Wisconsin Public Television University Place  The Ecology of Society  Simon Levin  9/11/13 UP921  cc >> Well, welcome. I've been told not to stand too close to the mic. It's great to see a wonderful turnout again, which I feel invigorated that this town has genuine intellectual curiosity that we get such a great turnout. Oh, yes. Who are you? So, I'm David Krakauer. I'm the director of the Wisconsin Institute for Discovery, and I'm the co-director of C4, the group that hosts this von Neumann event. Just a few points of information. For those of you who require help with a listening device, we do have some at the desk out front. So there are some that have been set aside for those who might need them. I also want to thank a few people. 

I want to thank John Wiley, the former chancellor who personally helped to underwrite this lecture series because he believed in the value of complexity science in this community. Also, the Templeton Foundation and then our own internal team for all their help making this possible, wheeling out all these chairs and advertising and so forth. There's Alan and Tim, Maria, Marianne, Laura, and many others. Just a reminder that on October the 9th we have James Evans coming from the University of Chicago, who is one of the principal exponents in field of culturomics, which is the application of computers to the study of society that obviously bears on our interests here. So let me just remind you about John von Neumann since this is the beginning of our new term. John von Neumann was an extraordinary individual. He lived from 1903 to 1957. He was a Hungarian American super genius. Many people thought he was probably an extraterrestrial. He was just so inhumanly intelligent. 

He was a mathematician, an early computer science pioneer, and a computational biologist. I think his life sets the gold standard for working at the interface, for doing truly creative and deep transdisciplinary work. He is what we would now call a complexity scientist, studying large-scale adaptive systems. So, collections of transistors, he pioneered the field of fault tolerant computation, neurons, a pioneer in the field of computational neuroscience, and Individuals in Society, one of the co-inventors of mathematical game theory. So his work, in some sense, was a unified contribution to the field that we now call collective behavior. And here's a quote from John von Neumann: "If people do not realize that mathematics is simple, it is only because they do not realize how complicated life is." And today's speaker, I think, Simon Levin, a former colleague at Princeton, on-going colleague at the Santa Fe Institute, I think is very much in the von Neumann tradition of bringing the simplicities and clarity of mathematical reasoning to the complexities of social and ecological phenomena. So, here's Simon's sort of long list of achievements. I won't give them all. But he's a George Moffett Professor of Biology at Princeton. He got his bachelor's degree in mathematics at Johns Hopkins, his PhD in mathematics at University of Maryland. 

Prior to be in Princeton, he was professor of applied mathematics at Cornell. He's won the Heineken Prize, which presumably involved drinking lots of beer. [LAUGHTER] He won the Kyoto Prize and the Margalef Prize in Spain. He has three honorary doctorates, including one from Michigan State. You basically cannot be in the field of ecology without being aware of the contributions of Simon. It's as simple as that. But not only academically but as an engaged citizen and as an educator. He's been on the board of directors of Concerned Scientists since 1979, he's been on the board of the Santa Fe Institute since the 1990s, and he supervised over 100 graduate students and postdocs. His work, in a nutshell, which he'll talk about, is concerned on the origin of complex pattern and the disappearance of complex pattern. So things you've heard about in this lecture series, the origin of swarms or herds or societies and their extinction. 

And he's extended this ecological framework beyond biology to encompass financial markets and culture as a whole. For those interested in Simon's work in an accessible form that might go beyond this lecture, I'd recommend his book, Fragile Dominions: Complexity in the Commons, published by Basic Books. Simon, welcome. [APPLAUSE]  >> Thank you, David, for your very kind introduction, and thank you for your very nice review of my book when it came out, also. And thanks to all of you for coming today. So here you see a prototypical collective phenomenon that I'll talk about a little bit later is starlings over Rome. But today I'm going to talk about public goods. That's what the title says, and public goods is a concept clarified by the great economist Paul Samuelson, who said, "these are goods which all enjoy in common in the sense that one individual's consumption of it leads to no subtractions from the ability of others to enjoy it." Now, in that sense, it distinguishes them from what are called common pool resources, like fisheries, where if I take a fish out of the ocean, then that reduces your access to them, but for the purposes of this lecture, I'm basically going to lump them together. These are goods that we all share in common, we all have interest in maintaining, but maybe individually none of us has sufficient interest to maintain. Now, this is not just a problem in economics and sustainability, it's a problem that occurs at all levels of biological organization. 

