What is anxiety for?

Sep 17 JDN 2460205

As someone who experiences a great deal of anxiety, I have often struggled to understand what it could possibly be useful for. We have this whole complex system of evolved emotions, and yet more often than not it seems to harm us rather than help us. What’s going on here? Why do we even have anxiety? What even is anxiety, really? And what is it for?

There’s actually an extensive body of research on this, though very few firm conclusions. (One of the best accounts I’ve read, sadly, is paywalled.)

For one thing, there seem to be a lot of positive feedback loops involved in anxiety: Panic attacks make you more anxious, triggering more panic attacks; being anxious disrupts your sleep, which makes you more anxious. Positive feedback loops can very easily spiral out of control, resulting in responses that are wildly disproportionate to the stimulus that triggered them.

A certain amount of stress response is useful, even when the stakes are not life-or-death. But beyond a certain point, more stress becomes harmful rather than helpful. This is the Yerkes-Dodson effect, for which I developed my stochastic overload model (which I still don’t know if I’ll ever publish, ironically enough, because of my own excessive anxiety). Realizing that anxiety can have benefits can also take some of the bite out of having chronic anxiety, and, ironically, reduce that anxiety a little. The trick is finding ways to break those positive feedback loops.

I think one of the most useful insights to come out of this research is the smoke-detector principle, which is a fundamentally economic concept. It sounds quite simple: When dealing with an uncertain danger, sound the alarm if the expected benefit of doing so exceeds the expected cost.

This has profound implications when risk is highly asymmetric—as it usually is. Running away from a shadow or a noise that probably isn’t a lion carries some cost; you wouldn’t want to do it all the time. But it is surely nowhere near as bad as failing to run away when there is an actual lion. Indeed, it might be fair to say that failing to run away from an actual lion counts as one of the worst possible things that could ever happen to you, and could easily be 100 times as bad as running away when there is nothing to fear.

With this in mind, if you have a system for detecting whether or not there is a lion, how sensitive should you make it? Extremely sensitive. You should in fact try to calibrate it so that 99% of the time you experience the fear and want to run away, there is not a lion. Because the 1% of the time when there is one, it’ll all be worth it.

Yet this is far from a complete explanation of anxiety as we experience it. For one thing, there has never been, in my entire life, even a 1% chance that I’m going to be attacked by a lion. Even standing in front of a lion enclosure at the zoo, my chances of being attacked are considerably less than that—for a zoo that allowed 1% of its customers to be attacked would not stay in business very long.

But for another thing, it isn’t really lions I’m afraid of. The things that make me anxious are generally not things that would be expected to do me bodily harm. Sure, I generally try to avoid walking down dark alleys at night, and I look both ways before crossing the street, and those are activities directly designed to protect me from bodily harm. But I actually don’t feel especially anxious about those things! Maybe I would if I actually had to walk through dark alleys a lot, but I don’t, and in the rare occasion I would, I think I’d feel afraid at the time but fine afterward, rather than experiencing persistent, pervasive, overwhelming anxiety. (Whereas, if I’m anxious about reading emails, and I do manage to read emails, I’m usually still anxious afterward.) When it comes to crossing the street, I feel very little fear at all, even though perhaps I should—indeed, it had been remarked that when it comes to the perils of motor vehicles, human beings suffer from a very dangerous lack of fear. We should be much more afraid than we are—and our failure to be afraid kills thousands of people.

No, the things that make me anxious are invariably social: Meetings, interviews, emails, applications, rejection letters. Also parties, networking events, and back when I needed them, dates. They involve interacting with other people—and in particular being evaluated by other people. I never felt particularly anxious about exams, except maybe a little before my PhD qualifying exam and my thesis defenses; but I can understand those who do, because it’s the same thing: People are evaluating you.

This suggests that anxiety, at least of the kind that most of us experience, isn’t really about danger; it’s about status. We aren’t worried that we will be murdered or tortured or even run over by a car. We’re worried that we will lose our friends, or get fired; we are worried that we won’t get a job, won’t get published, or won’t graduate.

And yet it is striking to me that it often feels just as bad as if we were afraid that we were going to die. In fact, in the most severe instances where anxiety feeds into depression, it can literally make people want to die. How can that be evolutionarily adaptive?

