if moral responsibility didn’t exist, and then tells people they should go on believing in noncausality so that they don’t have to give up moral responsibility.

Let me be absolutely clear here: Noncausality could not possibly exist.

Noncausality isn’t even a coherent concept. Actions, insofar as they are actions, must, necessarily, by definition, be caused by the laws of nature.

I can sort of imagine an event not being caused; perhaps virtual electron-positron pairs can really pop into existence without ever being caused. (Even then I’m not entirely convinced; I think quantum mechanics might actually be deterministic at the most fundamental level.)

But an action isn’t just a particle popping into existence. It requires the coordinated behavior of some 10^26 or more particles, all in a precisely organized, unified way, structured so as to move some other similarly large quantity of particles through space in a precise way so as to change the universe from one state to another state according to some system of objectives. Typically, it involves human muscles intervening on human beings or inanimate objects. (Recently it has come to mean specifically human fingers on computer keyboards a rather large segment of the time!) If what you do is an action—not a muscle spasm, not a seizure, not a slip or a trip, but something you did on purpose—then it must be caused. And if something is caused, it must be caused according to the laws of nature, because the laws of nature are the laws underlying all causality in the universe!

And once you realize that, the “problem of free will” should strike you as one of the stupidest “problems” ever proposed. Of course our actions are caused by the laws of nature! Why in the world would you think otherwise?

If you think that noncausality is necessary—or even useful—for free will, what kind of universe do you think you live in? What kind of universe could someone live in, that would fit your idea of what free will is supposed to be?

It’s like I said in that much earlier post about The Basic Fact of Cognitive Science (we are our brains): If you don’t think a mind can be made of matter, what do you think minds are made of? What sort of magical invisible fairy dust would satisfy you? If you can’t even imagine something that would satisfy the constraints you’ve imposed, did it maybe occur to you that your constraints are too strong?

Noncausality isn’t worth fretting over for the same reason that you shouldn’t fret over the fact that pi is irrational and you can’t make a square circle. There is no possible universe in which that isn’t true. So if it bothers you, it’s not that there’s something wrong with the universe—it’s clearly that there’s something wrong with you. Your thinking on the matter must be too confused, too dependent on unquestioned intuitions, if you think that murder can’t be wrong unless 2+2=5.

In philosophical jargon I am called a “compatibilist” because I maintain that free will and determinism are “compatible”. But this is much too weak a term. I much prefer Eleizer Yudkowsky’s “requiredism”, which he explains in one of the greatest blog posts of all time (seriously, read it immediately if you haven’t before—I’m okay with you cutting off my blog post here and reading his instead, because it truly is that brilliant), entitled simply “Thou Art Physics”. This quote sums it up briefly:

My position might perhaps be called “Requiredism.” When agency, choice, control, and moral responsibility are cashed out in a sensible way, they require determinism—at least some patches of determinism within the universe. If you choose, and plan, and act, and bring some future into being, in accordance with your desire, then all this requires a lawful sort of reality; you cannot do it amid utter chaos. There must be order over at least over those parts of reality that are being controlled by you. You are within physics, and so you/physics have determined the future. If it were not determined by physics, it could not be determined by you.

Free will requires a certain minimum level of determinism in the universe, because the universe must be orderly enough that actions make sense and there isn’t simply an endless succession of random events. Call me a “requiredist” if you need to call me something. I’d prefer you just realize the whole debate is silly because moral responsibility exists and noncausality couldn’t possibly.

We could of course use different terms besides “free will”. “Moral responsibility” is certainly a good one, but it is missing one key piece, which is the issue of why we can assign moral responsibility to human beings and a few other entities (animals, perhaps robots) and not to the vast majority of entities (trees, rocks, planets, tables), and why we are sometimes willing to say that even a human being does not have moral responsibility (infancy, duress, impairment).

This is why my favored term is actually “rational volition”. The characteristic that human beings have (at least most of us, most of the time), which also many animals and possibly some robots share (if not now, then soon enough), which justifies our moral responsibility is precisely our capacity to reason. Things don’t just happen to us the way they do to some 99.999,999,999% of the universe; we do things. We experience the world through our senses, have goals we want to achieve, and act in ways that are planned to make the world move closer to achieving those goals. We have causes, sure enough; but not just any causes. We have a specific class of causes, which are related to our desires and intentions—we call these causes reasons.

So if you want to say that we don’t have “free will” because that implies some mysterious nonsensical noncausality, sure; that’s fine. But then don’t go telling us that this means we don’t have moral responsibility, or that we should somehow try to delude ourselves into believing otherwise in order to preserve moral responsibility. Just recognize that we do have rational volition.

How do I know we have rational volition? That’s the best part, really: Experiments. While you’re off in la-la land imagining fanciful universes where somehow causes aren’t really causes even though they are, I can point to not only centuries of human experience but decades of direct, controlled experiments in operant conditioning. Human beings and most other animals behave quite differently in behavioral experiments than, say, plants or coffee tables. Indeed, it is precisely because of this radical difference that it seems foolish to even speak of a “behavioral experiment” about coffee tables—because coffee tables don’t behave, they just are. Coffee tables don’t learn. They don’t decide. They don’t plan or consider or hope or seek.

Japanese, as it turns out, may be a uniquely good language for cognitive science, because it has two fundamentally different verbs for “to be” depending on whether an entity is sentient. Humans and animals imasu, while inanimate objects merely arimasu. We have free will because and insofar as we imasu.

Once you get past that most basic confusion of moral responsibility with noncausality, there are a few other confusions you might run into as well. Another one is two senses of “reductionism”, which Dennett refers to as “ordinary” and “greedy”:

1. Ordinary reductionism: All systems in the universe are ultimately made up of components that always and everywhere obey the laws of nature.

2. Greedy reductionism: All systems in the universe just are their components, and have no existence, structure, or meaning aside from those components.

I actually had trouble formulating greedy reductionism as a coherent statement, because it’s such a nonsensical notion. Does anyone really think that a pile of two-by-fours is the same thing as a house? But people do speak as though they think this about human brains, when they say that “love is just dopamine” or “happiness is just serotonin”. But dopamine in a petri dish isn’t love, any more than a pile of two-by-fours is a house; and what I really can’t quite grok is why anyone would think otherwise.

Maybe they’re simply too baffled by the fact that love is made of dopamine (among other things)? They can’t quite visualize how that would work (nor can I, nor, I think, can anyone in the world at this level of scientific knowledge). You can see how the two-by-fours get nailed together and assembled into the house, but you can’t see how dopamine and action potentials would somehow combine into love.

But isn’t that a reason to say that love isn’t the same thing as dopamine, rather than that it is? I can understand why some people are still dualists who think that consciousness is somehow separate from the functioning of the brain. That’s wrong—totally, utterly, ridiculously wrong—but I can at least appreciate the intuition that underlies it. What I can’t quite grasp is why someone would go so far the other way and say that the consciousness they are currently experiencing does not exist.

