In these lectures, I describe some of the reasons why a person would want to take a modeling course. These reasons fall into four broad categories: 1)To be an intelligent citizen of the world 2) To be a clearer thinker 3) To understand and use data 4) To better decide, strategize, and design. There are two readings for this section. These should be read either after the first video or at the completion of all of the videos.We now jump directly into some models. We contrast two types of models that explain a single phenomenon, namely that people tend to live and interact with people who look, think, and act like themselves. After an introductory lecture, we cover famous models by Schelling and Granovetter that cover these phenomena. We follows those with a fun model about standing ovations that I wrote with my friend John Miller.
Why Model?
Hi, my name is Scotty Page. I'm a professor of complex systems, political science and economics at the University of Michigan in Ann Arbor. And I'd like to welcome you to this free online course called Model Thinking. In this opening lecture, I just want to do four things. The first thing I want to do is I want to sort of explain to you why you know, I personally think it's, it's so important and fun to take a course in models. Second, what I'd like to do is, I want to give you a sense of the outline of the course. Like, what we're gonna cover, a little bit, and how it's gonna be structured. Third thing is, I'll talk a little bit about an online course that you, I've never taught an online course before, you probably haven't taken one. So, let's talk a little bit how it's, just how it's structured, how it's set up, you know, what, what's out there on the web, that sort of thing. And then the last thing I'll do is I'll talk about, sort of, how I'm gonna structure particular units. Each unit will focus on a single model or a class of models. I wanna give you some sense of exactly how we're gonna unpack those things, analyze them and think about them, alright? Okay, so let's get started. Why model?. First reason, I think, is this. In order to be an intelligent citizen of the world, I think you have to understand models. Why do I say that? Well, when you think about, like, a liberal arts education, I think some of us classically think of, sort of, the great books, like, this long shelf of books that everyone should know. And when the great books curriculum was formed, right, and I'll talk about this some in the next lecture, you know, most of human knowledge didn't have models in it. Models are a relatively new phenomena. Right? So, if you take, you know, whether you go from anthropology to zoology, anywhere in between. When you go to college, you'll sorta find, like, oh my gosh, I'm learning models in this course. And we'll talk, in a minute, about some of the reasons why we're using models, right? But models are everywhere. And so in order to just be involved in a conversation, it's important these days that you can use and understand models. Alright. Reason number two. The reason models are everywhere, the reason they're everywhere from anthropology to zoology is, they're better, right? They sort of make us clearer, better thinkers. Anytime anybody's ever run a horse race between models making, you know, people using models to make decisions, and people not using models to make decisions, the people with models do better. So models just make you a better thinker. The reason why is that they sort of weed out the logical inconsistencies. They're a crutch, right, they just, you know, we sort of are crazy, you know, think silly things, can't think through all the logical consequences. Models sort of tie us to the mast a little bit. And in doing so, right, we think better. We get better at what we do. All right. Reason number three to use and understand data. So. There's just so much data out there, right? When I first became a social scientist, I mean, it was, it would be a real effort for somebody to go grab a data set. Now there's just a ton of it. I like to think of it as a fire hose of data, but my friends who are computer scientists, they call it a hairball of data, right, cuz it's just sort of all mangled and messed up. So, models, they'll just take that data, right, and sort of structure it into information, and then turn that information into knowledge. And so, without models, all we've just got is a whole bunch of numbers out there. With models, we actually get information and knowledge and eventually maybe even some wisdom. At least we can hope, right? Okay. Reason number four: last piece of main category reason. And by the way, the next