Here it may be helpful to remember that in our ancestral environment, status and survival were oft one and the same. Humans are the most social organisms on Earth; I even sometimes describe us as hypersocial, a whole new category of social that no other organism seems to have achieved. We cooperate with others of our species on a mind-bogglingly grand scale, and are utterly dependent upon vast interconnected social systems far too large and complex for us to truly understand, let alone control.

At this historical epoch, these social systems are especially vast and incomprehensible; but at least for most of us in First World countries, they are also forgiving in a way that is fundamentally alien to our ancestors’ experience. It was not so long ago that a failed hunt or a bad harvest would let your family starve unless you could beseech your community for aid successfully—which meant that your very survival could depend upon being in the good graces of that community. But now we have food stamps, so even if everyone in your town hates you, you still get to eat. Of course some societies are more forgiving (Sweden) than others (the United States); and virtually all societies could be even more forgiving than they are. But even the relatively cutthroat competition of the US today has far less genuine risk of truly catastrophic failure than what most human beings lived through for most of our existence as a species.

I have found this realization helpful—hardly a cure, but helpful, at least: What are you really afraid of? When you feel anxious, your body often tells you that the stakes are overwhelming, life-or-death; but if you stop and think about it, in the world we live in today, that’s almost never true. Failing at one important task at work probably won’t get you fired—and even getting fired won’t really make you starve.

In fact, we might be less anxious if it were! For our bodies’ fear system seems to be optimized for the following scenario: An immediate threat with high chance of success and life-or-death stakes. Spear that wild animal, or jump over that chasm. It will either work or it won’t, you’ll know immediately; it probably will work; and if it doesn’t, well, that may be it for you. So you’d better not fail. (I think it’s interesting how much of our fiction and media involves these kinds of events: The hero would surely and promptly die if he fails, but he won’t fail, for he’s the hero! We often seem more comfortable in that sort of world than we do in the one we actually live in.)

Whereas the life we live in now is one of delayed consequences with low chance of success and minimal stakes. Send out a dozen job applications. Hear back in a week from three that want to interview you. Do those interviews and maybe one will make you an offer—but honestly, probably not. Next week do another dozen. Keep going like this, week after week, until finally one says yes. Each failure actually costs you very little—but you will fail, over and over and over and over.

In other words, we have transitioned from an environment of immediate return to one of delayed return.

The result is that a system which was optimized to tell us never fail or you will die is being put through situations where failure is constantly repeated. I think deep down there is a part of us that wonders, “How are you still alive after failing this many times?” If you had fallen in as many ravines as I have received rejection letters, you would assuredly be dead many times over.

Yet perhaps our brains are not quite as miscalibrated as they seem. Again I come back to the fact that anxiety always seems to be about people and evaluation; it’s different from immediate life-or-death fear. I actually experience very little life-or-death fear, which makes sense; I live in a very safe environment. But I experience anxiety almost constantly—which also makes a certain amount of sense, seeing as I live in an environment where I am being almost constantly evaluated by other people.

One theory posits that anxiety and depression are a dual mechanism for dealing with social hierarchy: You are anxious when your position in the hierarchy is threatened, and depressed when you have lost it. Primates like us do seem to care an awful lot about hierarchies—and I’ve written before about how this explains some otherwise baffling things about our economy.

But I for one have never felt especially invested in hierarchy. At least, I have very little desire to be on top of the hiearchy. I don’t want to be on the bottom (for I know how such people are treated); and I strongly dislike most of the people who are actually on top (for they’re most responsible for treating the ones on the bottom that way). I also have ‘a problem with authority’; I don’t like other people having power over me. But if I were to somehow find myself ruling the world, one of the first things I’d do is try to figure out a way to transition to a more democratic system. So it’s less like I want power, and more like I want power to not exist. Which means that my anxiety can’t really be about fearing to lose my status in the hierarchy—in some sense, I want that, because I want the whole hierarchy to collapse.

If anxiety involved the fear of losing high status, we’d expect it to be common among those with high status. Quite the opposite is the case. Anxiety is more common among people who are more vulnerable: Women, racial minorities, poor people, people with chronic illness. LGBT people have especially high rates of anxiety. This suggests that it isn’t high status we’re afraid of losing—though it could still be that we’re a few rungs above the bottom and afraid of falling all the way down.