For example, you can think about cancer as something that goes against where individual cells and their behaviors are going against the public goods and the maintenance of the organism in which they live. And in the same way, there are people who are thinking about, including some of my collaborators, David Dingli and George Pacheco, thinking about cancer, and this paper people thinking about pathogens, and the degree in which they depend upon public goods, the production of cytokines, for example, in the cancer, and maybe we could take advantage of this to interfere with the production of the public goods as mechanisms to deal, in this case, with pathogens and, in the case of Dingli and Pacheco, with cancer. So these are very interesting problems in everything from ecology and society down to how the body operates. Now, despite the importance of public goods and common pool resources, we are depleting them. They are central to the future of humanity, but, as you can see here, this projection is now somewhat old from the World Resources Institute, the renewable resources per capita are going down. This is a simulation taken from the web of where you can simulate pollution events in Beijing. We are eroding our public goods. Why? Well, because of discounting. We discount the future. This is a picture of me my wife took a while ago, and every time I sit down to dinner I say I'm going to eat well, but it's just too attractive. 

So I'll worry about that tomorrow. That's discounting the future. And we also discount the interests of other individuals. This may be what we have in store for us when cell phones are made legal on airplanes. And these two things go together. So there are fundamental questions about how we should discount the future, how do we discount our own futures, and how much do we discount the futures of other individuals, and how do we discount other individual's interest even that are contemporary with us. The problem is that we live in a global commons in which individual agents act in their own self-interest, to a large extent, and they don't take into account the social costs. This is the fundamental problem in dealing, for example, with environmental problems is that the markets don't really account adequately for the externalities, the social costs of our behavior. And the problem, of course, are free riders, like this guy, who hitch a ride without paying the full cost. Now, the prototypical problem of this sort was the one that John Nash talk about in his thesis, the prisoner's dilemma. 

For those who don't know the prisoner's dilemma, the idea is that two prisoners have been captured, suspected of taking part of a crime, put in separate rooms, told that there's enough evidence to send them to prison but if they will give evidence on their compatriot, they'll get lighter sentences. The trouble is that both of them have incentives to defect, and if they defect, they're both worse off. So they'd be better to cooperate, that is with each other, by not giving evidence, but the only stable solution, as Nash showed, is what's called the Nash equilibrium, defection. And when we're dealing with public goods problems, this was identified two centuries ago by William Forster Lloyd as The Tragedy of the Commons, popularized in the last century, about 50 years ago, by Garrett Hardin, who said that the problem with the commons, as you see here, is that this is an area that everybody shares, for example, a grazing ground, but nobody has sufficient interest on their own. Only collective behaviors are going to be able to provide solutions to this problem. And Hardin identified this as mutual coercion, mutually agreed upon. And the maintenance of cooperation in small societies depends upon the development of shared and mutually agreed upon norms. And one person in my circle of acquaintances who really demonstrated that this works was the late Elinor Ostrom, who showed how it worked for small fishing communities. There are other examples. The lobster gangs of Maine, for example, that regulated lobster fisheries there. 

Stephen Lansing's wonderful work on the water temples of Bali that I don't have time to go into, but I recommend his book Priests and Programmers to you. And one of the oldest democratic institutions, certainly the oldest in Europe, being a millennium old, the Tribunal de los Aquas of Valencia, which resolves irrigation disputes and has been around and working for a long time. So it is possible, but the challenge to us is how do we extend this cooperative behavior from these smaller societies to the global level, like the G20, or can we actually even do that? The problem is that ecosystems and the biosphere are what are called complex adaptive systems. That means they are systems that are made up of lots of individual agents that interact with each other, each pursuing their own selfish agendas. And, on the base of this, microscopic patterns emerge that feedback to affect individual behaviors but on different time scales. In financial markets and economics, this is close to some of the ideas of Adam Smith, everybody is familiar with his discussion of the invisible hand. The idea that, and this is a quote from Adam Smith, "By pursuing his own interest, he frequently promotes that of the society more effectually than when he really intends to promote it." So the idea of the invisible hand, and Adam Smith, people give this quote but they don't give the caveats that he listed, was the notion that if individuals acting on their own in their own selfish interest would produce an efficient society. But we learned that that's not a guarantee. At least it's not a guarantee of producing the sort of outcome that we want. The invisible hand does not protect society. 