Another thing that might confuse people is the fact that minds, as far as we know, are platform independent—that is, your mind could most likely be created out of a variety of different materials, from the gelatinous brain it currently is to some sort of silicon supercomputer, to perhaps something even more exotic. This independence follows from the widely-believed Church-Turing thesis, which essentially says that all computation is computation, regardless of how it is done. This may not actually be right, but I see many reasons to think that it is, and if so, this means that minds aren’t really what they are made of at all—they could be made of lots of things. What makes a mind a mind is how it is structured and above all what it does.

If this is baffling to you, let me show you how platform-independence works on a much simpler concept: Tables. Tables are also in fact platform-independent. You can make a table out of wood, or steel, or plastic, or ice, or bone. You could take out literally every single atom of a table and replace it will a completely different atom of a completely different element—carbon for iron, for example—and still end up with a table. You could conceivably even do so without changing the table’s weight, strength, size, etc., though that would be considerably more difficult.
Does this mean that tables somehow exist “beyond” their constituent matter? In some very basic sense, I suppose so—they are, again, platform-independent. But not in any deep, mysterious sense. Start with a wooden table, take away all the wood, and you no longer have a table. Take apart the table and you have a bunch of wood, which you could use to build something else. There is no “essence” comprising the table. There is no “table soul” that would persist when the table is deconstructed.

And—now for the hard part—so it is with minds. Your mind is your brain. The constituent atoms of your brain are gradually being replaced, day by day, but your mind is the same, because it exists in the arrangement and behavior, not the atoms themselves. Yet there is nothing “extra” or “beyond” that makes up your mind. You have no “soul” that lies beyond your brain. If your brain is destroyed, your mind will also be destroyed. If your brain could be copied, your mind would also be copied. And one day it may even be possible to construct your mind in some other medium—some complex computer made of silicon and tantalum, most likely—and it would still be a mind, and in all its thoughts, feelings and behaviors your mind, if not numerically identical to you.

Thus, when we engage in rational volition—when we use our “free will” if you like that term—there is no special “extra” process beyond what’s going on in our brains, but there doesn’t have to be. Those particular configurations of action potentials and neurotransmitters are our thoughts, desires, plans, intentions, hopes, fears, goals, beliefs. These mental concepts are not in addition to the physical material; they are made of that physical material. Your soul is made of gelatin.

Again, this is not some deep mystery. There is no “paradox” here. We don’t actually know the details of how it works, but that makes this no different from a Homo erectus who doesn’t know how fire works. Maybe he thinks there needs to be some extra “fire soul” that makes it burn, but we know better; and in far fewer centuries than separate that Homo erectus from us, our descendants will know precisely how the brain creates the mind.

Until then, simply remember that any mystery here lies in us—in our ignorance—and not in the universe. And take heart that the kind of “free will” that matters—moral responsibility—has absolutely no need for the kind of “free will” that doesn’t exist—noncausality. They’re totally different things.

The real crisis in education is access, not debt

PNRJ current events, ethics, public policy , , , , , , , , , , , , , ,

Jan 8, JDN 2457762

A few weeks ago I tried to provide assurances that the “student debt crisis” is really not much of a crisis; there is a lot of debt, but it is being spent on a very good investment both for individuals and for society. Student debt is not that large in the scheme of things, and it more than pays for itself in the long run.

But this does not mean we are not in the midst of an education crisis. It’s simply not about debt.

The crisis I’m worried about involves access.

As you may recall, there are a substantial number of people with very small amounts of student debt, and they tend to be the most likely to default. The highest default rates are among the group of people with student debt greater than $0 but less than $5000.

So how is it that there are people with only $5,000 in student debt anyway? You can’t buy much college for $5,000 these days, as tuition prices have risen at an enormous rate: From 1983 to 2013, in inflation-adjusted dollars, average annual tuition rose from $7,286 at public institutions and $17,333 at private institutions to $15,640 at public institutions and $35,987 at private institutions—more than doubling in each case.

Enrollments are much higher, but this by itself should not raise tuition per student. So where is all the extra money going? Some of it is due to increases in public funding that have failed to keep up with higher enrollments; but a lot of it just seems to be going to higher pay for administrators and athletic coaches. This is definitely a problem; students should not be forced to subsidize the millions of dollars most universities lose on funding athletics—the NCAA, who if anything are surely biased in favor of athletics, found that the total net loss due to athletics spending at FBS universities was $17 million per year. Only a handful of schools actually turn a profit on athletics, all of them Division I. So it might be fair to speak of an “irresponsible college administration crisis”, administrators who heap wealth upon themselves and their beloved athletic programs while students struggle to pay their bills, or even a “college tuition crisis” where tuition keeps rising far beyond what is sustainable. But that’s not the same thing as a “student debt crisis”—just as the mortgage crisis we had in 2008 is distinct from the slow-burning housing price crisis we’ve been in since the 1980s. Making restrictions on mortgages tighter might prevent banks from being as predatory as they have been lately, but it won’t suddenly allow people to better afford houses.

And likewise, I’m much more worried about students who don’t go to college because they are afraid of this so-called “debt crisis”; they’re going to end up much worse off. As Eduardo Porter put it in the New York Times:

And yet Mr. Beltrán says he probably wouldn’t have gone to college full time if he hadn’t received a Pell grant and financial aid from New York State to defray the costs. He has also heard too many stories about people struggling under an unbearable burden of student loans to even consider going into debt. “Honestly, I don’t think I would have gone,” he said. “I couldn’t have done four years.”

And that would have been the wrong decision.

His reasoning is not unusual. The rising cost of college looms like an insurmountable obstacle for many low-income Americans hoping to get a higher education. The notion of a college education becoming a financial albatross around the neck of the nation’s youth is a growing meme across the culture. Some education experts now advise high school graduates that a college education may not be such a good investment after all. “Sticker price matters a lot,” said Lawrence Katz, a professor of Harvard University. “It is a deterrent.”

 

[…]

 

And the most perplexing part of this accounting is that regardless of cost, getting a degree is the best financial decision a young American can make.

According to the O.E.C.D.’s report, a college degree is worth $365,000 for the average American man after subtracting all its direct and indirect costs over a lifetime. For women — who still tend to earn less than men — it’s worth $185,000.

College graduates have higher employment rates and make more money. According to the O.E.C.D., a typical graduate from a four-year college earns 84 percent more than a high school graduate. A graduate from a community college makes 16 percent more.

A college education is more profitable in the United States than in pretty much every other advanced nation. Only Irish women get more for the investment: $185,960 net.

So, these students who have $5,000 or less in student debt; what does that mean? That amount couldn’t even pay for a single year at most universities, so how did that happen?

Well, they almost certainly went to community college; only a community college could provide you with a nontrivial amount of education for less than $5,000. But community colleges vary tremendously in their quality, and some have truly terrible matriculation rates. While most students who start at a four-year school do eventually get a bachelor’s degree (57% at public schools, 78% at private schools), only 17% of students who start at community college do. And once students drop out, they very rarely actually return to complete a degree.