four lectures I'm gonna un-, I'm gonna sort of work through and unpack each of these four reasons in more depth. But I just sorta want to lay them out there, this first lecture. So, reason number four: to decide, strategize, and design. So, when you've gotta make a decision, whether it's, you know, whether you're the President of the United States or whether you're running your local PTO organization, it's helpful to build or structure that information in a way to make better decisions. So we'll learn about things like decision trees and game theory models and stuff like that, to just help us make better decisions and to strategize better. And also, at the very end of the class, we'll talk about design issues, right? You can use models to design things like institutions and policies and stuff like that. So, models just make it better at making choices, better at taking actions. Okay, so those are the big four. Now let's talk a little bit about, the outline of the course, what it's like. So, this isn't gonna be a typical course, not just because it's online, but because the structure of the course is very different. So most courses, like if you take a math course, it sort of starts here and moves along, right, with each thing building on the thing before it. Now the difficulty with a course like that is if you ever, like fall off the train, right? Fall behind. That's it. You're just lost. Because you know, everything, what I'm doing in lecture six you need to know lecture five. And for lecture five you need to know lecture four. Well this course is going to be very different. This course is going to be a little bit more like, a trip to the zoo. Right? So we're gonna learn about giraffes, and then we're gonna learn about rhinos, and then we go over the lion cage. So if you didn't quite understand the rhinos, it's not gonna hurt you too much when we go over the lion cage, right? So it's more like just moving from one topic to the next. They're somewhat related in that they're all sort of animals, but you don't need to fully know the giraffe to move to the rhino, but obviously like we're not gonna take like giraffes and rhinos, we're gonna study models and . So what kind of models. We're gonna study models like collective action models. These are models where individuals have to decide how much to contribute to something that's for the public good. We'll study things like the wisdom of crowds. Like, how is it that groups of people can be really smart? We'll study models that have, like, fancy names like models and Markov models. These are models of sort of processes, right? So they, they sound scary, but they're actually always sort of fun and interesting. We'll study game theory models. We'll study something called the Colonel Blotto game, which is a game where you have to decide how many resources to allocate across different front. So this can be thought of as a really interesting model of war. It can also be an interesting model of, you know, firm competition or sports, or legal defenses, all sorts of stuff. So. We're going to just you know, play with a whole bunch of moth. Everything from economic growth to tipping points. You know, a whole bunch in between. So it should be lots and lots of fun. Okay. What's the format for this? How's this going to work? What does an online course even look like? Okay. Well. Let's think about it. So first thing, there's these videos. You're watching one right now. I'm going to try to keep them between eight and fifteen minutes in length. Right? Sometimes I may sneak to sixteen but mostly I'll be creating fifteen minutes in length. And inside the videos there'll be questions. So I may, all of a sudden the video may stop and it'll say, what's the capital of Delaware? Well actually it won't say that, but something germane, hopefully, you know, to the, to the lecture. So, there'll be these fifteen eight to fifteen minute lectures. Each module, each section will have, you know, somewhere between like three and six of those. Right? Okay. In addition, there'll be readings. So on the wiki you'll find links to the reading. Not a bunch of these readings will come out of some books that I'm, I've written, and some, one that I'm about to write about actually this course, and it'll all be free. So, you'll know that Princeton University Press has been very generous in letting a lot of that content of my books be out there. So we're going to you'll be free to download whatever you need to look at. All right? There's some assignments. So there's an assignment on the web page. You'll see a little assignment thing, so all sorts of assignments. So, just make sure you're following. What's going on with the course, and then finally there will be some quizzes, right so there are some quizzes out there just to make sure you know hey am I really getting this. You'll, you'll watch me and you'll think, yea Scott gets these models but that's not what this is about, right this is about you understanding the models. So there'll be some quizzes, right but all in good fun. Okay, and finally, there's the discussion form. I mean, there's 40 to 50,000 people in this class, right, so, office hours can get sort of crowded. So, we're gonna have a discussion forum where people are gonna ask questions. I'll answer some. I've got some graduate students who'll answer some. Other students can answer things, but there'll be a place for people to sorta share ideas, share thoughts, give feedback and should be, hopefully, you know, really useful and structured in a way that will work for everybody. Okay so how does it work, what's one of these sections gonna look like, well each section which of course is gonna be 21. It's gonna