The system will find some equilibrium, but it's not necessarily one that's in the collective good. People have suggested similar phenomena for ecological systems. The idea introduced three decades ago of Gaia. Gaia, the goddess that helped the biosphere self-organize itself, and again led people to think the biosphere will take care of itself. Well, it probably will. It will reach some equilibrium. It's not necessarily an equilibrium that we'll be part of, though. So if you have particular outcome that you favor, you can't rely on a totally free market, whether it's in the financial system or whether it's in dealing with environmental problems. There is no goddess Gaia. So not just ecological systems but ecological systems and socioeconomic systems alike are complex adaptive systems. 

And the objective, therefore, in managing these must be to integrate bottom-up mechanisms, like evolved prosociality, that is caring about others, and collective action, about which I'll discuss a great deal today, together with top-down mechanisms, like rewards and punishments. Some balance between bottom-up free-market sort of approach and a regulatory approach, if we're going to achieve the sorts of governance that's both adaptive and as Lin Ostrom and her late husband Vincent Ostrom argued for polycentric, meaning have multiple centers, governance and agreements if we're going to deal with problems like climate change. And some of Lin's last papers were on approaches to climate change. There are a lot of challenges in managing complex adaptive systems. First of all, they play out on multiple scales. Individuals and whole systems are operating on very different scales. Scales of space, of time, and of organizational complexity. That means there are patterns that are emergent, self-organized, and consequently, to some extent, unpredictable because they don't come out the same way each time. Stephen Jay Gould pointed this out when he talked about running the tap of evolution over and over again. You wouldn't get the same results. 

These systems may have multiple stable states, which can lead to what's called path dependence, meaning depending on how you get started may influence where you end up, and hysteresis, meaning when you perturb a system from one state to another it's not so easy to get back. And there's been a lot of work done recently, including here by Steve Carpenter and colleagues on shallow lakes and in the Netherlands by Marten Scheffer, on how lakes can flip from a oligotrophic, namely healthy states, to eutrophic algae choked states. And we've done work on system flips in other systems. Indeed, these complex adaptive systems, like the economic markets, have the potential for contagious spread and therefore systemic risk, and the potential, as you can see illustrated in this figure, for destabilization and shifts from one regime to another, in other words from a healthy economy to an unhealthy one, or from an unhealthy one back to a healthy one, through the evolution of things you're not paying attention to that are operating on slower time scales, like pollution or the erosion of the regulatory feedbacks in the system. So stock markets crashed. This was the most famous crash, the depression of 1929, but we saw something almost as bad in 2008, in October of 2008. In March of 2008, I wrote a paper together with Bob May and George Sugihara that appeared in Nature called Ecology for Bankers. And what we said is we're just poor, modest ecologists but financial systems look scarily similar to ecosystems, and what we know about ecosystems is as they get over connected, their potential for collapse increases. Maybe we should worry about this for financial systems. We said, who knows, for instance, how the present concern over subprime loans will pan out. 

[LAUGHTER] Well, I wish I read this paper and not just written it. [LAUGHTER] Because I thought this was nice theory, but in fact the markets collapsed. It has made all three of us popular with financial consulting firms since, so there is some silver lining to it. Transition of this sort, though, are not limited to the financial markets. They're widespread. Marten Scheffer has been leading an effort to look for these sorts of patterns and early warning indicators of them and a variety of systems. He's written a book that I recommend to you called Critical Transitions in Nature and Society and been the lead author on a number of recent papers that involves several of us, including Steve Carpenter and Buz Brock and me, all here, and recently become particularly interested in how one could look for these early warning indicators of system change in medical practice. Things like migraine headaches, epileptic seizures, cardiac arrhythmias, all of these things involve sudden changes in the behavior of the systems and all of them potentially have some early warning indicators. So very active and exciting area of research. In general, the problem in all of these systems which are complex adaptive systems and which one has what I'll call microscopic elements giving rise to macroscopic patterns is that features emerge from the microscopic interactions and so it's analogous to what was faced in statistical physics in trying to understand the macroscopic properties of materials, of fluids for example, and how they transition, how water freezes or boils. 

Everybody understood that this was the result of the interactions of large numbers of molecules and equally understood that you didn't need to account for what every molecule was doing. That would be silly. Somehow we have to develop a way to scale from the microscopic to the macroscopic understanding what the collective properties are that are important and what detail can be ignored. So how do patterns emerge? Well, patterns emerge from individual interactions in all sorts of systems, even in bacterial communities like these wonderful patterns here that Eshel Ben-Jacob and Herbie Levine have produced. But similar problems of pattern formation have been addressed for a wide variety of organisms. For slime molds, about which I'll say a little bit later, for swarming bacteria, for insects, for invertebrates like krill in the ocean, for birds, for fish, and for ungulates. And even societies emerge as multi-cellular organisms. The cities we live in, the societies we live in are not societies that generally have been designed. Rather, the reason we have doctors and lawyers and professors and pharmacists and grocers is because there's a need that arises, and, therefore, people go to fill these gaps. Now, it's an interesting question to ask whether it's adequate to let systems self-organize or is there a role that government policies can stimulate because we don't have enough doctors, and to ask what's the optimal distribution of professions. 

