Consider, to begin with, this problem. There’s a local bar that you like. Actually, it’s a bar that lots of people like. The problem with the bar is that when it’s crowded, no one has a good time. You’re planning on going to the bar Friday night. But you don’t want to go if it’s going to be too crowded. What do you do?
To answer the question, you need to assume, if only for the sake of argument, that everyone feels the way you do. In other words, the bar is fun when it’s not crowded, but miserable when it is. As a result, if everyone thinks the bar will be crowded on. Friday night, then few people will go. The bar, therefore will be empty, and anyone who goes will have a good time. On the other hand, if everyone thinks the bar won’t be crowded, everyone will go. Then the bar will be packed, and no one will have a good time. (This problem was captured perfectly, of course, by Yogi Berra, when he said of Toots Shor’s nightclub: “No one goes there anymore. It’s too crowded.”) The trick, of course, is striking the right balance, so that every week enough—but not too many—people go.
There is, of course, an easy solution to this problem: just invent an all-powerful central planner—a kind of uber-doorman—-- who tells people when they can go to the bar. Every week the central planner would issue his dictate, banning some, allowing others in, thereby ensuring that the bar was full but never crowded. Although this solution makes sense in theory, it would be intolerable in practice. Even if central planning of this sort were possible, it would represent too great an interference with freedom of choice. We want people to be able to go to a bar if they want, even if it means that they’ll have a bad time. Any solution worth talking about has to respect people’s right to choose their own course of action, which means that it has to emerge out of the collective mix of all the potential bargoers’ individual choices.
In the early 1 990s, the economist Brian Arthur tried to figure out whether there really was a satisfying solution to this problem. He called the problem the “El Farol problem,” after a local bar in Santa Fe that sometimes got too crowded on nights when it featured Irish music. Arthur set up the problem this way: If El Farol is less than 60 percent full on any night, everyone there will have fun. If it’s more than 60 percent full, no one will have fun. Therefore, people will go only if they think the bar will be less than 60 percent full otherwise, they stay home.
How does each person decide what to do on any given Friday? Arthur’s suggestion was that since there was no obvious answer, no solution you could deduce mathematically, different people would rely on different strategies. Some would just assume that the same number of people would show up at El Farol this Friday as showed up last Friday. Some would look at how many people showed up the last time they’d actually been in the bar, (Arthur assumed that even if you didn’t go yourself, you could find out how many people had been in the bar.) Some would use an average of the last few weeks. And some would assume that this week’s attendance would be the opposite of last week’s (if it was empty last week, it’ll he full this week).
What Arthur did next was run a series of computer experiments designed to simulate attendance at El Farol over the period of one hundred weeks. (Essentially, he created a group of computer agents, equipped them with the different strategies, and let them go to work.) Because the agents followed different strategies, Arthur found, the number who ended up at the bar fluctuated sharply from week to week. The fluctuations weren’t regular, but were random, so that there was no obvious pattern. Sometimes the bar was more than 60 percent full three or four weeks in a row, while other times it was less than 60 percent full four out of five weeks. As a result, there was no one strategy that a person could follow and be sure of making the right decision. Instead, strategies worked for a while and then had to be tossed away
The fluctuations in attendance meant that on some Friday nights El Farol was too crowded for anyone to have fun, while on other Fridays people stayed home who, had they gone to the bar, would have had a good time. What was remarkable about the experiment, though, was this: during those one hundred weeks, the bar was—on average—exactly 60 percent full, which is precisely what the group as a whole wanted it to be. (When the bar is 60 percent full, the maximum number of people possible are having a good time, and no one is having a bad time.) In other words, even in a case where people’s individual strategies depend on each other’s behavior, the group’s collective judgment can be good.
A few years after Arthur first formulated the El Farol problem, engineers Ann M. Bell and William A. Sethares took a different approach to solving it. Arthur had assumed that the would-be bargoers would adopt diverse strategies in trying to anticipate the crowd’s behavior. Bell and Sethares’s bargoers, though, all followed the same strategy: if their recent experiences at the bar had been good, they went. If their recent experiences had been bad, they didn’t.
Bell and Sethares’s bargoers were therefore much less sophisticated than Arthur’s. They didn’t worry much about what the other bargoers might be thinking, and they did not know—as Arthur’s bargoers did—how many people were at El Farol on the nights when they didn’t show up. All they really knew was whether they’d recently enjoyed themselves at El Farol or not. If they’d had a good time, they wanted to go back. If they’d had a bad time, they didn’t. You might say, in fact, that they weren’t worrying about coordinating their behavior with the other bargoers at all. They were just relying on their feelings about El Farol.
Unsophisticated or not, this group of bargoers produced a different solution to the problem than Arthur’s bargoers did. After a certain amount of time had passed—giving each bargoer the experience he needed to decide whether to go back to El Farol—the group’s weekly attendance settled in at just below 60 percent of the bar’s capacity, just a little bit worse than that ideal central planner would have done. In looking only to their own experience, and not worrying about what everyone else was going to do, the bargoers came up with a collectively intelligent answer, which suggests that even when it comes to coordination problems, independent thinking may be valuable.
There was, though, a catch to the experiment. The reason the group’s weekly attendance was so stable was that the group quickly divided itself into people who were regulars at El Farol and people who went only rarely. In other words, El Farol started to look a lot like Cheers. Now, this wasn’t a bad solution. In fact, from a utilitarian perspective (assuming everyone derived equal pleasure from going to the bar on any given night), it was a perfectly good one. More than half the people got to go to El Farol nearly every week, and they had a good time while they were there (since the bar was only rarely crowded). And yet it’d be hard to say that it was an ideal solution, since a sizable chunk of the group rarely went to the bar and usually had a bad time when they did.
The truth is that it’s not really obvious (at least not to me) which solution—Arthur’s or Sethares and Bell’s—is better, though both of them seem surprisingly good. This is the nature of coordination problems: they are very hard to solve, and coming up with any good answer is a triumph, When what people want to do depends on what everyone else wants to do, every decision affects every other decision, and there is no outside reference point that can stop the self-reflexive spiral. When Francis Galton’s fairgoers made their guesses about the ox’s weight, they were trying to evaluate a reality that existed outside the group. When Arthur’s computer agents made their guesses about El Farol, though, they were trying to evaluate a reality that their own decisions would help construct. Given those circumstances, getting even the average attendance right seems miraculous.