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Authors: Duncan J. Watts

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In social science, Thatcher’s philosophical position goes by the name of methodological individualism, which claims that until one has succeeded in explaining some social
phenomenon—the popularity of the
Mona Lisa
or the relation between interest rates and economic growth—exclusively in terms of the thoughts, actions, and intentions of individual people, one has not fully succeeded in explaining it at all. Explanations that ascribe individual psychological motivations to aggregate entities like firms, markets, and governments might be convenient, but they are not, as the philosopher John Watkins put it, “rock bottom” explanations.
8

Unfortunately, attempts to construct the kind of rock-bottom explanations that methodological individualists imagined have all run smack into the micro-macro problem. In practice, therefore, social scientists invoke what is called a representative agent, a fictitious individual whose decisions stand in for the behavior of the collective. To take a single example, albeit an important one, the economy is composed of many thousands of firms and millions of individuals all making decisions about what to buy, what to sell, and what to invest in. The end result of all this activity is what economists call the business cycle—in effect, a time series of aggregate economic activity that seems to exhibit periodic ups and downs. Understanding the dynamics of the business cycle is one of the central problems of macroeconomics, in no small part because it affects how policy makers deal with events like recessions. Yet the mathematical models that economists rely on do not attempt to represent the vast complexity of the economy at all. Rather, they specify a single “representative firm” and ask how that firm would rationally allocate its resources given certain information about the rest of the economy. Roughly speaking, the response of that firm is then interpreted as the response of the economy as a whole.
9

By ignoring the interactions between thousands or millions of individual actors, the representative agent simplifies the analysis of business cycles enormously. It assumes, in effect,
that as long as economists have a good model of how individuals behave, they effectively have a good model for how the economy behaves as well. In eliminating the complexity, however, the representative-agent approach effectively ignores the crux of the micro-macro problem—the very core of what makes macroeconomic phenomena “macro” in the first place. It was for precisely this reason, in fact, that the economist Joseph Schumpeter, who is often regarded as the founding father of methodological individualism, attacked the representative-agent approach as flawed and misleading.
10

In practice, however, methodological individualists have lost the battle, and not just in economics. Pick up any work of history, sociology, or political science that deals with “macro” phenomena, like class, race, business, war, wealth, innovation, politics, law, or government, and you will find a world populated with representative agents. So common is their use in social science, in fact, that the substitution of a fictitious individual for what is in reality a collective typically happens without so much as an acknowledgment, like the magician placing the rabbit in the hat while the audience is looking elsewhere. No matter how it is done, however, the representative agent is only and always a convenient fiction. And no matter how we try to dress them up in mathematics or other finery, explanations that invoke representative agents are making essentially the same error as commonsense explanations that talk about firms, markets, and societies in the same terms that we use to describe individual people.
11

GRANOVETTER’S RIOT MODEL

The sociologist Mark Granovetter highlighted this problem using a very simple mathematical model of a crowd poised on the brink of a riot. Say a crowd of a hundred students is
gathered in a town square, protesting the government’s proposed increase in student fees. The students are angry about the new policy and frustrated with their lack of input to the political process. There’s a possibility of things getting out of hand. But being educated, civilized people, they also understand that reason and dialogue are preferable to violence. To oversimplify somewhat, each individual in the crowd is torn between two instincts—one to go berserk and smash things up, and the other to remain calm and protest peacefully. Everyone, whether they are conscious of it or not, has to make a choice between these two actions. But they are not making a choice between violence and peaceful protest independently—they are doing so, at least in part, in response to what other people are doing. The greater the number of individuals who engage in a riot, the more likely their efforts will force the politicians to pay attention, and the less likely that any one of them will be caught and punished. Also, riots have a primal energy of their own that can undermine otherwise strong social conventions against physical destruction, even skewing our psychological estimation of risk. In a riot, even sensible people can go crazy. For all these reasons, the choice about whether to remain calm or to engage in violence is subject to the general rule that the more other people are rioting, the more likely any particular individual is to join in.

Nevertheless, in this crowd, as everywhere, individual people have different tendencies toward violence. Perhaps those who are better off or who are less affected financially by the new policy are less inclined to risk jail time to make a point. Others are more persuaded that violence, although regrettable, is a useful political device. Some may have an unrelated gripe against the police or the politicians or society, and this event is giving them an excuse to vent. And perhaps some of them are just crazier than others. Whatever the reason—and
the reasons can be as many and as complicated as you can imagine—each individual in the crowd can be thought of as having a “threshold,” a point at which, if enough other people join in the riot, they will too, but below which they will refrain. Some people—the “rabble rousers”—have very low thresholds, while others, like the president of the student society, have very high thresholds. But everyone has a threshold of social influence, above which they will “tip” from calm to violence. This might seem like a strange way to characterize individual behavior. But the benefit of describing people in the crowd in terms of their threshold is that the distribution of thresholds over the whole crowd, from crazy (“I will riot even if no one else does”) to Gandhi (“I will not riot even if everyone else does”) turns out to capture some interesting and surprising lessons about crowd behavior.
12

To illustrate what could happen, Granovetter posited a very simple distribution in which each of the hundred people has a unique threshold. Exactly one person that is, has a threshold of zero, while another has a threshold of one other person, another has a threshold of two other people, and so on all the way up to the most conservative person, who will join in only after all ninety-nine others have. What will happen? Well, first Mr. Crazy—the one with the threshold of zero—will start throwing things, apropos of nothing. Then, his sidekick with the threshold of one (who needs only one other person to riot before joining in) joins him. Together, these two troublemakers prompt a third person—the guy with the threshold of two—to join in as well, and that’s enough to get the threshold-three person going, which is enough to … well, you get the idea: Given this particular threshold distribution, the entire crowd ends up joining the riot, one after the other. Chaos reigns.