But our societies have self-organized with different individuals filling different roles. So, managing the commons is both an environmental and an evolutionary challenge. In human societies, remember Garrett Hardin emphasized the need for mutual coercion mutually agreed upon. Users self-organized to develop norms, like Lin Ostrom discussed, and institutions and to design sanctions that can maintain them. In order to establish and maintain cooperation, cooperation meaning individual restraint in dealing with these public goods and common pool resources, from short-sighted resource overexploitation. And the question again is, can we extend this to the global level? Now, this really gets us back to thinking about evolutionary biology and the origins of altruism and cooperation. Altruism was a puzzle for Charles Darwin. It delayed the publication of The Origin of Species for nearly 20 years, and Darwin really never satisfactorily resolved this. It got resolved later, well understood, an offhand comment of JBS Haldane who said I would lay down my life for two siblings or for eight cousins, making the calculation. [LAUGHTER] One of the more detailed work of Bill Hamilton, who never believed that Haldane actually said that, on his work on social insects, demonstrating how genetic relatedness could play a role that you engage in activities to benefit your siblings. 

So this is well understood, at least it used to be well understood. It's not as well understood as it used to be. This very controversial paper by Martin Nowak, Corina Tarnita is my colleague at Princeton, and EO Wilson, came out a few years ago arguing both against the importance of kin selection and also about the way the bookkeeping is usually done. So I don't have time to talk about that, fortunately, but I wanted to introduce it. Now, public goods problems also represent central challenges in evolutionary biology. I've given you some examples of this. Organisms produce many public goods. These are leaf cutter ants, and in any sort of collective motion, information itself is a public good. If I'm moving towards the target and you observe me, you're learning something from me so I'm contributing something to the public good. I may or may not care about that. 

It depends on how competitive we are. I mentioned the cellular slime mold before, Dictyostelium discoideum. In this, individual cells organize themselves into these slugs that then move along, eventually stand up on end, the cells at the top spoliate and produce others, and the stalk cells aren't reproductive, so why should they engage in this activity? This remains an open and exciting question. How does this sort of altruistic or cooperative behavior evolve. But there are lots of other examples. But organisms engage in  chelation or production of siderophores, which are ways to sequester nutrients in the system so they're available. They fix nitrogen, and in all these cases there are advantages to the organisms but there are also advantages to the other organisms nearby who may not bother producing this if they can just steal from their neighbors things that leak out. The production of antibiotics in nature is a public good because if I'm a plant, if I'm a bacteria, I produce an antibiotic and you're next to me, all you have to do is be resistant to it. You will still gain the competitive advantage that I'm gaining by producing antibiotics. But we can think about antibiotics in another sense as well, namely as we overuse antibiotics in society, we are eroding a public good which is the effectiveness. 

So how do we get to cooperation? Bacteria produce extracellular polymers. So let me go a little bit more into that because this is work that I've been involved with together with my former student Carey Nadell and Kevin Foster and Bonnie Bassler. So the reason we all go to dentists is because we have bacteria that have caused this problem with your teeth. These bacteria produce things called biofilms which may involve, when you wake up in the morning, you've got hundreds of species of bacteria on your teeth. Sorry to tell you. And it won't do you any good not to get up in the morning. [LAUGHTER] The bacteria are still there. And what happens is that they formulate these super entities by the production of stuff that's technically called slime, these extracellular polymers, and based on that we get biofilms. So I want to take a look at that. Now, some bacteria produce these constitutively. 

That means they're just producing them all the time. Some of them only produce them when the density of other individuals is high enough. Some of them only produce it when it's low enough, and some of them never do it. So we looked at, and by we I mean this group up here, if I ever say I, I mean we. If I say we, I mean they did it. [LAUGHTER] So Carey Nadell led this paper that we published in PLOS Computational Biology, and Pseudomonas aeruginosa is an organism that only produces these extracellular polymers. By the way, what do the polymers do? They are both a signal to other individuals and they also provide a matrix for growth. And so they build on this. But Vibrio cholerae, which is the agent that's responsible for cholera only produces at a low density. So, why? I'm not going to give you the complete answer to this. 