Indeed, the only way to really have that little student debt is to drop out quickly. Most students who drop out do so chiefly for reasons that really aren’t all that surprising: Mostly, they can’t afford to pay their bills. “Unable to balance school and work” is the number 1 reported reason why students drop out of college.

In the American system, student loans are only designed to pay the direct expenses of education; they often don’t cover the real costs of housing, food, transportation and healthcare, and even when they do, they basically never cover the opportunity cost of education—the money you could be making if you were working full-time instead of going to college. For many poor students, simply breaking even on their own expenses isn’t good enough; they have families that need to be taken care of, and that means working full-time. Many of them even need to provide for their parents or grandparents who may be poor or disabled. Yet in the US system it is tacitly assumed that your parents will help you—so when you need to help them, what are you supposed to do? You give up on college and you get a job.

The most successful reforms for solving this problem have been comprehensive; they involved working to support students directly and intensively in all aspects of their lives, not just the direct financial costs of school itself.

Another option would be to do something more like what they do in Sweden, where there is also a lot of student debt, but for a very different reason. The direct cost of college is paid automatically by the government. Yet essentially all Swedish students have student debt, and total student debt in Sweden is much larger than other European countries and comparable to the United States; why? Because Sweden understands that you should also provide for the opportunity cost. In Sweden, students live fully self-sufficient on student loans, just as if they were working full-time. They are not expected to be supported by their parents.

The problem with American student loans, then, is not that they are too large—but that they are too small. They don’t provide for what students actually need, and thus don’t allow them to make the large investment in their education that would have paid off in the long run. Panic over student loans being too large could make the problem worse, if it causes us to reduce the amount of loanable funds available for students.

The lack of support for poor students isn’t the only problem. There are also huge barriers to education in the US based upon race. While Asian students do as well (if not better) than White students, Black and Latino students have substantially lower levels of educational attainment. Affirmative action programs can reduce these disparities, but they are unpopular and widely regarded as unfair, and not entirely without reason.

A better option—indeed one that should be a no-brainer in my opinion—is not to create counter-biases in favor of Black and Latino students (which is what affirmative action is), but to eliminate biases in favor of White students that we know exist. Chief among these are so-called “legacy admissions”, in which elite universities attract wealthy alumni donors by granting their children admission and funding regardless of whether they even remotely deserve it or would contribute anything academically to the university.

These “legacy admissions” are frankly un-American. They go against everything our nation supposedly stands for; in fact, they reek of feudalism. And unsurprisingly, they bias heavily in favor of White students—indeed, over 90 percent of legacy admits are White and Protestant. Athletic admissions are also contrary to the stated mission of the university, though their racial biases are more complicated (Black students are highly overrepresented in football and basketball admits, for example) and it is at least not inherently un-American to select students based upon their athletic talent as opposed to their academic talent.

But this by itself would not be enough; the gaps are clearly too large to close that way. Getting into college is only the start, and graduation rates are much worse for Black students than White students. Moreover, the education gap begins well before college—high school dropout rates are much higher among Black and Latino studentsas well.

In fact, even closing the education gap by itself would not be enough; racial biases permeate our whole society. Black individuals with college degrees are substantially more likely to be unemployed and have substantially lower wages on average than White individuals with college degrees—indeed, a bachelor’s degree gets a Black man a lower mean wage than a White man would get with only an associate’s degree.

Fortunately, the barriers against women in college education have largely been conquered. In fact, there are now more women in US undergraduate institutions than men. This is not to say that there are not barriers against women in society at large; women still make about 75% as much income as men on average, and even once you adjust for factors such as education and career choice they still only make about 95% as much. Moreover, these factors we’re controlling for are endogenous. Women don’t choose their careers in a vacuum, they choose them based upon a variety of social and cultural pressures. The fact that 93% of auto mechanics are men and 79% of clerical workers are women might reflect innate differences in preferences—but it could just as well reflect a variety of cultural biases or even outright discrimination. Quite likely, it’s some combination of these. So it is not obvious to me that the “adjusted” wage gap is actually a more accurate reflection of the treatment of women in our society than the “unadjusted” wage gap; the true level of bias is most likely somewhere in between the two figures.

Gender wage gaps vary substantially across age groups and between even quite similar countries: Middle-aged women in Germany make 28% less than middle-aged men, while in France that gap is only 19%. Young women in Latvia make 14% less than young men, but in Romania they make 1.1% more. This variation clearly shows that this is not purely the effect of some innate genetic difference in skills or preferences; it must be at least in large part the product of cultural pressures or policy choices.

Even within academia, women are less likely to be hired full-time instead of part-time, awarded tenure, or promoted to administrative positions. Moreover, this must be active discrimination in some form, because gaps in hiring and wage offers between men and women persist in randomized controlled experiments. You can literally present the exact same resume and get a different result depending on whether you attached a male name or a female name.

But at least when it comes to the particular question of getting bachelor’s degrees, we have achieved something approaching equality across gender, and that is no minor accomplishment. Most countries in the world still have more men than women graduating from college, and in some countries the difference is terrifyingly large. I found from World Bank data that in the Democratic Republic of Congo, only 3% of men go to college—and less than 1% of women do. Even in Germany, 29% of men graduate from college but only 19% of women do. Getting both of these figures over 30% and actually having women higher than men is a substantial achievement for which the United States should be proud.

Yet it still remains the case that Americans who are poor, Black, Native American, or Latino are substantially less likely to ever make it through college. Panic about student debt might well be making this problem worse, as someone whose family makes $15,000 per year is bound to hear $50,000 in debt as an overwhelming burden, even as you try to explain that it will eventually pay for itself seven times over.

We need to instead be talking about the barriers that are keeping people from attending college, and pressuring them to drop out once they do. Debt is not the problem. Even tuition is not really the problem. Access is the problem. College is an astonishingly good investment—but most people never get the chance to make it. That is what we need to change.

Why New Year’s resolutions fail

PNRJ cognitive science, heuristics and biases, Uncategorized , , , , , , , , , ,

Jan 1, JDN 2457755

Last week’s post was on Christmas, so by construction this week’s post will be on New Year’s Day.

It is a tradition in many cultures, especially in the US and Europe, to start every new year with a New Year’s resolution, a promise to ourselves to change our behavior in some positive way.

Yet, over 80% of these resolutions fail. Why is this?

If we are honest, most of us would agree that there is something about our own behavior that could stand to be improved. So why do we so rarely succeed in actually making such improvements?

One possibility, which I’m guessing most neoclassical economists would favor, is to say that we don’t actually want to. We may pretend that we do in order to appease others, but ultimately our rational optimization has already chosen that we won’t actually bear the cost to make the improvement.

I think this is actually quite rare. I’ve seen too many people with resolutions they didn’t share with anyone, for example, to think that it’s all about social pressure. And I’ve seen far too many people try very hard to achieve their resolutions, day after day, and yet still fail.

