Social networks and the law of the few

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<p style="padding: 0px 0px 0.5em; margin: 0px;"><em>Romesh Vaitilingam interviews Sanjeev Goyal for Vox</em></p>
<p style="padding: 0px 0px 0.5em; margin: 0px;"><em>January 2011</em></p>
<p style="padding: 0px 0px 0.5em; margin: 0px;"><em>Transcription of an VoxEU audio interview [http://www.voxeu.org/index.php?q=node/6038]</em></p>
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<p><strong>Romesh Vaitilingam:</strong> Welcome to Vox Talks, a series of audio interviews with leading economists from around the world. My name is Romesh Vaitilingam, and today's interview is with Sanjeev Goyal, professor of Economics at the University of Cambridge. Sanjeev and I met in August, 2010, at the European Economic Association's annual meetings in Glasgow, where we spoke about his research program on the economics of social networks.</p>
<p><strong>Sanjeev Goyal:</strong> A very nice and very simple way of thinking about social networks, or networks more generally, because I think many networks are, like networks between firms or networks between web pages, they're more technological, if you like, in some sense. But networks more generally, they sort of sit somewhere in between small number economics a few bidders in an auction and large competitor markets, like farmers selling grains, consumers buying food, or traders in financial markets.</p>
<p>So the way I like to think about networks and why I think they're very important is, I think if you think about things that economists really care about, whether it's getting jobs, whether it's choosing which medicine to use, maybe which brands of products to buy for doctors and which medicines to prescribe, I think these are all choices that people make where a lot of what goes on is, they share information, they talk to each other.</p>
<p>That shapes their attitudes, but it also gives them information, which shapes their choices. And choices is what economics is mostly about. So in some sense, we've been missing this crucial social interaction element, which is usually in small numbers. We interact with a few hundred friends. But they in turn interact with other people, and that's what gets us to networks and graphs.</p>
<p>So that's how I see networks as being central to understanding a lot of what economics is about. I see it as being intimately related to mathematics or graphs, and intimately related to sociology, because sociology is very much concerned with social structure.</p>
<p><strong>Romesh:</strong> Can you give us a broad depiction of how the economics of social networks has evolved? It's a relatively new area, and perhaps a bit more of the feel about how it connects with other disciplines. As you said, it's a field that sociologists have been thinking about for a while. Have economists come in and in a way colonized this field of study?</p>
<p><strong>Sanjeev:</strong> In the late 80s, early 90s, people started doing evolutionary game theory. So they started thinking about large populations, games being played amongst large populations, and at the same time they started thinking about bounded rationality. Once we started thinking about population as in bounded rationality and dynamics, some of us started also realizing that interaction is not uniform or global. Not random, in a sense, but there are structures.</p>
<p>We talk a lot to some people and rarely to some others, and never talk to most people. We look at some newspapers, we read some books, and we share this information, but a few friends and colleagues. Somehow it seemed to matter, if you just talked about it.</p>
<p>And then there was work, of course, in evolutionary game theory, on cooperation, which was hinting at how it was this long, ongoing debate. This big controversy about whether you have group selection, whether you have altruism, and that seems to be about small numbers which are located in larger numbers. I'm talking about this sort of ferment in the early 90s.</p>
<p>So against this background, people started thinking about very simple models of interaction, like people on a line, and they interact with their neighbors. Now this is a very specific sort of a network, and they suddenly realized that things are quite different in this kind of a setting compared to a setting where they are interacting uniformly with everyone else.</p>
<p>This realization gradually led some of us to start thinking about a richer class of these sorts of interactions. These neighborhoods, if you like, overlapping neighborhoods. That led some of us to start thinking about networks, because that's the most natural way to write down overlapping interactions, interconnections between people.</p>
<p>And so the first wave of work in the 90s was really about taking problems that people had looked at, whether it's coordination problems in economics, the spread of language, the spread of social norms, cooperation and business dilemmas.</p>
<p>But now instead of people playing in a small group or in large groups, people playing them in structured networks. Where I play with you, and I play with X, and you play with some other friends, you play with some other people with whom I don't play. That's sort of a network.</p>