This is an open question, but we looked at this through simulations in which we dripped nutrients down, remember what we means, and in which we looked at competition between these different types and tried to ascertain under what conditions you would get those producing at low densities, etc. So, this is something one could look at through evolutionary models. But what do human societies do? Well, in human societies we develop all sorts of arrangements. We have reciprocal altruism. You scratch my back, I'll scratch yours. We have insurance arrangements in which we deal with risk and uncertainty by creating public goods and common pool resources that we all share. I've been interested, I've been doing some work with a wonderful economist named Avinash Dixit, and together we found an application in work that my colleague Dan Rubenstein has been doing. Tribes in east Africa share grazing grounds. Now, if we're sharing grazing grounds, it may be that this year I've got good conditions and you've got bad ones or vice versa. So suppose you've got the good conditions and I've got the bad ones, I'd say I don't have any land to graze my cattle on, can I graze my cattle on your land? And you say, why should I let you do that? And I say, well, because next year the situation might be reversed, and if you let me do it this year, I'll let you send it to me if you need it next year. 

So you have to make a calculation, and this is going to depend upon what your discount rate is. How much you care about next year versus this year. So let's make it simple. I'm not going to do much math in this lecture, but there's a little bit. Suppose there are good years and bad years, and when one has a good year and another has a bad year, we move cattle, let's say M as the number, from the bad to the good. I've also got to make an investment. I make an investment in my cattle. I make an investment in my land. And so the question is, what's the optimal investment I should make? So this is a repeated game. So the first thing we do is we compute the social optimum. 

Now, what does that mean? Well, here A1 is my payoff, with the payoff in the good environment, A2 is the payoff in the bad environment, X1 is how many cattle I've got, and M is the number that have moved over. And so this is some function, you don't have to worry about the details, of the number of cattle in my land and how much I moved. This is what the commonists call a Cobb-Douglas function. It's not the only one you could use. And then there's still cattle left on the other land that's getting a payoff of A2. So that's X2 minus M that goes in there, plus my investment. And these are the cost functions of our investment. So the form of this function doesn't matter much, but the social planner, if I'm in charge of this whole system, I say I'm just going to move cattle from here to here, how do I maximize this quantity? And I find the optimum. But now the central planner goes away, and I have to ask is this social optimum self-enforcing? Will you and I reach an agreement which is going to last if there's not somebody there regulating it? And that is going to depend upon the discount rate. But if it doesn't work, if we can't come to an agreement, I can still come back to you and say, well, how about some reduced solution? I'll send you 10 cattle. 

And you say, okay, that I can deal with. And so this so-called second best solution asked what's the most, how closely can we get to the social optimum by the sorts of arrangements that are stable on their own. So I think these exchange agreements among east African herdsmen are interesting, but what I think is really interesting is that this same sort of reasoning goes into building international contracts and compacts and things of that sort. One thing I didn't mention is that many of these individuals are related to each other, and therefore prosociality, caring about others, those are my cousins over in the other place, may also facilitate cooperation. So, in general, contributions to public goods depend upon reciprocal arrangements like the ones I just talked about, intrinsic prosociality, just caring about others, and, the thing I want to talk about now, the establishment of norms, of laws, of taxes and incentives that really create effective prosociality. Some of the most famous work on social norms has been carried out by Ernst Fehr, and what he does are experiments like he'll take a room full of people, like this, give each one of them a certain amount of resources, and say, okay, now you have to spend your resources. You can either say you're going to spend it on yourself, you can put it into the public pool, or you can use it to punish other individuals because we're going to play this game repeatedly, everybody's going to know what everybody else did, and if you don't like what somebody else did, you can use your resources to punish them. It costs you but it costs them much more. And so what happens is when you play this repeatedly, individuals, over time, punish other individuals who deviate from the social norm at cost to themselves, and punishment itself becomes a norm. You can asked whether second order punishment, do people punish individuals who don't punish, that doesn't seem to be a major factor. 

But the lesson here, and from other work, is that norms are important to understand much apparently prosocial behavior, and these norms become formalized into rules and laws. A classic example that economists and behaviorists and anthropologists love is something called the ultimatum game. In the ultimatum game, I give Buz Brock here $100,000. I play this game in my class. I give him $100,000 and say you've got to share with that person over there that you don't know, that you'll never see again, but they know all the rules. And the rules are you decide how to share it. You can give them half, you can give them all, you could give them a dollar. And then they decide whether to accept it. There's no negotiation. They'll never play it again. 