Sometimes we make resolutions that are not entirely within our control, such as “get a better job” or “find a girlfriend” (last year I made a resolution to publish a work of commercial fiction or a peer-reviewed article—and alas, failed at that task, unless I somehow manage it in the next few days). Such resolutions may actually be unwise to make in the first place, as it can feel like breaking a promise to yourself when you’ve actually done all you possibly could.

So let’s set those aside and talk only about things we should be in control over, like “lose weight” or “save more money”. Even these kinds of resolutions typically fail; why? What is this “weakness of will”? How is it possible to really want something that you are in full control over, and yet still fail to accomplish it?

Well, first of all, I should be clear what I mean by “in full control over”. In some sense you’re not in full control, which is exactly the problem. Your conscious mind is not actually an absolute tyrant over your entire body; you’re more like an elected president who has to deal with a legislature in order to enact policy.

You do have a great deal of power over your own behavior, and you can learn to improve this control (much as real executive power in presidential democracies has expanded over the last century!); but there are fundamental limits to just how well you can actually consciously will your body to do anything, limits imposed by billions of years of evolution that established most of the traits of your body and nervous system millions of generations before there even was such a thing as rational conscious reasoning.

One thing that makes a surprisingly large difference lies in whether your goals are reduced to specific, actionable objectives. “Lose weight” is almost guaranteed to fail. “Lose 30 pounds” is still unlikely to succeed. “Work out for 2 hours per week,” on the other hand, might have a chance. “Save money” is never going to make it, but “move to a smaller apartment and set aside $200 per month” just might.

I think the government metaphor is helpful here; if you President of the United States and you want something done, do you state some vague, broad goal like “Improve the economy”? No, you make a specific, actionable demand that allows you to enforce compliance, like “increase infrastructure spending by 24% over the next 5 years”. Even then it is possible to fail if you can’t push it through the legislature (in the metaphor, the “legislature” is your habits, instincts and other subconscious processes), but you’re much more likely to succeed if you have a detailed plan.

Another technique that helps is to visualize the benefits of succeeding and the costs of failing, and keep these in your mind. This counteracts the tendency for the costs of succeeding and the benefits of giving up to be more salient—losing 30 pounds sounds nice in theory, but that treadmill is so much work right now!

This salience effect has a lot to do with the fact that human beings are terrible at dealing with the future.

Rationally, we are supposed to use exponential discounting; each successive moment is supposed to be worth less to us than the previous by a fixed proportion, say 5% per year. This is actually a mathematical theorem; if you don’t discount this way, your decisions will be systematically irrational.

And yet… we don’t discount that way. Some behavioral economists argue that we use hyperbolic discounting, in which instead of discounting time by a fixed proportion, we use a different formula that drops off too quickly early on and not quickly enough later on.

But I am increasingly convinced that human beings don’t actually use discounting at all. We have a series of rough-and-ready heuristics for making future judgments, which can sort of act like discounting, but require far less computation than actually calculating a proper discount rate. (Recent empirical evidence seems to be tilting this direction.)

In any case, whatever we do is clearly not a proper rational discount rate. And this means that our behavior can be time-inconsistent; a choice that seems rational at one time can not seem rational at a later time. When we’re planning out our year and saying we will hit the treadmill more, it seems like a good idea; but when we actually get to the gym and feel our legs ache as we start running, we begin to regret our decision.

The challenge, really, is determining which “version” of us is correct! A priori, we don’t actually know whether the view of our distant self contemplating the future or the view of our current self making the choice in the moment is the right one. Actually, when I frame it this way, it almost seems like the self that’s closer to the choice should have better information—and yet typically we think the exact opposite, that it is our past self making plans that really knows what’s best for us.

So where does that come from? Why do we think, at least in most cases, that the “me” which makes a plan a year in advance is the smart one, and the “me” that actually decides in the moment is untrustworthy.

Kahneman has a good explanation for this, in his model of System 1 and System 2. System 1 is simple and fast, but often gets the wrong answer. System 2 usually gets the right answer, but it is complex and slow. When we are making plans, we have a lot of time to think, and we can afford to expend the extra effort to engage the full power of System 2. But when we are living in the moment, choosing what to do right now, we don’t have that luxury of time, and we are forced to fall back on System 1. System 1 is easier—but it’s also much more likely to be wrong.

How, then, do we resolve this conflict? Commitment. (Perhaps that’s why it’s called a New Year’s resolution!)

We make promises to ourselves, commitments that we will feel bad about not following through.

If we rationally discounted, this would be a baffling thing to do; we’re just imposing costs on ourselves for no reason. But because we don’t discount rationally, commitments allow us to change the calculation for our future selves.

This brings me to one last strategy to use when making your resolutions: Include punishment.

“I will work out at least 2 hours per week, and if I don’t, I’m not allowed to watch TV all weekend.” Now that is a resolution you are actually likely to keep.

To see why, consider the decision problem for your System 2 self today versus your System 1 self throughout the year.

Your System 2 self has done the cost-benefit analysis and ruled that working out 2 hours per week is worthwhile for its health benefits.

If you left it at that, your System 1 self would each day find an excuse to procrastinate the workouts, because at least from where they’re sitting, working out for 2 hours looks a lot more painful than the marginal loss in health from missing just this one week. And of course this will keep happening, week after week—and then 52 go by and you’ve had few if any workouts.

But by adding the punishment of “no TV”, you have imposed an additional cost on your System 1 self, something that they care about. Suddenly the calculation changes; it’s not just 2 hours of workout weighed against vague long-run health benefits, but 2 hours of workout weighed against no TV all weekend. That punishment is surely too much to bear; so you’d best do the workout after all.

Do it right, and you will rarely if ever have to impose the punishment. But don’t make it too large, or then it will seem unreasonable and you won’t want to enforce it if you ever actually need to. Your System 1 self will then know this, and treat the punishment as nonexistent. (Formally the equilibrium is not subgame perfect; I am gravely concerned that our nuclear deterrence policy suffers from precisely this flaw.) “If I don’t work out, I’ll kill myself” is a recipe for depression, not healthy exercise habits.

But if you set clear, actionable objectives and sufficient but reasonable punishments, there’s at least a good chance you will actually be in the minority of people who actually succeed in keeping their New Year’s resolution.

And if not, there’s always next year.

The game theory of holidays

PNRJ cognitive science, core principles , , , , , , , ,

Dec 25, JDN 2457748

When this post goes live, it will be Christmas; so I felt I should make the topic somehow involve the subject of Christmas, or holidays in general.

I decided I would pull back for as much perspective as possible, and ask this question: Why do we have holidays in the first place?

All human cultures have holidays, but not the same ones. Cultures with a lot of mutual contact will tend to synchronize their holidays temporally, but still often preserve wildly different rituals on those same holidays. Yes, we celebrate “Christmas” in both the US and in Austria; but I think they are baffled by the Elf on the Shelf and I know that I find the Krampus bizarre and terrifying.

