Hi. In this lecture we're going to look at a model that's a favorite of mine, known as the standing ovation model. Now this is a model that builds off the [inaudible] model it's just really an extension. But it can allow us to sort of think about threshold based models of participation and pure effects in a little more subtle ways. Why standing ovations, those are kind of a funny thing to study. Well here's why. Think about a standing ovation. When The performance ends, you don't have a lot of time to decide whether you are going to stand up or not. You gotta make sort of a fairly quick judgment. You're going to clap of course but then you gotta decide do I stand or do I not stand. And then after the standing ovation either starts or doesn't start you gotta make another decision, do I stand up, do I follow these people, or do I you know stay sitting. So when you think about human behavior there's going to be different models that we play with throughout the course about how humans act. One model will be that people are optimizing, that they make rational choices in all setting. When it comes [inaudible] of a standing ovations that is probably a difficult thing to do because it is all happening so fast. So instead, what people probably do is they follow rules. So standing ovations are a nice place to sort of get people, it is a nice domain to get people thinking about rule based behavior, about people following simple rules and then ask me how the rules aggregate. So it is kind of the [inaudible] model that way, right people follow rules in the aggregate and we are going to see what is going to happen, only here right this is a model of ... I think of it as like peer effect. Now, why, so we think of a standing ovation, one way to think about it is as a peer effect. Right? Other people stand and then you stand. What's nice about standing ovations, another thing that is nice about it, is that it can also be information. So what I mean by that. So suppose you, you're sitting in the theater and you notice that the woman sitting in front of you to the left, you know is talking with her neighbor and she seems to know a lot about the theater, about the performance you're going to see. And she seems like someone who's a little more sophisticated than you are. So, play ends and you're kinda said do I stand or not stand? And you see her just pop up. She pops up, she's applauding like crazy. Well, you figure she's conveying some information that could be useful to you about the quality of the show and so you decide to stand up. Right, so it's not just that you're copying her for the sake of copying her, like in the Granovetter model, like with the purple hats. Here you're copying her because you think she's telling you something about how good the show is. Okay, so that's an information effect. So what we want to do in a model that's going to capture these sort of pure effects and information effects. So, just like in the Granovetter model we're going to have a threshold, and there's going to be a threshold in which I stand up but it is going to be somewhat different. So in the [inaudible] model, the thresholds were the number of other people doing the action. Because spreading the collective action, rioting, wearing the purple hat, was there are some other number of other people I needed for me to do it. Here the threshold is going to be related to the quality of the show. So you can think of it ... Let's suppose shows have qualities between zero and one hundred And your threshold may be 70 or 60. Any show above 70 you stand, any show below 70 you don't stand. So if the quality is above the threshold you stand. If the quality is below your threshold you don't stand. But let's make this a little bit more sophisticated so let's suppose instead of there just being you know you see the quality, let's suppose you get something called a signal. Now the signal is going to be the quality plus some other term. Some term E, which we can think of as an error, right? So you don't see the true quality, you see the quality plus some noise. And now your decision to stand doesn't depend on the quality of your threshold, it depends on your signal. And the threshold. If your signal's above the threshold, you stand. If your signal's below the threshold, you don't stand. Okay, so that's the model. Well, one more thing, one more thing, because that was the initial decision to stand. Now you've got decide, okay, after the sort of initial decision, do you stand once you see other people standing. So we can assume is that you've got some sort of threshold at Right, it says if ten percent of people are standing, I'll stand. Or maybe if thirty percent of people are standing, I'll stand. Right? And that also affects your behavior. So the rule really depends on just two things. One, this, your individual, your initial threshold for quality. And then two, this second threshold for how many other people have to be standing for you to continue to stand. Okay? So that's the model. So now let's think through some of the results we can get from this model. So the first claim is higher the quality of the show, the more likely to be a standing ovation. Now why is that true? Well, think about it. You stand if the quality plus the air, which is your signal, is above the threshold. So if the quality is higher, your quality plus your air [inaudible] is higher, you're more likely to be over the threshold, more likely to get a standing ovation. Again, not surprising, one thing we want