If they turn you down, neither one of you gets anything. So I play this game in my class, Buz is not in the class, I wouldn't take a chance, and I gave $100,000 to one fellow, he didn't try to collect, luckily, and he offered another student $30,000. And she rejected it. And I said, but it's costing you $30,000. And she said, yeah, but it's costing him $70,000. So, people will do that. Now, most of us would not turn down $30,000, but we all have our price. If Buz offered you $3, you'd probably say for that it's worth punishing him, the pleasure I'll get out of him. There have been lots of studies in this in different societies. There's a paper I recommend to you by Joe Henrich and many collaborators called The Weirdest People in the World. 

And they looked at the different societies. Turns out people in the US are pretty generous. They're offering close to 50%, or maybe they're not generous, maybe they're playing this as a game theory problem, because from Buz's point of view he knows that he's got to take into account both the fairness of what he's offering and whether it's going to be accepted. The recipient has only to make a calculation on fairness. And economists would think you ought to take a dollar, right? So there's great variations across societies. And by the way, there's a variant on this game called the dictator game in which the other person that doesn't get a choice, and sometimes people become more generous now because it's all on them. It's just your sense of fairness. So if you look at these figures across different cultures, you'll see there's great variation not only in what people offer but in what they will accept. For example, in Kenya, almost any offer would be accepted. So they're much more sensible. 

But why do individuals do this? Why do they engage in behaviors that cost them in order to sustain a social norm? If I go in to buy a car and I expect it to cost $30,000 and it's $30,020, I'll say, okay, that's about what I expected to pay. If I go in to buy a cup of coffee and I expect it to be $3, I've adjusted my expectations from when I was younger, and it's $23 I'll be infuriated. So I've created a fairness heuristic. Individuals embed their decisions in some broader context in which they develop rules of thumb. I'll say in a minute why they have these rules of thumb. Heuristics, like fairness, to tell them what they should do under certain circumstances. The substitutes for calculation because they don't have the time to calculate what's the right thing to do. Obviously your history may be important here. And I think to understand this, we don't have a very good set of models for this, I think what one needs to do is to think about metagames where you develop responses to a class of situations but you don't know what the game is going to be. You don't know whether you're buying a car or a cup of coffee. 

You need some rules of thumb so you can make a quick decision. Brian Skyrms and his student Kevin Zollman have one paper, it's the only one I know, on metagames and approaches to these problems. It really goes back to ideas of Herbert Simon, we talked about bounded rationality, who said that in decision making you don't have time or you don't have the capability to make the full calculation of what's best so you need to develop some rules of thumb, some heuristics to allow you to make these decisions rapidly. So how do these fairness norms arise? I'll give you just one example. This is work done with two former, well one former student and a postdoc, Alessandro Tavoni and Maja Schluter, and we were interested in common pool resources where individuals withdraw, say, water or fish from a common pool. Maja works in Uzbekistan on water withdrawal systems. And the idea, and this is the other math in the lecture, is that you have two kinds of individuals, those that are cooperators, that withdraw at very low cooperative rates, and those that withdraw at higher rates. Well, obviously, those that withdraw at higher rates are getting more out of the system. But the cooperators band together to punish, they get in agreement, and they're are going to punish, through ostracism, the cooperators. And so we look at the dynamics of this system. 

We set up what's called a replicator dynamic to see who wins out, and it's pretty interesting. The answer is it all depends. And it depends on things like the uncertainty of the resource, etc, that I don't have time to talk about. But this axis here tells us how much more the selfish individuals withdraw multiplied in relationship to the cooperators. And this is the number of cooperators in the system. That is, the frequency of the cooperators in the system. And what this shows you is there are two possible equilibria here. One, where the norm is not established, where everybody withdraws as much as they can, but if you get above this threshold here, then you get the maintenance of the cooperative norm. And so this principle actually has become incorporated into lots of efforts and international agreements, things of that sort, that these agreements only go into effect if the number of signatories is above a certain amount. How do you get there, above that amount? It's a wonderful subject, the science of these agreements. 