It also suggests that anxiety isn’t entirely pathological. Our brains are genuinely responding to circumstances. Maybe they are over-responding, or responding in a way that is not ultimately useful. But the anxiety is at least in part a product of real vulnerabilities. Some of what we’re worried about may actually be real. If you cannot carry yourself with the confidence of a mediocre White man, it may be simply because his status is fundamentally secure in a way yours is not, and he has been afforded a great many advantages you never will be. He never had a Supreme Court ruling decide his rights.

I cannot offer you a cure for anxiety. I cannot even really offer you a complete explanation of where it comes from. But perhaps I can offer you this: It is not your fault. Your brain evolved for a very different world than this one, and it is doing its best to protect you from the very different risks this new world engenders. Hopefully one day we’ll figure out a way to get it calibrated better.

The winner-takes-all effect

JDN 2457054 PST 14:06.

As I write there is some sort of mariachi band playing on my front lawn. It is actually rather odd that I have a front lawn, since my apartment is set back from the road; yet there is the patch of grass, and there is the band playing upon it. This sort of thing is part of the excitement of living in a large city (and Long Beach would seem like a large city were it not right next to the sprawling immensity that is Los Angeles—there are more people in Long Beach than in Cleveland, but there are more people in greater Los Angeles than in Sweden); with a certain critical mass of human beings comes unexpected pieces of culture.

The fact that people agglomerate in this way is actually relevant to today’s topic, which is what I will call the winner-takes-all effect. I actually just finished reading a book called The Winner-Take-All Society, which is particularly horrifying to read because it came out in 1996. That’s almost twenty years ago, and things were already bad; and since then everything it describes has only gotten worse.

What is the winner-takes-all effect? It is the simple fact that in competitive capitalist markets, a small difference in quality can yield an enormous difference in return. The third most popular soda drink company probably still makes drinks that are pretty good, but do you have any idea what it is? There’s Coke, there’s Pepsi, and then there’s… uh… Dr. Pepper, apparently! But I didn’t know that before today and I bet you didn’t either. Now think about what it must be like to be the 15th most popular soda drink company, or the 37th. That’s the winner-takes-all effect.

I don’t generally follow football, but since tomorrow is the Super Bowl I feel some obligation to use that example as well. The highest-paid quarterback is Russell Wilson of the Seattle Seahawks, who is signing onto a five-year contract worth $110 million ($22 million a year). In annual income that will make him pass Jay Cutler of the Chicago Bears who has a seven-year contract worth $127 million ($18.5 million a year). This shift may have something to do with the fact that the Seahawks are in the Super Bowl this year and the Bears are not (they haven’t since 2007). Now consider what life is like for most football players; the median income of football players is most likely zero (at least as far as football-related income), and the median income of NFL players—the cream of the crop already—is $770,000; that’s still very good money of course (more than Krugman makes, actually! But he could make more, if he were willing to sell out to Wall Street), but it’s barely 1/30 of what Wilson is going to be making. To make that million-dollar salary, you need to be the best, of the best, of the best (sir!). That’s the winner-takes-all effect.

To go back to the example of cities, it is for similar reasons that the largest cities (New York, Los Angeles, London, Tokyo, Shanghai, Hong Kong, Delhi) become packed with tens of millions of people while others (Long Beach, Ann Arbor, Cleveland) get hundreds of thousands and most (Petoskey, Ketchikan, Heber City, and hundreds of others you’ve never heard of) get only a few thousand. Beyond that there are thousands of tiny little hamlets that many don’t even consider cities. The median city probably has about 10,000 people in it, and that only because we’d stop calling it a city if it fell below 1,000. If we include every tiny little village, the median town size is probably about 20 people. Meanwhile the largest city in the world is Tokyo, with a greater metropolitan area that holds almost 38 million people—or to put it another way almost exactly as many people as California. Huh, LA doesn’t seem so big now does it? How big is a typical town? Well, that’s the thing about this sort of power-law distribution; the concept of “typical” or “average” doesn’t really apply anymore. Each little piece of the distribution has basically the same shape as the whole distribution, so there isn’t a “typical” size or scale. That’s the winner-takes-all effect.