<p>And it turned out that, through the 90s, there was a body of work which explored this. I think one of the big things that happened in that period was how information diffuses in networks. How people choose, make choices, how that shapes information generation and diffusion in networks.</p>
<p>So there was a body of work in the 90s which really bought into using networks to understand learning and diffusion of ideas. But once we started doing that, we started then asking, &quot;Where do these networks come from?&quot; That led some of us to write down models of network formation. I think that was actually a big revolution because that, as I said, it connects very intimately to social structure, which connects to sociology.</p>
<p>So we are now thinking of how social structure evolves, because people decide, make choices about who to connect with and who not to connect with. And that was, that's quite new. We started, as economists, getting much closer to discrete mathematics, graph theory. There was this old literature, 50s and 60s, Erdős&ndash;R&eacute;nyi, random graph models, and there was this work in &quot;Philosophy of Science,&quot; by Price, on citation networks.</p>
<p>Suddenly we were in touch with these bodies of work. We brought game theory, strategic thinking, into this sort of world, which is what economists bring to problems. Incentives, and strategic interaction. That's sort of how things started, really, in the mid and late 90s. And since then, there has been an absolute explosion. Through the last ten years, it's been one of the most dynamic and I think one of the most exciting fields.</p>
<p><strong>Romesh:</strong> What has been the significance of the Internet giving? Because in a way, when you talk about networks now, you're connecting with regular people. Because everyone thinks about social media, talks about their connections through Facebook, and their friends connected online, online world. We all have a kind of understanding of this network, the way it connected to people and they connected to other people. Has that been significant in a way? The development, one way of providing you data to actually analyze some of the models you're writing now?</p>
<p><strong>Sanjeev:</strong> Yes, and this is, I think this is, I'd say broadly, slightly more broadly than the Internet. The Internet has clearly been, it just makes you think of networks, and the web. You can see these links the web pages, and you can see, &quot;This is a network.&quot; It just makes everything so visual and graphic. But more generally what the web and Internet reflect is really this enormous growth in computing power. But of the course the Internet is more than that, it's the interconnections. But that has enabled us to actually collect and process very rich and large datasets. Traditionally, 50s, 60s, 70s, there is a very rich literature in networks, but mostly it was challenged and ultimately constrained by computing power considerations, by how much you could collect, how you could process this information.<br />
Once this computing power's available and this network was so salient, the Internet, you could actually collect very large sets of data and you could analyze them. You could process them.</p>
<p>And around the time of the Internet of course in the last five years or so, we've had this I just think of it as a revolution of social networking, online social networking, which has made everything even more... I mean, it made everything so transparent.</p>
<p>People create their social space. They construct it by forming links, deleting links. You can visualize it, you see things happening in this network and it's almost irresistible. Really, ongoing construction, dynamic construction of social networks, it's in your face, really.</p>
<p>So clearly, it has made it very salient and it has made it much more feasible. And there is no denying that the computing power and the visibility of the Net have been very, very major factors.</p>
<p>So I think they've done two things. They've made things feasible that and I'll ask questions about how information about jobs, for instance or about a variety of things, product adoption, happen. But they're also probably my sense is that they've actually brought creative new phenomena entirely online versus offline, what is their relationship? And that raises fundamental, absolutely deep and fundamental questions. Some of them I think are quite new, actually.</p>
<p><strong>Romesh:</strong> Practically speaking, how does network analysis think about the sort of key issues that the economics addresses about individuals making decisions about their consumption, about their labor supply, about firms making decisions about markets they go into, about their pricing decisions? How does the network economics think about those kinds of things?</p>
