Hi. In this lecture, we're going to look at our first model of peer effects. This is going to be a very short lecture. But I just want to get the idea of pure effects out there, and introduce what I believe is an interesting point, and that is namely that when we think about. These sort of contagion phenomena that happened [inaudible] pure effects. That sometimes. The tail wags the dog. What do I mean by that. What I mean is that sometimes. The people at the end of distribution. The extremists. Are the ones that really drive what happens. And as a result. That means it's gonna be incredibly difficult to predict what's gonna go on. So that's the basic lesson of this model. That the tail is gonna wag the dog. So, this model's gonna mark [inaudible]. He's the sociologist in Stanford university. And it's really fun. It's one of my favorite models just because of its simplicity and elegance. So, before I present the model, I want to, again, get to this point about predictability. So recently we've had some events, we've had uprisings in Libya and Egypt, and these caught everybody off-guard. There weren't experts lined up saying Egypt's about to topple, Libya?s about to topple. In fact, no one predicted it at all. You know, you don't have to go back, that far back in time to the Orange Revolution and see that nobody predicted that either, when Ukraine suddenly had this giant uprising, this political uprising, that too was unexpected. Dido for the Berlin Wall, you didn't have anybody seeing this coming. Now it's easy to say oh my gosh, you know, these experts aren't really experts. And there's a sense in which, well, you know, we can be critical with how smart the talking heads on TV are. But it wasn't just the talking heads. It was no one anywhere saw this stuff coming. So we're going to use [inaudible] model to explain, you know, why that's the case; why that can be very, very hard to anticipate a set of a whole bunch of people moving or joining some cause. Alright so, here's the model very simple, super simple. So there is n individuals to n people. Each person has a threshold. And the expression is like, how many other people would have to join the movement in order for them to join the movement. So if your threshold is zero, if your threshold is as well as the earnings, nobody's else has to join. You're gonna, you know, grab your stick and run out there in the streets, right. If your threshold is 50, then you need to seek 50 people out there before you joining them, before you joining a sort of collective movement. So each person has a different sort of threshold, for, whether they sort of join in and participate in some collective activity. So that's the model. What we want to do, we wanna analyze how that outcome varies depending on the distribution of these. Thresholds, right? What causes the collective action to occur, collective movement to occur, and when doesn't it. Okay, to, to sorta make this more fun and less heavy, instead of thinking about, you know, people rising up and overthrowing some dictator lets think about people wearing some silly thing, lie a purple hat. So, suppose you have a group of friends, just like, you know, five of you, and, you know, any one of you, at any given moment in time, could decide to start wearing a purple hat, and there's a question of, like, do you wear a purple hat? Well, lets suppose here's how it works. We've got five people, right? And here's their thresholds. So, the thresholds are 0,1,2, and two, and two. So. This person who's got a threshold of zero, you know what, they like how they look in, he likes how he looks in purple hats so he's just gonna get one. These three people who have thresholds of two, they're really not that keen on purple hats, but if their other two friends wear purple hats, then they're gonna get one. So let's see what happens. So the person who said the threshold of zero, well they buy the half, they put it on, because the threshold was zero. Once they buy the hat, the person who's got a threshold of one buys the hat, right, because one of their friends has the hat so they think well, you know, that's fine. I'll wear the hat. But once the two of them wear the hat, right, then these three people around here, these three people with a threshold of two, they buy the hat, and everybody ends up buying the hat, right. So you get this collective purple hat movement within your group of five people. Okay, that's example one. Okay, let's do another example. This time there's five people. Three of them have thresholds of one and two of them have thresholds of two. But what happens in this case? That's right. Nothing. Nobody ever buys the hat, because nobody's got a threshold of one. This is what I mean by the tail wagging the dog. There's no one that's got that threshold of zero. There's no one that really, really wants to wear the purple hat. So it never takes place. ?Kay? Let's do one more. So in this one we've got five people, and now their thresholds are zero, one, two, three, four, and five. So we've got someone at zero and someone at four. So zero through four are the thresholds. All right? Well, what happens in this case? Well, in this case, the person who's got a threshold of zero buys the hat. Right? Because they want the hat. Once he buys the hat, the person whose got a threshold of one buys the hat. Once those two have the hat, the person whose got the threshold of two buys the hat. Right? Once those three have the hat, the person with the threshold of three buys the hat. And once those four have the hat, this last person who really didn't want the purple hat, right?, gets the purple hat because all of his friends have it. So you end with all five people having the hat even though. The people really weren't that keen on having purple hats. So what do I mean by [inaudible]? Let's compare the last two examples in a little bit more detail. Remember the one example where nobody gets the [inaudible] the average value three with one and two with two. So the average number of people that'd have to get a [inaudible] for someone to get [inaudible] is 1.4. So people are pretty willing to get purple hats but there's just no one to get it started. In a second case where you've got zero, one, two, three, and four, the average [inaudible] 2.5, right? And so here you've got people who are really, really willing, is not very willing to get hats, but what happens is, they do get the hats because you've got this person at zero and this person at one, so the tail's able to wag the dog. Alright, so what do we learn from this? We learn that collective actions, collective participation is more likely to happen if -- right? -- there's lower thresholds. The people are really angry, really upset, or really wanna wear the purple hat. But we also learn, and this is the surprising part, that it's more likely to happen if there's more variation in the threshold, if there's more people that sort of, at the low end. Wonder where the hats are or participate in the collective action. That sort of cause the whole system to [inaudible] cuz the cascading effect in which you get the collective action. That's why. It can be very difficult to figure out if there's going to be some sort of uprising. Cuz you not only need to know the average level of discontent, right, you need to know the distribution of discontent. You gotta know, are there a handful of people, a group of people who are really willing to sort of rise up. And in addition to knowing that, you've gotta know were those people connected to one another interesting way. And that's what we'll start looking at in the next lecture. We're gonna push this a little bit further, and we're gonna do something called the standing ovation model, which allows us to look at this sort of pure effect phenomena in a little bit more detail. But for now, right, this simple [inaudible] model gives us a lot. It tells us, if you wanna ask, do you see collective action, yes. It matters how much people are willing to participate, right? What their, how low their thresholds are. But it also matters what that distribution of thresholds are. And if you get more ahead of geneity, more diversity, more people in that tail, really willing to riot, you're more likely to get a collective action. Thank you.