As they freely admit in the book, it isn’t literally that a single winner takes everything. That is the theoretical maximum level of wealth inequality, and fortunately no society has ever quite reached it. The closest we get in today’s society is probably Saudi Arabia, which recently lost its king—and yes I do mean king in the fullest sense of the word, a man of virtually unlimited riches and near-absolute power. His net wealth was estimated at $18 billion, which frankly sounds low; still even if that’s half the true amount it’s oddly comforting to know that he is still not quite as rich as Bill Gates ($78 billion), who earned his wealth at least semi-legitimately in a basically free society. Say what you will about intellectual property rents and market manipulation—and you know I do—but they are worlds away from what Abdullah’s family did, which was literally and directly robbed from millions of people by the power of the sword. Mostly he just inherited all that, and he did implement some minor reforms, but make no mistake: He was ruthless and by no means willing to give up his absolute power—he beheaded dozens of political dissidents, for example. Saudi Arabia does spread their wealth around a little, such that basically no one is below the UN poverty lines of $1.25 and $2 per day, but about a fourth of the population is below the national poverty line—which is just about the same distribution of wealth as what we have in the US, which actually makes me wonder just how free and legitimate our markets really are.

The winner-takes-all effect would really be more accurately described as the “top small fraction takes the vast majority” effect, but that isn’t nearly as catchy, now is it?

There are several different causes that can all lead to this same result. In the book, Robert Frank and Philip Cook argue that we should not attribute the cause to market manipulation, but in fact to the natural functioning of competitive markets. There’s something to be said for this—I used to buy the whole idea that competitive markets are the best, but increasingly I’ve been seeing ways that less competitive markets can make better overall outcomes.

Where they lose me is in arguing that the skyrocketing compensation packages for CEOs are due to their superior performance, and corporations are just being rational in competing for the best CEOs. If that were true, we wouldn’t find that the rank correlation between the CEO’s pay and the company’s stock performance is statistically indistinguishable from zero. Actually even a small positive correlation wouldn’t prove that the CEOs are actually performing well; it could just be that companies that perform well are willing to pay their CEOs more—and stock option compensation will do this automatically. But in fact the correlation is so tiny as to be negligible; corporations would be better off hiring a random person off the street and paying them $50,000 for all the CEO does for their stock performance. If you adjust for the size of the company, you find that having a higher-paid CEO is positively related to performance for small startups, but negatively correlated for large well-established corporations. No, clearly there’s something going on here besides competitive pay for high performance—corruption comes to mind, which you’ll remember was the subject of my master’s thesis.

But in some cases there isn’t any apparent corruption, and yet we still see these enormously unequal distributions of income. Another good example of this is the publishing industry, in which J.K. Rowling can make over $1 billion (she donated enough to charity to officially lose her billionaire status) but most authors make little or nothing, particularly those who can’t get published in the first place. I have no reason to believe that J.K. Rowling acquired this massive wealth by corruption; she just sold an awful lot of booksover 100 million of the first Harry Potter book alone.

But why would she be able to sell 100 million while thousands of authors write books that are probably just as good or nearly so make nothing? Am I just bitter and envious, as Mitt Romney would say? Is J.K. Rowling actually a million times as good an author as I am?

Obviously not, right? She may be better, but she’s not that much better. So how is it that she ends up making a million times as much as I do from writing? It feels like squaring the circle: How can markets be efficient and competitive, yet some people are being paid millions of times as others despite being only slightly more productive?

The answer is simple but enormously powerful: positive feedback.Once you start doing well, it’s easier to do better. You have what economists call an economy of scale. The first 10,000 books sold is the hardest; then the next 10,000 is a little easier; the next 10,000 a little easier still. In fact I suspect that in many cases the first 10% growth is harder than the second 10% growth and so on—which is actually a much stronger claim. For my sales to grow 10% I’d need to add like 20 people. For J.K. Rowling’s sales to grow 10% she’d need to add 10 million. Yet it might actually be easier for J.K. Rowling to add 10 million than for me to add 20. If not, it isn’t much harder. Suppose we tried by just sending out enticing tweets. I have about 100 Twitter followers, so I’d need 0.2 sales per follower; she has about 4 million, so she’d need an average of 2.5 sales per follower. That’s an advantage for me, percentage-wise—but if we have the same uptake rate I sell 20 books and she sells 800,000.