from models is we want them to give us results that make sense, right, basic things that make sense. And then the other stuff, right, maybe more surprising, but we want some stuff to really accord with our logic right off the bat, okay? What's another result? Another result is lower our threshold make our T level more likely to get a standing ovation. Why is that true? Again, same logic, we need our signal only 40 plus appear to be bigger than our threshold. So if my threshold falls from 70 to 50 to 30 to twenty, I'm [inaudible] to stand up, right? Makes perfect sense, result three The lower X, remember X was the percentage of people who have to stand for me to stand subsequently, then there's going to be more ovations. Right, okay, that makes sense as well, right. And the logic is you stand more than X percent stand, so if X goes from, you know, 60%, if you need 60 percent of the people standing down to ten%, you only need ten percent of the people standing, then you are much more likely to get a standing ovation because if twelve percent of the people stand then everybody stands up. Alright, now, what would cause X to be big? And what would cause X to be small. So this is [inaudible] you should write down these little variables in terms of stuff, and then you got to think, what does that mean in the real world so what would it mean for X to be bigger, X to be smaller. That is sort of how willing you are to stand based on other peoples standing. So big X would mean... If you didn't stand initially you need to see a ton of people standing before you stand. So this would represent people who are really secure in who they are. A small act would be people who are really ready to jump on any bandwagon, right? So five percent of people are standing and then they stand. So this X tells us something about the people in the audience, right? Which is an interesting thing to think about. Okay, let's go back to this signal. Remember I said that you get this signal [inaudible] which is Q plus this term E what is E? Well remember I said E is error, right, so I said that there is a quality of the show that maybe like 55, and you don't see 55 maybe you see 58, 52. So it is variation in what we perceive. Well another way to think of that variation but what we perceive would be to think of it as diversity, right, if you and I care about different things we have had different life experiences, we may interpret the theatre, the performance differently then one another. And as a result what's a 50 to you may be a 60 to me, or what's a 70 to me maybe an 85 to you. So, because you and I are different we are actually going to have different qualities. So this E term Right, this Q plus C. We can think of this as either error or we can think of it as diversity and so that, why does that matter? Well it matters because when you think about interpreting the model, like what the model tells us in the one case it will tell us well what happens if people have more noise in terms of how they interpret this show oral kind of the way you can say, what does it mean if the audience is more diverse? Right? Okay, so, well, what does it mean? Well, to do that now we have to think a little bit, now we actually have to sort of do some math. So lets do an example. Assume we have 1,000 people. The threshold for all these people to make it simple is 60 and the [inaudible] is 50. So 50 is less than 60, right? So that means people aren't going to stand for the most part. So there's no error, no variation, nobody would stand up. Okay, so let's do a case first where the error comes really small so its 50. Now the mean here is 50 Right, and the error term is either between minus fifteen and plus fifteen. So someone who's got an error of minus fifteen gives it a 35 and someone who's got an error of plus fifteen gives it a 65. So it's right, 65 there. So all these people below 60, they're going to sit. They're going to clap, they may clap nicely but they are going to sit because it's below their threshold. So only this small set of people here stands up so unless X is really small, what's going to happen here is few people stand up, no standing ovation. But now let's increase the variation, let's suppose the variation goes from minus 50 to 50. Well now the people give a score of minus 50, they're going to give a score of zero. And the people who give a score of plus 50, they're going to give it a score of one hundred. Now once again, the average score is still 50, right, so that is less than 60, so the average person doesn't stand up, but here all these people stand up. So they assume people are sort of uniformly distributed between zero and a hundred, so they're equally distributed across there, that means that forty percent of people will stand up. What that means is, unless X is really small, as long as X is above you know, 40, below 40%, you're going to get a standing ovation. And think about it, if you go to the theater and you see 30 percent of people stand up, you're likely to stand up. So we get here, where we have this large diversity, or large air term, be more likely to get a standing ovation. Okay, so that's claim four If Q is less than T, so if its a bad show, well not if your a bad show, it's not a great show, you're more likely to get a standing ovation if the variance in E is larger, right? And again that's because you stand that Q plus E is bigger than the threshold if this has more, if there's more people with big E's, you're going to have more people that stand, and