<p><strong>Sanjeev:</strong> This has been one of the interesting developments. I think in each of these things you were mentioning, how do people make choices? So you might ask, how do people make choices between different crops, for example? Whether to grow cassava or to grow pineapples? To grow cotton or to grow some grains? You know, cash crops or grains? Farmers, how do they do these things? These are very big decisions in some parts of Africa and in other parts of the world. In fact, it's been very, very well documented that there has been an enormous surge in crops, what people grow. One of the things that some of us have done is actually to empirically investigate how this has come about in aggregate numbers, how has it come about? What is the time factor?</p>
<p>And then when they started thinking about it, we had to ask, is there local information sharing? Choosing a crop is a very complicated decision because it has to fit your soil, it has to fit your weather conditions. And the mix of chemicals, the mix of seeds and fertilizers and insecticides, there are many, many things that all have to hang together.</p>
<p>So you really do need to get a lot of things right and there are very big payoffs and big downsides, so you do need to it's very intricate. And so you rely a lot on what's happening around you. It's just unavoidable.</p>
<p>A World Bank expert comes and tells you to do something, you are unlikely to switch your crops because you really need to make sure that this works right. And you need to talk with people around you, people who are facing the same constraints, the same conditions.</p>
<p>And so indeed, we started thinking about empirical work. And then we started thinking, how would we write down theoretical models to understand how who talks to whom, how does that matter for the diffusion of crops, diffusion of new hybrid seeds, for instance? And it's been absolutely fascinating.</p>
<p>One of the things, just to carry on with this, because I think that communication networks broadly speaking has been one of the more visible and one of the more fascinating most studied phenomena.</p>
<p>One of the things in early work I did with Venkatesh Bala for instance in the 90s, what we were sort of able to formally establish was that in communication networks, if you have choices between unknown options... You know, more recently there's been this expression &quot;wisdom of crowds.&quot; If you have enough people, somehow the crowd will get it right. So we proved a theorem that crowds will sort of get it right, but only if they don't have too many opinion leaders. They don't have royal families or they don't have people who are too influential.</p>
<p>This is an important insight in more recently work by many other researchers in different fields in economics, but also in other fields, has generalized this insight that somehow if you want to get things right, you have lots of experimentation going on in different parts of the society. You don't want people to prematurely be only influenced by a few key people. That will dampen experimentation, and that might prematurely switch people off.</p>
<p>So this sort of insight is important because in many communication networks, indeed, this is exactly the structure of the network. Whether you look at the web or you look at Twitter, indeed what people have observed over the last 10 years is that this is exactly the structure. It is what as known as &quot;the law of the few.&quot; There are a few people who are observed by millions of people, and most of us have a few contacts.</p>
<p>But then all of us observe a few key people. It could be celebrities, it could be Barack Obama, it could be a musician, or it could be a research leader. It could be a news website like BBC.</p>
<p>But what's happening is that this is exactly the setting which our theorem hinted at as problematic from a point of view of long term learning or dynamism. Because if the leaders get it wrong, because there are so many people following these leaders, they can also switch and get it wrong. And so local experimentation which is going on will basically be postponed.</p>
<p>And this law of the few is a very robust kind of observation. If you look at many peer to peer networks, you look at many websites like Flickr or YouTube, you again see that a lot of the value or the excitement is because people place material there, they upload material.</p>
<p>But if you ask who are the people uploading this material, again you see that there is this law of the few at work. A few people actually do most of the uploading. A vast majority of the people do almost no uploading at all.</p>
<p>So this is very much, it's not quite a communication network, but it has in some sense the same sort of structure, you have a very large number of people who are quite passive, who have small local connections. And then there are these core hubs, these opinion leaders, the essential hubs. And they turn up in online social networks, they are then villages. And so the theorem has a fairly wide reach.</p>
<p>So that gives you a sense of how the empirics, you know, with regard to crop choice between pineapple and cassava for instance, the theory with regard to how network structures facilitate or hamper experimentation and dynamism. How that fits together and how it actually fits together with this new world of online social networks.</p>
<p><strong>Romesh:</strong> Sanjeev Goyal, thank you very much.</p>