If you have only a handful of book sales like I do, those sales are static; but once you cross that line into millions of sales, it’s easy for that to spread into tens or even hundreds of millions. In the particular case of books, this is because it spreads by word-of-mouth; say each person who reads a book recommends it to 10 friends, and you only read a book if at least 2 of your friends recommended it. In a city of 100,000 people, if you start with 50 people reading it, odds are that most of those people don’t have friends that overlap and so you stop at 50. But if you start at 50,000, there is bound to be a great deal of overlap; so then that 50,000 recruits another 10,000, then another 10,000, and pretty soon the whole 100,000 have read it. In this case we have what are called network externalitiesyou’re more likely to read a book if your friends have read it, so the more people there are who have read it, the more people there are who want to read it. There’s a very similar effect at work in social networks; why does everyone still use Facebook, even though it’s actually pretty awful? Because everyone uses Facebook. Less important than the quality of the software platform (Google Plus is better, and there are some third-party networks that are likely better still) is the fact that all your friends and family are on it. We all use Facebook because we all use Facebook? We all read Harry Potter books because we all read Harry Potter books? The first rule of tautology club is…

Languages are also like this, which is why I can write this post in English and yet people can still read it around the world. English is the winner of the language competition (we call it the lingua franca, as weird as that is—French is not the lingua franca anymore). The losers are those hundreds of New Guinean languages you’ve never heard of, many of which are dying. And their distribution obeys, once again, a power-law. (Individual words actually obey a power-law as well, which makes this whole fractal business delightfully ever more so.)
Network externalities are not the only way that the winner-takes-all effect can occur, though I think it is the most common. You can also have economies of scale from the supply side, particularly in the case of information: Recording a song is a lot of time and effort, but once you record a song, it’s trivial to make more copies of it. So that first recording costs a great deal, while every subsequent recording costs next to nothing. This is probably also at work in the case of J.K. Rowling and the NFL; the two phenomena are by no means mutually exclusive. But clearly the sizes of cities are due to network externalities: It’s quite expensive to live in a big city—no supply-side economy of scale—but you want to live in a city where other people live because that’s where friends and family and opportunities are.

The most worrisome kind of winner-takes-all effect is what Frank and Cook call deep pockets: Once you have concentration of wealth in a few hands, those few individuals can now choose their own winners in a much more literal sense: the rich can commission works of art from their favorite artists, exacerbating the inequality among artists; worse yet they can use their money to influence politicians (as the Kochs are planning on spending $900 million—$3 for every person in America—to do in 2016) and exacerbate the inequality in the whole system. That gives us even more positive feedback on top of all the other positive feedbacks.

Sure enough, if you run the standard neoclassical economic models of competition and just insert the assumption of economies of scale, the result is concentration of wealth—in fact, if nothing about the rules prevents it, the result is a complete monopoly. Nor is this result in any sense economically efficient; it’s just what naturally happens in the presence of economies of scale.

Frank and Cook seem most concerned about the fact that these winner-take-all incomes will tend to push too many people to seek those careers, leaving millions of would-be artists, musicians and quarterbacks with dashed dreams when they might have been perfectly happy as electrical engineers or high school teachers. While this may be true—next week I’ll go into detail about prospect theory and why human beings are terrible at making judgments based on probability—it isn’t really what I’m most concerned about. For all the cost of frustrated ambition there is also a good deal of benefit; striving for greatness does not just make the world better if we succeed, it can make ourselves better even if we fail. I’d strongly encourage people to have backup plans; but I’m not going to tell people to stop painting, singing, writing, or playing football just because they’re unlikely to make a living at it. The one concern I do have is that the competition is so fierce that we are pressured to go all in, to not have backup plans, to use performance-enhancing drugs—they may carry awful risks, but they also work. And it’s probably true, actually, that you’re a bit more likely to make it all the way to the top if you don’t have a backup plan. You’re also vastly more likely to end up at the bottom. Is raising your probability of being a bestselling author from 0.00011% to 0.00012% worth giving up all other career options? Skipping chemistry class to practice football may improve your chances of being an NFL quarterback from 0.000013% to 0.000014%, but it will also drop your chances of being a chemical engineer from 95% (a degree in chemical engineering almost guarantees you a job eventually) to more like 5% (it’s hard to get a degree when you flunk all your classes).