Most cultures from temperate climates have some sort of celebration around the winter solstice, probably because this is an ecologically important time for us. Our food production is about to get much, much lower, so we’d better make sure we have sufficient quantities stored. (In an era of globalization and processed food that lasts for months, this is less important, of course.) But they aren’t the same celebration, and they generally aren’t exactly on the solstice.

What is a holiday, anyway? We all get off work, we visit our families, and we go through a series of ritualized actions with some sort of symbolic cultural meaning. Why do we do this?

First, why not work all year round? Wouldn’t that be more efficient? Well, no, because human beings are subject to exhaustion. We need to rest at least sometimes.

Well, why not simply have each person rest whenever they need to? Well, how do we know they need to? Do we just take their word for it? People might exaggerate their need for rest in order to shirk their duties and free-ride on the work of others.

It would help if we could have pre-scheduled rest times, to remove individual discretion.

Should we have these at the same time for everyone, or at different times for each person?

Well, from the perspective of efficiency, different times for each person would probably make the most sense. We could trade off work in shifts that way, and ensure production keeps moving. So why don’t we do that?
Well, now we get to the game theory part. Do you want to be the only one who gets today off? Or do you want other people to get today off as well?

You probably want other people to be off work today as well, at least your family and friends so that you can spend time with them. In fact, this is probably more important to you than having any particular day off.

We can write this as a normal-form game. Suppose we have four days to choose from, 1 through 4, and two people, who can each decide which day to take off, or they can not take a day off at all. They each get a payoff of 1 if they take the same day off, 0 if they take different days off, and -1 if they don’t take a day off at all. This is our resulting payoff matrix:

1 2 3 4 None
1 1/1 0/0 0/0 0/0 0/-1
2 0/0 1/1 0/0 0/0 0/-1
3 0/0 0/0 1/1 0/0 0/-1
4 0/0 0/0 0/0 1/1 0/-1
None -1/0 -1/0 -1/0 -1/0 -1/-1

 

It’s pretty obvious that each person will take some day off. But which day? How do they decide that?
This is what we call a coordination game; there are many possible equilibria to choose from, and the payoffs are highest if people can somehow coordinate their behavior.

If they can actually coordinate directly, it’s simple; one person should just suggest a day, and since the other one is indifferent, they have no reason not to agree to that day. From that point forward, they have coordinated on a equilibrium (a Nash equilibrium, in point of fact).

But suppose they can’t talk to each other, or suppose there aren’t two people to coordinate but dozens, or hundreds—or even thousands, once you include all the interlocking social networks. How could they find a way to coordinate on the same day?

They need something more intuitive, some “obvious” choice that they can call upon that they hope everyone else will as well. Even if they can’t communicate, as long as they can observe whether their coordination has succeeded or failed they can try to set these “obvious” choices by successive trial and error.

The result is what we call a Schelling point; players converge on this equilibrium not because there’s actually anything better about it, but because it seems obvious and they expect everyone else to think it will also seem obvious.

This is what I think is happening with holidays. Yes, we make up stories to justify them, or sometimes even have genuine reasons for them (Independence Day actually makes sense being on July 4, for instance), but the ultimate reason why we have a holiday on one day rather than other is that we had to have it some time, and this was a way of breaking the deadlock and finally setting a date.

In fact, weekends are probably a more optimal solution to this coordination problem than holidays, because human beings need rest on a fairly regular basis, not just every few months. Holiday seasons now serve more as an opportunity to have long vacations that allow travel, rather than as a rest between work days. But even those we had to originally justify as a matter of religion: Jews would not work on Saturday, Christians would not work on Sunday, so together we will not work on Saturday or Sunday. The logic here is hardly impeccable (why not make it religion-specific, for example?), but it was enough to give us a Schelling point.

This makes me wonder about what it would take to create a new holiday. How could we actually get people to celebrate Darwin Day or Sagan Day on a large scale, for example? Darwin and Sagan are both a lot more worth celebrating than most of the people who get holidays—Columbus especially leaps to mind. But even among those of us who really love Darwin and Sagan, these are sort of half-hearted celebrations that never attain the same status as Easter, much less Thanksgiving or Christmas.

I’d also like to secularize—or at least ecumenicalize—the winter solstice celebration. Christianity shouldn’t have a monopoly on what is really something like a human universal, or at least a “humans who live in temperate climates” universal. It really isn’t Christmas anyway; most of what we do is celebrating Yule, compounded by a modern expression in mass consumption that is thoroughly borne of modern capitalism. We have no reason to think Jesus was actually born in December, much less on the 25th. But that’s around the time when lots of other celebrations were going on anyway, and it’s much easier to convince people that they should change the name of their holiday than that they should stop celebrating it and start celebrating something else—I think precisely because that still preserves the Schelling point.

Creating holidays has obviously been done before—indeed it is literally the only way holidays ever come into existence. But part of their structure seems to be that the more transparent the reasons for choosing that date and those rituals, the more empty and insincere the holiday seems. Once you admit that this is an arbitrary choice meant to converge an equilibrium, it stops seeming like a good choice anymore.

Now, if we could find dates and rituals that really had good reasons behind them, we could probably escape that; but I’m not entirely sure we can. We can use Darwin’s birthday—but why not the first edition publication of On the Origin of Species? And Darwin himself is really that important, but why Sagan Day and not Einstein Day or Niels Bohr Day… and so on? The winter solstice itself is a very powerful choice; its deep astronomical and ecological significance might actually make it a strong enough attractor to defeat all contenders. But what do we do on the winter solstice celebration? What rituals best capture the feelings we are trying to express, and how do we defend those rituals against criticism and competition?

In the long run, I think what usually happens is that people just sort of start doing something, and eventually enough people are doing it that it becomes a tradition. Maybe it always feels awkward and insincere at first. Maybe you have to be prepared for it to change into something radically different as the decades roll on.

This year the winter solstice is on December 21st. I think I’ll be lighting a candle and gazing into the night sky, reflecting on our place in the universe. Unless you’re reading this on Patreon, by the time this goes live, you’ll have missed it; but you can try later, or maybe next year.

In fifty years all the cool kids will be doing it, I’m sure.

Student debt crisis? What student debt crisis?

PNRJ development economics, public policy , , , , , , , , , ,

Dec 18, JDN 2457741
As of this writing, I have over $99,000 in student loans. This is a good thing. It means that I was able to pay for my four years of college, and two years of a master’s program, in order to be able to start this coming five years of a PhD. When I have concluded these eleven years of postgraduate education and incurred six times the world per-capita income in debt, what then will become of me? Will I be left to live on the streets, destitute and overwhelmed by debt?