So, the fairness norm can promote sustainable resource use if social disapproval is strong enough, there are implications for global agreements, and enforcement is essential. And it's not just in these situations that enforcement is essential. Jessica Flack and David Krakauer and their colleagues have written this interesting paper on how policing stabilizes the construction of social niches in primates. It's widespread. So far, collective action can be effective if it includes enforcement. Prosociality is an important contributor, caring about others, to the maintenance of public goods and common pool resources. And the last question I want to address is, how are collective decision made? How do we get there? Now, this has been a rich mathematical subject for a while. There's a whole subject called voting theory that people like Don Saari and Steven Brams have been involved with that asks how do individuals reach collective decisions? And a lot of this is applicable to how you as an individual reach decisions because you've got competing, going back to that discounting and why I eat those big meals every night, you've got competing motives that you have to weigh every time you make a decision. So this leads to discounting. It also leads to something I don't have time to talk about called hyperbolic discounting. 

So I want to talk about the dynamics of collective phenomena and collective decision making in the last 15 minutes. So these are the starlings that you saw at the beginning. I thank Claudia --, but you can see this on the web. This remarkable picture, these are not quite all starlings. Those of you who are ornithologists will somewhere in there see a hawk, there it is, that's driving much of this behavior. But if you're training was in fluid dynamics, like mine, you say you've got to be able to explain that macroscopic behavior in terms of the microscopic behavior of individuals. And there's a lot of work on that that I won't say too much about. What I'm particularly interested in is the role of leadership and collective decision making in these groups. And this is work led by my former postdoc and now colleague Iain Couzin, work we published together in Nature, a lot of papers on this. The starting point is a very simple model. 

These are golden shiners. And the idea is that each individual at each point of time is moving in a certain direction, that's the velocity vector V, and it updates its movement in relation to two things. G, it's intrinsic information about where it thinks it ought to be going, and D, information about its neighbors. Where they are, what direction they're going, etc. I don't want to say too much about the political analogies to this, but think about this in terms of our politicians who have very strong senses of where they ought to be going and most of us who were following along. And so, in this model I'm going to show you, every individual has their own vector, their own G, their own D, and weights them differently. So some individuals are only leaders and some are only followers, and indeed we allow the weighting to change. If I'm going in a certain direction, this doesn't apply to politicians, if I'm going in a certain direction and nobody is following me, maybe I should think about going back in the other direction. So, in the first video I'll show here, there are a hundred individuals, 99 of them, the green dots, are followers, and one of them is a leader who wants to go up here. And so you see it's moving slowly, but the leader keeps being drawn in. 

Now, if I change that to five leaders, they make their way to the front, like on the slime mold, and eventually the slug moves up and to the right. And if I make that 10, the slug moves rather rapidly to the front. So all it takes is five or 10 individuals. These animals groups can be led by a very small number of individuals. These are groups of different sizes. This is the proportion of informed individuals. It's more instructive to look at the actual number, and in all of these, by the time you get up to five or 10, the speed with which you moved towards the goal is about as good as you can get. So animal groups are led by a very small number of individuals. So, too, are human societies. A few leaders, and most people using heuristics, should I follow, don't think through things by themselves and we get collective motion. 

Now, everything I showed you so far all of the leaders wanted to go the same direction. So we also looked at what happens if, say, five want to go here and five want to go here. My pointer's not working that well, but you can see that. And if the difference is not too great, they'll split the difference. But as the difference becomes large, the group has to make some kind of decision. Either it goes one way or the other or it bifurcates. So, for example, you see that behavior is possible here. Five individuals want to go north, five want to go south, and eventually the group splits. Or, this is a stochastic model, so the group goes back and forth. When it gets up towards that goal, all the arrows are no longer pointing in towards the same goal. 

So it goes back and forth. So we tried to understand all of these sorts of behaviors with some simple mathematical models. And this is work with Naomi Leonard and her students, Yannis Kevrekidis and his students, and with Iain Couzin. And there are strong connections to control theory. Naomi Leonard is a control theorist who's interested in putting robots out to gather information and how you maximize their collective information. Now, in building a model, we were inspired, to some extent, by some work by the great physicist Christiaan Huygens. Many of you have heard of Huygens. You may not know that he was also reportedly the inventor of the pendulum clock. And when he hung those clocks up on boards, he noticed that they would synchronize. Actually, they they would synchronize out of phase. 