that's more likely to cascade into a full blown standing ovation. Okay, so let's think about what would cause E to be big, well one thing would be... The audience, right? So if you have an unsophisticated audience. You know maybe they don't get it. That means some people will think it's great, some people think it's bad, you know, you're just going to get more variation. Or, you could have a diverse audience, right? You could have people from different backgrounds, you're going to get more variation. The performance itself could matter. If it's really complex and hard to figure out, that could cause variation. Or if it's multi-dimensional, if there's lots going on, that could cause more variation. So, different attributes of the audience and the performance could result in more variation in that E term, which could lead to more standing ovations. So let's think about what we know. What did we learn? Higher quality show, more likely to be a standing ovation. Not a surprise. Lower threshold for standing, right? We are not going to do a standing ovation. Again, not a huge surprise. So, are people are more willing to stand and jump on the bandwagon, lower X? More likely to be a standing ovation or, you know, larger peer effects when they call that. And the last thing is like more variation. When there's more variation, more diversity, in that error term, then More likely to get extinguished, and so here we've got these four sort of nice results that help us sort of understand when we are going to get standing ovations and when we are not. Now you could "say how much did the model help up?" Well my guess is that if you just thought about standing ovations without constructing a model you might figure out, yeah, better shows get standing ovations, you know, people more willing to give standing ovations are giving standing ovations, and if people are more susceptible to influence you are going to get standing ovations, but you probably wouldn't have gotten this one. You probably wouldn't have gotten more variation, now you might have if you learned the Granovetter model, right, but, most likely you wouldn't have had it. Now, that's the simple standing ovation, let's, let's ramp it up, let's have some fun, right? [inaudible] Let's do an advanced standing ovation model, now I used to give the standing ovation model, as this assignment for students and, they construct models a lot like the ones we just did. Now what's funny is if you, if you don't give it to a student, if you just ask somebody on the street to start describing a standing ovation or, just go into the theater, they'll include two things that weren't in the model. Now modeling requires leaving things out, but here are two things that almost everybody leaves out of standing ovation mode. The first one is the theatre itself, right, I mean your actually in a theatre, your not, in our model we just had these people who sort of saw everybody, but that's not true. The other thing is this, most people when they go to the theatre, they go with a date or a group. Sometimes you go alone, right if I am traveling to New York or something without my family, I may go to the theatre alone pick up one cheap ticket, but for the most part, when I am sitting in the theatre, I know I said most people are there in groups, so now we can ask Do these things matter? I mean these are features of the real world not in the model. Do they matter? Well, let's see. Lets look at the auditorium first. Here the auditorium After the standing ovation starts, mainly you have some site lines so you get some sort of cone in which you can see who's standing and not standing. Thinking about why that might matter, well Suppose, you know, I am sitting here I have this cone. I am sitting here I get this cone. Here I have that cone. Here I have that cone. So you see there are small cones and there's big cones. Let's think about the difference between those two. So what's a small cone person? A small cone person is somewhere in the front. They don't see anybody, right? But notice almost everybody sees them. So, they influence everybody but they're not influenced by hardly anybody. They're like celebrities. Right? They're celebrities who like we all care what these celebrities do, but they don't care much what we do. Right? Now, what about People in the back, because people in the back they can see almost everybody, right? But, almost nobody can see them, right? Anybody sitting in here, nobody can see these people, right? They can't look to the back of their heads or turn around or something. Well, these are more like academics, these are more like people like me, spend a lot of time studying how the world works but not that many people pay attention to what we say. More people care what Oprah or Ashton Kutcher say than what I say. So as a result, even though we have a better sense of what's going on, right, nobody listens to us. Let's think about the you know, ramifications of that. What that means is what we'd like is to get a standing ovation if the performance was good, and we'd like to not get one if the performance was bad. But what's happening is everybody is queuing off these celebrities, who really don't know what other people think and nobody's paying attention to the people in the back, who really do know what everyone thought. So this means that maybe the system isn't going to aggregate as well as we'd like it to. Right, so maybe we're not going to get the right answer as often as we would expect to. Okay, what