No. I’ll have a PhD. The average lifetime income of individuals with PhDs in the United States is $3.4 million. Indeed, the median annual income for economists in the US is almost exactly what I currently owe in debt—so if I save well, I could very well pay it off in just a few years. With an advanced degree in economics like mine, or similarly high-paying fields such as physics, medicine, and law one can expect the higher end of that scale, $4 million or more; with a degree in a less-lucrative field such as art, literature, history, or philosophy, one would have to settle for “only” say $3 million. The average lifetime income in the US for someone without any college education is only $1.2 million. So even in literature or history, a PhD is worth about $2 million in future income.

On average, an additional year of college results in a gain in lifetime future earnings of about 15% to 20%. Even when you adjust for interest rates and temporal discounting, this is a rate of return that would make any stock trader envious.

Fitting the law of diminishing returns, the rates of return on education in poor countries are even larger, often mind-bogglingly huge; the increase in lifetime income from a year of college education in Botswana was estimated at 38%. This implies that someone who graduates from college in Botswana earns four times as much money as someone who only finished high school.

We who pay $100,000 to receive an additional $2 to $3 million can hardly be called unfortunate.

Indeed, we are mind-bogglingly fortunate; we have been given an opportunity to better ourselves and the society we live in that is all but unprecedented in human history granted only to a privileged few even today. Right now, only about half of adults in the most educated countries in the world (Canada, Russia, Israel, Japan, Luxembourg, South Korea, and the United States) ever go to college. Only 30% of Americans ever earn a bachelor’s degree, and as recently as 1975 that figure was only 20%. Worldwide, the majority of people never graduate from high school. The average length of schooling in developing countries today is six years—that is, sixth grade—and this is an enormous improvement from the two years of average schooling found in developing countries in 1950.

If we look a bit further back in history, the improvements in education are even more staggering. In the United States in 1910, only 13.5% of people graduated high school, and only 2.7% completed a bachelor’s degree. There was no student debt crisis then, to be sure—because there were no college students.

Indeed, I have been underestimating the benefits of education thus far, because education is both a public and private good. The figures I’ve just given have been only the private financial return on education—the additional income received by an individual because they went to college. But there is also a non-financial return, such as the benefits of working in a more appealing or exciting career and the benefits of learning for its own sake. The reason so many people do go into history and literature instead of economics and physics very likely has to do with valuing these other aspects of education as highly as or even more highly than financial income, and it is entirely rational for people to do so. (An interesting survey question I’ve alas never seen asked: “How much money would we have to give you right now to convince you to quit working in philosophy for the rest of your life?”)

Yet even more important is the public return on education, the increased productivity and prosperity of our society as a result of greater education—and these returns are enormous. For every $1 spent on education in the US, the economy grows by an estimated $1.50. Public returns on college education worldwide are on the order of 10%-20% per year of education. This is over and above the 15-20% return already being made by the individuals going to school. This means that raising the average level of education in a country by just one year raises that country’s income by between 25% and 40%.

Indeed, perhaps the simplest way to understand the enormous social benefits of education is to note the strong correlation between education level and income level. This graph comes from the UN Human Development Report Data Explorer; it plots the HDI education index (which ranges from 0, least educated, to 1, most educated) and the per-capita GDP at purchasing power parity (on a log scale, so that each increment corresponds to a proportional increase in GDP); as you can see, educated countries tend to be rich countries, and vice-versa.

hdi_education_income_labeled

Of course, income drives education just as education drives income. But more detailed econometric studies generally (though not without some controversy) show the same basic result: The more educated a country’s people become, the richer that country becomes.

And indeed, the United States is a spectacularly rich country. The figure of “$1 trillion in college debt” sounds alarming (and has been used to such effect in many a news article, ranging from the New York Daily News, Slate, and POLITICO to USA Today and CNN all the way to Bloomberg, MarketWatch, and Business Insider, and even getting support from the Consumer Financial Protection Bureau and The Federal Reserve Bank of New York).

But the United States has a total GDP of over $18.6 trillion, and total net wealth somewhere around $84 trillion. Is it really so alarming that our nation’s most important investment would result in debt of less than two percent of our total nation’s wealth? Democracy Now asks who is getting rich off of $1.3 trillion in student debt? All of us—the students especially.

In fact, the probability of defaulting on student loans is inversely proportional to the amount of loans a student has. Students with over $100,000 in student debt default only 18% of the time, while students with less than $5,000 in student debt default 34% of the time. This should be shocking to those who think that we have a crisis of too much student debt; if student debt were an excess burden that is imposed upon us for little gain, default rates should rise as borrowing amounts increase, as we observe, for example, with credit cards: there is a positive correlation between carrying higher balances and being more likely to default. (This also raises doubts about the argument that higher debt loads should carry higher interest rates—why, if the default rate doesn’t go up?) But it makes perfect sense if you realize that college is an investment—indeed, almost certainly both the most profitable and the most socially responsible investment most people will ever have the opportunity to make. More debt means you had access to more credit to make a larger investment—and therefore your payoff was greater and you were more likely to be able to repay the debt.

Yes, job prospects were bad for college graduates right after the Great Recession—because it was right after the Great Recession, and job prospects were bad for everyone. Indeed, the unemployment rate for people with college degrees was substantially lower than for those without college degrees, all the way through the Second Depression. The New York Times has a nice little gadget where you can estimate the unemployment rate for college graduates; my hint for you is that I just said it’s lower, and I still guessed too high. There was variation across fields, of course; unsurprisingly computer science majors did extremely well and humanities majors did rather poorly. Underemployment was a big problem, but again, clearly because of the recession, not because going to college was a mistake. In fact, unemployment for college graduates (about 9%) has always been so much lower than unemployment for high school dropouts that the maximum unemployment rate for young college graduates is less than the minimum unemployment rate for young high school graduates (10%) over the entire period since the year 2000. Young high school dropouts have fared even worse; their minimum unemployment rate since 2000 was 18%, while their maximum was a terrifying Great Depression-level of 32%. Education isn’t just a good investment—it’s an astonishingly good investment.

There are a lot of things worth panicking about, now that Trump has been elected President. But student debt isn’t one of them. This is a very smart investment, made with a reasonable portion of our nation’s wealth. If you have student debt like I do, make sure you have enough—or otherwise you might not be able to pay it back.

What good are macroeconomic models? How could they be better?

PNRJ core principles, critique of neoclassical economics, macroeconomics , , , , , , , , , ,

Dec 11, JDN 2457734

One thing that I don’t think most people know, but which immediately obvious to any student of economics at the college level or above, is that there is a veritable cornucopia of different macroeconomic models. There are growth models (the Solow model, the Harrod-Domar model, the Ramsey model), monetary policy models (IS-LM, aggregate demand-aggregate supply), trade models (the Mundell-Fleming model, the Heckscher-Ohlin model), large-scale computational models (dynamic stochastic general equilibrium, agent-based computational economics), and I could go on.

This immediately raises the question: What are all these models for? What good are they?

A cynical view might be that they aren’t useful at all, that this is all false mathematical precision which makes economics persuasive without making it accurate or useful. And with such a proliferation of models and contradictory conclusions, I can see why such a view would be tempting.