Imagine, however, that in the next town over, a second
crowd of students, of exactly the same size, has gathered for exactly the same reason. As unlikely as it may sound, let’s imagine that this crowd has almost exactly the same distribution of thresholds as the first one. So closely matched are these two crowds, in fact, that they differ with respect to just one person: Whereas in the first crowd each person had a unique threshold, in this one nobody has a threshold of three, and two people have a threshold of four. To an outside observer, this difference is so minute as to be undetectable. We know they’re different because we’re playing God here, but no feasible psychological test or statistical model could tell these two crowds apart. So what happens now to the crowd’s behavior? It starts out the same: Mr. Crazy leads off just as before, and his sidekick and the guy with a threshold of two join in like clockwork. But then it hits a snag, because nobody has a threshold of three. The next most susceptible individuals are the pair who both have thresholds of four; yet we have only three rioters. So the potential riot stops before it even gets started.

Now imagine, finally, what observers in these two neighboring towns would see. In town A, they would witness an all-out riot, complete with smashed shop windows and overturned cars. In town B, they would see a few loutish individuals jostling an otherwise orderly crowd. If these observers were to compare notes later, they would try to figure out what it was about the
people
or their
circumstances
that must have been different. Perhaps the students in town A were angrier or more desperate than those in town B. Perhaps the shops were less well protected, or perhaps the police were more aggressive, or perhaps the crowd in town A had a particularly inflammatory speaker. These are the kinds of explanations that common sense would suggest. Obviously
something must have been different, or else how can we explain such dramatically divergent outcomes? But in fact we know that apart from the threshold of a single individual,
nothing
about the people or their circumstances was different at all. This last point is critical because the only way a representative agent model could account for the different outcomes observed in town A and town B would be if there were some critical difference between the average properties of the two populations, and the averages are for all intents and purposes the same.

The problem sounds similar to the one my students encountered when trying to explain the difference between organ-donor rates in Austria and Germany, but it’s actually quite different. In the organ-donor case, remember, the problem was that my students tried to understand the difference in terms of rational incentives, when in reality it was dominated by the default setting. In other words, they had the wrong model of individual behavior. But in the organ-donor case at least, once you understand how important the default bias is, it becomes clear why the donor rates are so wildly different. In Granovetter’s riot model, by contrast, it doesn’t matter
what
model of individual behavior you have—because in any reasonable sense the two populations are indistinguishable. To understand how the different outcomes emerge, you must take into account the interactions
between
individuals, which in turn requires that you follow the full sequence of individual decisions, each unfolding on top of the others. This is the micro-macro problem arriving in full force. And the minute you try to skip over it, say by substituting a representative agent for the behavior of the collective, you will have missed the whole essence of what is happening, no matter what you assume about the agent.

CUMULATIVE ADVANTAGE

Granovetter’s “riot model” makes a profound statement about the limits of what can be understood about collective behavior by thinking only about individual behavior. That said, the model is extremely—almost comically—simple, and is likely to be wrong in all sorts of ways. In most real-world choices, for example, we are choosing between potentially many options, not just the two—riot or don’t riot—in Granovetter’s model. Nor does it seem likely that the manner in which we influence one another in the real world is anything as simple as the threshold rule that Granovetter proposed. In many routine situations, when choosing, say, a new artist to listen to, a new book to read, or a new restaurant to visit, it often makes sense to ask other people for advice, or simply to pay attention to the choices they have made, on the grounds that if they like something you’re more likely to like it too. In addition, your friends may influence which music you choose to listen to or which books you choose to read not only because you assume that they have already done some work filtering out the various options but also because you will enjoy talking about them and sharing the same cultural references.
13

Social influence of this general kind is likely ubiquitous. But unlike the simple threshold of Granovetter’s thought experiment, the resulting decision rule is neither binary nor deterministic. Rather, when people tend to like something that other people like, differences in popularity are subject to what is called cumulative advantage, meaning that once, say, a song or a book becomes more popular than another, it will tend to become more popular still. Over the years, researchers have studied a number of different types of cumulative advantage models, but they all have the flavor that even tiny
random fluctuations tend to get bigger over time, generating potentially enormous differences in the long run, a phenomenon that is similar to the famous “butterfly effect” from chaos theory, which says that a butterfly fluttering its wings in China can lead to a hurricane months later and oceans away.
14

As with Granovetter’s model, cumulative advantage models have disruptive implications for the kinds of explanations that we give of success and failure in cultural markets. Commonsense explanations, remember, focus on the thing itself—the song, the book, or the company—and account for its success solely in terms of its intrinsic attributes. If we were to imagine history being somehow “rerun” many times, therefore, explanations in which intrinsic attributes were the only things that mattered would predict that the same outcome would pertain every time. By contrast, cumulative advantage would predict that even identical universes, starting out with the same set of people and objects and tastes, would nevertheless generate different cultural or marketplace winners. The
Mona Lisa
would be popular in this world, but in some other version of history it would be just one of many masterpieces, while another painting that most of us have never heard of would be in its place. Likewise, the success of
Harry Potter
, Facebook, and
The Hangover
would turn out to be a product of chance and timing as much as of intrinsic quality.

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