about dates? What about the fact that you know, hey look you know, I got a date, going to the theater, how does that matter? Well think of this, with respect to the X term, like before I said I'm going to stand, I'm going to look around, I'm going to stand if, you know, X percent of people are standing up, but once I've got a date, if she stands up then I'm probably going to stand up. So what this means is, if you think about people in groups or in pairs, if one person in that pair stands up, then everybody might be more likely to stand up, which means that adding groups or adding dates or pairs means that you're going to get more standing ovations because if one person could them both to stand up that's going to increase the percentage of people standing up which will in turn is going to create more of a standing ovation. Okay, so what do we got? How do we increase the probability of standing ovation? Right? We had before we had before. Higher quality show, right, lower threshold larger peer effect, those are the obvious ones, right? More variation, the unobvious one. And now we have two more. Use celebrities, put people in the front, right? Put people in the front who are gonna stand up for sure. So pay somebody in the front to start an ovation. And then big groups, create groups of people and then if one of those people in the group stands up the whole group stands up, and that causes more people to stand up. So now we've got six ways you can cause standing ovations and I'm willing to guess that like these three might not be things you thought of, right. The people in the front matter more and that you want to create groups. So the model's actually helped us figure things out. Okay, so, wait, this point you can say okay Scott, this is all fun and good, but this is standing ovation, not that important. True, absolutely true, but again we are using this model, right, to help us sort of make sense about rule based behavior in environments where there are pure effects. One of the reasons we construct models is for fertility, so once we construct a standing ovation model we can use it someplace else, but where else can we use it? Well, we just studied, right, collective action problems or you know, participation problems, in political uprisings, riots and things like that. That looks a lot like the standing ovation model. And now you can think of who are celebrities? Right? And who are ... What does it mean to have big groups in that sort of context? Well, the celebrity is someone who has a lot of influence on other people. So if you want to start a political uprising you need those sorts of people. So this tells us something about that. It also works for things like academic performance. Suppose you got a school that's under performing and you want to sort of have people lift themselves up to work harder. How do you do it? Well, you can think we need to sort of raise quality, lower, you know, sort of lower these sort of thresholds of The barriers to be able to sort of engage in this productive behavior. You can do things like use celebrities. Right? And you can even create groups, okay, groups of students to work together to all do well, right, and that may cause other people to do well. Urban renewal, right? You can think of each one of these people instead of a, each one of these boxes, instead of it being a person standing up you can think of it as someone fixing up their house. Now what's interesting here is, let's go to that sort of variation idea. Well you could think we want to improve some city, let's give everybody a thousand dollars if they'll fix up their house. Well it could be that nobody does it, because it doesn't push anybody above their threshold to fix up their house. But the variation idea says if we give a handful of people a lot of money to fix up their house, they may do it and then that could cascade. In fact a lot of people who are studying urban renewal, push that sort of logic, that you should target particular areas where people are likely to do it, get things started, and help the process log rules. Alright, fitness and health, if you want to get a group of people of society even to become more healthy, that's a lot like a standing ovation. You need some people to do it and then you hope other people do it. Now that could be pure effects, right I see other people being healthy, I want to just copy them, or it could be information. I see them acting healthily, engaged in fitness and then I think, you know what, they're doing better than I'm doing, so maybe, you know, they seem happier and healthier, so I'll copy what they're doing. Even like, right, this online course, if I don't... This online course is like a standing ovation model. Each person deciding, do I stand up or not? Is the quality above my threshold, right? So, if I want people to take the online course I can draw lessons from the standing ovation model and think about how do I do it, you know, by using celebrities. And that's sometimes what I did, right, is I tried to get a lot of my friends who are celebrities from the academic world to say hey this is a cool course. Alright, so, that's the standing ovation model. It's a pure effect model, but it's also this sort of information model and it explains, again, why we see groups of people all doing, you know, similar stuff. Right? Because we see other people doing it, and then we copy them. And this tells us when we're likely to see it and when we're not likely to see it. Okay, thank you. [sound]