But many of these models are useful, at least in certain circumstances. They aren’t completely arbitrary. Indeed, one of the litmus tests of the last decade has been how well the models held up against the events of the Great Recession and following Second Depression. The Keynesian and cognitive/behavioral models did rather well, albeit with significant gaps and flaws. The Monetarist, Real Business Cycle, and most other neoclassical models failed miserably, as did Austrian and Marxist notions so fluid and ill-defined that I’m not sure they deserve to even be called “models”. So there is at least some empirical basis for deciding what assumptions we should be willing to use in our models. Yet even if we restrict ourselves to Keynesian and cognitive/behavioral models, there are still a great many to choose from, which often yield inconsistent results.

So let’s compare with a science that is uncontroversially successful: Physics. How do mathematical models in physics compare with mathematical models in economics?

Well, there are still a lot of models, first of all. There’s the Bohr model, the Schrodinger equation, the Dirac equation, Newtonian mechanics, Lagrangian mechanics, Bohmian mechanics, Maxwell’s equations, Faraday’s law, Coulomb’s law, the Einstein field equations, the Minkowsky metric, the Schwarzschild metric, the Rindler metric, Feynman-Wheeler theory, the Navier-Stokes equations, and so on. So a cornucopia of models is not inherently a bad thing.

Yet, there is something about physics models that makes them more reliable than economics models.

Partly it is that the systems physicists study are literally two dozen orders of magnitude or more smaller and simpler than the systems economists study. Their task is inherently easier than ours.

But it’s not just that; their models aren’t just simpler—actually they often aren’t. The Navier-Stokes equations are a lot more complicated than the Solow model. They’re also clearly a lot more accurate.

The feature that models in physics seem to have that models in economics do not is something we might call nesting, or maybe consistency. Models in physics don’t come out of nowhere; you can’t just make up your own new model based on whatever assumptions you like and then start using it—which you very much can do in economics. Models in physics are required to fit consistently with one another, and usually inside one another, in the following sense:

The Dirac equation strictly generalizes the Schrodinger equation, which strictly generalizes the Bohr model. Bohmian mechanics is consistent with quantum mechanics, which strictly generalizes Lagrangian mechanics, which generalizes Newtonian mechanics. The Einstein field equations are consistent with Maxwell’s equations and strictly generalize the Minkowsky, Schwarzschild, and Rindler metrics. Maxwell’s equations strictly generalize Faraday’s law and Coulomb’s law.
In other words, there are a small number of canonical models—the Dirac equation, Maxwell’s equations and the Einstein field equation, essentially—inside which all other models are nested. The simpler models like Coulomb’s law and Newtonian mechanics are not contradictory with these canonical models; they are contained within them, subject to certain constraints (such as macroscopic systems far below the speed of light).

This is something I wish more people understood (I blame Kuhn for confusing everyone about what paradigm shifts really entail); Einstein did not overturn Newton’s laws, he extended them to domains where they previously had failed to apply.

This is why it is sensible to say that certain theories in physics are true; they are the canonical models that underlie all known phenomena. Other models can be useful, but not because we are relativists about truth or anything like that; Newtonian physics is a very good approximation of the Einstein field equations at the scale of many phenomena we care about, and is also much more mathematically tractable. If we ever find ourselves in situations where Newton’s equations no longer apply—near a black hole, traveling near the speed of light—then we know we can fall back on the more complex canonical model; but when the simpler model works, there’s no reason not to use it.

There are still very serious gaps in the knowledge of physics; in particular, there is a fundamental gulf between quantum mechanics and the Einstein field equations that has been unresolved for decades. A solution to this “quantum gravity problem” would be essentially a guaranteed Nobel Prize. So even a canonical model can be flawed, and can be extended or improved upon; the result is then a new canonical model which we now regard as our best approximation to truth.

Yet the contrast with economics is still quite clear. We don’t have one or two or even ten canonical models to refer back to. We can’t say that the Solow model is an approximation of some greater canonical model that works for these purposes—because we don’t have that greater canonical model. We can’t say that agent-based computational economics is approximately right, because we have nothing to approximate it to.

I went into economics thinking that neoclassical economics needed a new paradigm. I have now realized something much more alarming: Neoclassical economics doesn’t really have a paradigm. Or if it does, it’s a very informal paradigm, one that is expressed by the arbitrary judgments of journal editors, not one that can be written down as a series of equations. We assume perfect rationality, except when we don’t. We assume constant returns to scale, except when that doesn’t work. We assume perfect competition, except when that doesn’t get the results we wanted. The agents in our models are infinite identical psychopaths, and they are exactly as rational as needed for the conclusion I want.

This is quite likely why there is so much disagreement within economics. When you can permute the parameters however you like with no regard to a canonical model, you can more or less draw whatever conclusion you want, especially if you aren’t tightly bound to empirical evidence. I know a great many economists who are sure that raising minimum wage results in large disemployment effects, because the models they believe in say that it must, even though the empirical evidence has been quite clear that these effects are small if they are present at all. If we had a canonical model of employment that we could calibrate to the empirical evidence, that couldn’t happen anymore; there would be a coefficient I could point to that would refute their argument. But when every new paper comes with a new model, there’s no way to do that; one set of assumptions is as good as another.

Indeed, as I mentioned in an earlier post, a remarkable number of economists seem to embrace this relativism. “There is no true model.” they say; “We do what is useful.” Recently I encountered a book by the eminent economist Deirdre McCloskey which, though I confess I haven’t read it in its entirety, appears to be trying to argue that economics is just a meaningless language game that doesn’t have or need to have any connection with actual reality. (If any of you have read it and think I’m misunderstanding it, please explain. As it is I haven’t bought it for a reason any economist should respect: I am disinclined to incentivize such writing.)

Creating such a canonical model would no doubt be extremely difficult. Indeed, it is a task that would require the combined efforts of hundreds of researchers and could take generations to achieve. The true equations that underlie the economy could be totally intractable even for our best computers. But quantum mechanics wasn’t built in a day, either. The key challenge here lies in convincing economists that this is something worth doing—that if we really want to be taken seriously as scientists we need to start acting like them. Scientists believe in truth, and they are trying to find it out. While not immune to tribalism or ideology or other human limitations, they resist them as fiercely as possible, always turning back to the evidence above all else. And in their combined strivings, they attempt to build a grand edifice, a universal theory to stand the test of time—a canonical model.

Experimentally testing categorical prospect theory

PNRJ cognitive science, heuristics and biases , , , , , , , , , , , , ,

Dec 4, JDN 2457727

In last week’s post I presented a new theory of probability judgments, which doesn’t rely upon people performing complicated math even subconsciously. Instead, I hypothesize that people try to assign categories to their subjective probabilities, and throw away all the information that wasn’t used to assign that category.