Frank and Cook offer a solution that I think is basically right; they call it positional arms control agreements. By analogy with arms control agreements between nations—and what is war, if not the ultimate winner-takes-all contest?—they propose that we use taxation and regulation policy to provide incentives to make people compete less fiercely for the top positions. Some of these we already do: Performance-enhancing drugs are banned in professional sports, for instance. Even where there are no regulations, we can use social norms: That’s why it’s actually a good thing that your parents rarely support your decision to drop out of school and become a movie star.

That’s yet another reason why progressive taxation is a good idea, as if we needed another; by paring down those top incomes it makes the prospect of winning big less enticing. If NFL quarterbacks only made 10 times what chemical engineers make instead of 300 times, people would be a lot more hesitant to give up on chemical engineering to become a quarterback. If top Wall Street executives only made 50 times what normal people make instead of 5000, people with physics degrees might go back to actually being physicists instead of speculating on stock markets.

There is one case where we might not want fewer people to try, and that is entrepreneurship. Most startups fail, and only a handful go on to make mind-bogglingly huge amounts of money (often for no apparent reason, like the Snuggie and Flappy Bird), yet entrepreneurship is what drives the dynamism of a capitalist economy. We need people to start new businesses, and right now they do that mainly because of a tiny chance of a huge benefit. Yet we don’t want them to be too unrealistic in their expectations: Entrepreneurs are much more optimistic than the general population, but the most successful entrepreneurs are a bit less optimistic than other entrepreneurs. The most successful strategy is to be optimistic but realistic; this outperforms both unrealistic optimism and pessimism. That seems pretty intuitive; you have to be confident you’ll succeed, but you can’t be totally delusional. Yet it’s precisely the realistic optimists who are most likely to be disincentivized by a reduction in the top prizes.

Here’s my solution: Let’s change it from a tiny change of a huge benefit to a large chance of a moderately large benefit. Let’s reward entrepreneurs for trying—with standards for what constitutes a really serious, good attempt rather than something frivolous that was guaranteed to fail. Use part of the funds from the progressive tax as a fund for angel grants, provided to a large number of the most promising entrepreneurs. It can’t be a million-dollar prize for the top 100. It needs to be more like a $50,000 prize for the top 100,000 (which would cost $5 billion a year, affordable for the US government). It should be paid at the proposal phase; the top 100,000 business plans receive the funding and are under no obligation to repay it. It has to be enough money that someone can rationally commit themselves to years of dedicated work without throwing themselves into poverty, and it has to be confirmed money so that they don’t have to worry about throwing themselves into debt. As for the upper limit, it only needs to be small enough that there is still an incentive for the business to succeed; but even with a 99% tax Mark Zuckerberg would still be a millionaire, so the rewards for success are high indeed.

The good news is that we actually have such a system to some extent. For research scientists rather than entrepreneurs, NSF grants are pretty close to what I have in mind, but at present they are a bit too competitive: 8,000 research grants with a median of $130,000 each and a 20% acceptance rate isn’t quite enough people—the acceptance rate should be higher, since most of these proposals are quite worthy. Still, it’s close, and definitely a much better incentive system than what we have for entrepreneurs; there are almost 12 million entrepreneurs in the United States, starting 6 million businesses a year, 75% of which fail before they can return their venture capital. Those that succeed have incomes higher than the general population, with a median income of around $70,000 per year, but most of this is accounted for by the fact that entrepreneurs are more educated and talented than the general population. Once you factor that in, successful entrepreneurs have about 50% more income on average, but their standard deviation of income is also 60% higher—so some are getting a lot and some are getting very little. Since 75% fail, we’re talking about a 25% chance of entering an income distribution that’s higher on average but much more variable, and a 75% chance of going through a period with little or no income at all—is it worth it? Maybe, maybe not. But if you could get a guaranteed $50,000 for having a good idea—and let me be clear, only serious proposals that have a good chance of success should qualify—that deal sounds an awful lot better.