So he got very interested in that and suggested some experiments that many people have reproduced. What I'm going to show you is a simulation that once you see it, if you haven't, you'll, I think, never forget it. This happens to have been done by my friend and colleague Tim Buchman, who was a trauma surgeon, is interested in the interconnections between the different organs in the body. And so what this experiment does, that's a little loud, isn't it, is to take metronomes, put them on a board, and lift them up on these two soda cans. And you'll see what happens is the board begins to move, an emergent phenomenon. And as it does, it conveys momentum to the individual. You see this one in the middle think its on its own, but it can't last long. So, again, a very small bit of coupling can lead to synchronizing. So we said, can we model this the way we would model coupled oscillators? And there's a large literature on that. This is work inspired by Kuramoto. 

And how we've adapted here, forget these terms at the end for a moment, we said let's break this ensemble up into three groups. Individuals who want to go in the direction theta one bar, and for those who aren't mathematicians, writing theta J dot, which is the derivative, is equal to the sin of theta one bar minus theta J will drive those individuals in that direction. These individuals want to go indirection two, and these individuals don't care where they go. They're just followers. And then we couple individuals together. Here they're coupled together all the same by adding this K term, which is the coupling term, but we also look at variable topologies and even where the strength of commitment can change. You can make or break connections, strengthening your connection to the nearest neighbors. And what happens is this plays out on two time scales. The individuals who want to go in direction one organized themselves into a group, the individuals who want to go in direction two organized themselves into a group, and these naive individuals organized themselves into a group. And then those groups become associated, depending on the initial conditions, into various configurations. 

And we could reproduce the collective behavior where everybody is synchronized and the splitting behavior and everything with these sorts of models. Important here is that the unopinionated or uninformed individuals are crucial to the consensus. Those individuals at the bottom, if you didn't have them, then it's much harder to get consensus and the group's much more likely to split apart. So the last thing we looked at is we said, well, suppose that we have different numbers of individuals who want to go in these different directions. Well, obviously, you're more likely to go in the direction where more leaders want to go unless the minority hold their views much more strongly. So what's the tradeoff there? So we looked at that in a paper that appeared in Science two years ago in which we approach this problem in four different ways. We use the model I just showed you. Iain and his group did experiments with golden shiners where they actually train them to targets and could look at these tradeoffs. And we looked at two models of decision making in human society. I'll show you one of them later. 

And in all these cases, what we found is as you increased, at very low numbers of uninformed individuals, if everybody's informed, you're much more likely to go in the direction of the minority because they're the more opinionated. But as you increased the number of uninformed individuals, democracy tends to dominate. That may be good, that may be bad. That's why we call this paper Uninformed Individuals Promote Democratic Consensus. And so you're much more likely to go in the direction of the majority. Eventually, if you're just swamped with uninformed individuals, you go back to almost 50/50. The last model I'll mention to you, just to give you an idea of what we looked at in humans, this is a very simple model we adapted from a model of Huepe. You have a network with a large number of nodes. A random network with a random interconnectedness. And then each individual and each time step asks its neighbors what their opinions are and update its opinions based on what its neighbors are doing in some nonlinear fashion. 

There's also a random probability of switching and switching to what your own intrinsic predilection is. And, finally, we allowed individuals to look around and say, hey, I'm linked to all these other individuals, I don't agree with them on anything, and so I'm going to break my linkages. And we get the same sort of results there. So the conclusions of all of these models and of all of the experiments is if you don't have very many unopinionated individuals, then the minority can dominate if its strongly opinionated enough. If you increase the number of unopinionated individuals, it's much more difficult. And I think this has strong implications for collective decision making and how societies make their decisions and how to influence collective actions. So, in conclusion, can we learn from this about human groups and leaders and followers? I've talked a lot about public goods and common pool resources, from everything from bacteria up to societies. These represent fundamental challenges in economics and in social systems and in sustainability as well as in evolutionary biology. We've learned that collective action can emerge from local interactions, but there are problems that play on multiple scales. But these collective decisions can, under some circumstances, impose this mutual coercion mutually agreed upon. 

But it gets harder and harder as groups get larger and larger. So linking these is key to understanding how are we going to manage the global commons that we all live in. Can cooperation be extended to the global level? The challenge here is that cooperation has evolved many times in evolution, but often, and usually, it's for the benefit of competition and conflict with other groups. We cooperate together to gain an advantage over other groups. But we've got to realize now that we all have a collective problem and that people of different cloths have to learn to work together to deal with what, for those of you remember, Pogo said, "We have met the enemy, and he is us." So we have a common enemy here: environmental degradation. And the question is, can we learn how to achieve international cooperation? It's at the core of our ability to deal with environmental degradation so that we can achieve a sustainable future for our children and our grandchildren. Thank you very much. [APPLAUSE]