The way to most clearly distinguish this from cumulative prospect theory is to show discontinuity. Kahneman’s smooth, continuous function places fairly strong bounds on just how much a shift from 0% to 0.000001% can really affect your behavior. In particular, if you want to explain the fact that people do seem to behave differently around 10% compared to 1% probabilities, you can’t allow the slope of the smooth function to get much higher than 10 at any point, even near 0 and 1. (It does depend on the precise form of the function, but the more complicated you make it, the more free parameters you add to the model. In the most parsimonious form, which is a cubic polynomial, the maximum slope is actually much smaller than this—only 2.)

If that’s the case, then switching from 0.% to 0.0001% should have no more effect in reality than a switch from 0% to 0.00001% would to a rational expected utility optimizer. But in fact I think I can set up scenarios where it would have a larger effect than a switch from 0.001% to 0.01%.

Indeed, these games are already quite profitable for the majority of US states, and they are called lotteries.

Rationally, it should make very little difference to you whether your odds of winning the Powerball are 0 (you bought no ticket) or 0.000000001% (you bought a ticket), even when the prize is $100 million. This is because your utility of $100 million is nowhere near 100 million times as large as your marginal utility of $1. A good guess would be that your lifetime income is about $2 million, your utility is logarithmic, the units of utility are hectoQALY, and the baseline level is about 100,000.

I apologize for the extremely large number of decimals, but I had to do that in order to show any difference at all. I have bolded where the decimals first deviate from the baseline.

Your utility if you don’t have a ticket is ln(20) = 2.9957322736 hQALY.

Your utility if you have a ticket is (1-10^-9) ln(20) + 10^-9 ln(1020) = 2.9957322775 hQALY.

You gain a whopping 40 microQALY over your whole lifetime. I highly doubt you could even perceive such a difference.

And yet, people are willing to pay nontrivial sums for the chance to play such lotteries. Powerball tickets sell for about $2 each, and some people buy tickets every week. If you do that and live to be 80, you will spend some $8,000 on lottery tickets during your lifetime, which results in this expected utility: (1-4*10^-6) ln(20-0.08) + 4*10^-6 ln(1020) = 2.9917399955 hQALY.
You have now sacrificed 0.004 hectoQALY, which is to say 0.4 QALY—that’s months of happiness you’ve given up to play this stupid pointless game.

Which shouldn’t be surprising, as (with 99.9996% probability) you have given up four months of your lifetime income with nothing to show for it. Lifetime income of $2 million / lifespan of 80 years = $25,000 per year; $8,000 / $25,000 = 0.32. You’ve actually sacrificed slightly more than this, which comes from your risk aversion.

Why would anyone do such a thing? Because while the difference between 0 and 10^-9 may be trivial, the difference between “impossible” and “almost impossible” feels enormous. “You can’t win if you don’t play!” they say, but they might as well say “You can’t win if you do play either.” Indeed, the probability of winning without playing isn’t zero; you could find a winning ticket lying on the ground, or win due to an error that is then upheld in court, or be given the winnings bequeathed by a dying family member or gifted by an anonymous donor. These are of course vanishingly unlikely—but so was winning in the first place. You’re talking about the difference between 10^-9 and 10^-12, which in proportional terms sounds like a lot—but in absolute terms is nothing. If you drive to a drug store every week to buy a ticket, you are more likely to die in a car accident on the way to the drug store than you are to win the lottery.

Of course, these are not experimental conditions. So I need to devise a similar game, with smaller stakes but still large enough for people’s brains to care about the “almost impossible” category; maybe thousands? It’s not uncommon for an economics experiment to cost thousands, it’s just usually paid out to many people instead of randomly to one person or nobody. Conducting the experiment in an underdeveloped country like India would also effectively amplify the amounts paid, but at the fixed cost of transporting the research team to India.

But I think in general terms the experiment could look something like this. You are given $20 for participating in the experiment (we treat it as already given to you, to maximize your loss aversion and endowment effect and thereby give us more bang for our buck). You then have a chance to play a game, where you pay $X to get a P probability of $Y*X, and we vary these numbers.

The actual participants wouldn’t see the variables, just the numbers and possibly the rules: “You can pay $2 for a 1% chance of winning $200. You can also play multiple times if you wish.” “You can pay $10 for a 5% chance of winning $250. You can only play once or not at all.”

So I think the first step is to find some dilemmas, cases where people feel ambivalent, and different people differ in their choices. That’s a good role for a pilot study.

Then we take these dilemmas and start varying their probabilities slightly.

In particular, we try to vary them at the edge of where people have mental categories. If subjective probability is continuous, a slight change in actual probability should never result in a large change in behavior, and furthermore the effect of a change shouldn’t vary too much depending on where the change starts.

But if subjective probability is categorical, these categories should have edges. Then, when I present you with two dilemmas that are on opposite sides of one of the edges, your behavior should radically shift; while if I change it in a different way, I can make a large change without changing the result.

Based solely on my own intuition, I guessed that the categories roughly follow this pattern:

Impossible: 0%

Almost impossible: 0.1%

Very unlikely: 1%

Unlikely: 10%

Fairly unlikely: 20%

Roughly even odds: 50%

Fairly likely: 80%

Likely: 90%

Very likely: 99%

Almost certain: 99.9%

Certain: 100%

So for example, if I switch from 0%% to 0.01%, it should have a very large effect, because I’ve moved you out of your “impossible” category (indeed, I think the “impossible” category is almost completely sharp; literally anything above zero seems to be enough for most people, even 10^-9 or 10^-10). But if I move from 1% to 2%, it should have a small effect, because I’m still well within the “very unlikely” category. Yet the latter change is literally one hundred times larger than the former. It is possible to define continuous functions that would behave this way to an arbitrary level of approximation—but they get a lot less parsimonious very fast.

Now, immediately I run into a problem, because I’m not even sure those are my categories, much less that they are everyone else’s. If I knew precisely which categories to look for, I could tell whether or not I had found it. But the process of both finding the categories and determining if their edges are truly sharp is much more complicated, and requires a lot more statistical degrees of freedom to get beyond the noise.

One thing I’m considering is assigning these values as a prior, and then conducting a series of experiments which would adjust that prior. In effect I would be using optimal Bayesian probability reasoning to show that human beings do not use optimal Bayesian probability reasoning. Still, I think that actually pinning down the categories would require a large number of participants or a long series of experiments (in frequentist statistics this distinction is vital; in Bayesian statistics it is basically irrelevant—one of the simplest reasons to be Bayesian is that it no longer bothers you whether someone did 2 experiments of 100 people or 1 experiment of 200 people, provided they were the same experiment of course). And of course there’s always the possibility that my theory is totally off-base, and I find nothing; a dissertation replicating cumulative prospect theory is a lot less exciting (and, sadly, less publishable) than one refuting it.

Still, I think something like this is worth exploring. I highly doubt that people are doing very much math when they make most probabilistic judgments, and using categories would provide a very good way for people to make judgments usefully with no math at all.