be focused on, you know, particular model. Right, and so, we talk about the model and say, okay, what is the model? What are the assumptions? What are the parts? How does it work? You know, what are the main results? What are the applications? So, we just sort of you know talk through how the thing sort of plays out. Then it'll go into some technical details. Sometimes in the same lecture, I present the model. Sometimes in later lectures. This will be, you know, more technical stuff. A little bit more mathematics. Now, I'll try and be very clear about whether or not the math is, you know, easy, medium, or hard. You know, I'll let you know upfront. Like okay, this may require a lot of Algebra or this is just, you know, sort of simple logical thinking. Right, so. I'll be pretty clear about how much effort it's gonna take to get through, trudge through some of the examples. And there will be practice problems you can work on as well. And the other thing I'm gonna do in every one of these sections is talk about the fertility of the models. Tonight's memory is this kernel blotter model that was, could be used to model war or sports or legal defenses, right. Most of these models were developed for one purpose but we can apply them to other purposes. So we're going to talk a lot about how, okay, now that we just learned this model, where can we apply it. Where does it, you know, where else does it work? Right? Okay, so that's it. That's sort of how it's gonna work, right? Learning models is really important. It makes you a more intelligent citizen, probably just, you know, sort of, just a more engaged person out there in the world. ?Cause so much of how people think and what people do is now based on models. Makes you a clearer thinker. That's why so many people are using models. It helps you use and understand data, and it's gonna help you make better decisions, strategize better, and even, you know, design things better. So the course should be really, really useful. We're gonna cover a lot of topics. The don't necessarily build on the one before, right? There'll be some quizzes and videos and that sort of stuff. And this should be just a great time. Alright. Welcome, and let's get started. Thank you.
Intelligent Citizens of the World
Hi, welcome back. In this lecture, I want to talk a little bit more about how using models can help make you a more intelligent citizen of the world. And so, we're gonna break this down into a bunch of set of sub-reasons about why models make you better able to engage in all the things that are going on in this modern, complex world in which we live. Okay, so. When we think about models, they're simplifications. They're abstractions. So in a sense, there's a sense in which they're wrong. There's a famous quote by George Box, where he says, "All models are wrong." And that's true, right? They are. "But some are useful." And that's gonna be a mantra that comes up throughout this course. These models are gonna be abstractions, they're gonna be simplifications, but they're be useful to us. They're gonna help us do things in better ways. 'K? So. In a, in a sense, right? And this is a, a big thing in this course. Models are the new lingua franca. They're the language of not only the academy, you know, which I talked about some in the last lecture, but they're the language of business. They're the language of politics. They're the language of the nonprofit world. Wherever you go, where there's people are trying to do good, make money, cure disease, whatever it is that they wanna do, right? You're gonna find that people are using models to enable them to be better at what their purpose is. Okay? That's why they've really become the new lingua franca. So, if you think back. Remember, I talked about this in the first lecture. The whole idea of having a great books movement was that there was these... set of ideas that any person should know. So within the hundred and so great books, there were thousands of ideas. And one of our ad learners, Robert Hutchins President of the University of Chicago. They had this thing that they wrote called the Synopticon which was a list, right, as they put this together. This was kind of list of sort of all the ideas that someone should know, that an intelligent person should know. So what are those ideas? So one of those ideas was to tie yourself to the mast. And this comes from the Odyssey, you know, this says the ship is going past the sirens and he wants to hear the sirens beautiful love song. So what he does is he has his crew tie him to the mast. He tie. Ties himself to the mast so he can listen to them but pre-commit to not driving his boat over to hear the sirens, at the same time he puts wax in the ears of his crew so they also won't be, you know, encouraged to sort of drive the boat over there. Well this is an idea that recurs in history when we think about. Cortez burning his ships, right, so his men won't you know retreat, they'll continue to advance. So this idea to tie yourself to math, is a real worthwhile thing. But here's the problem. One of, one of my favorite websites is a website called Office of Proverbs. So on this websites, it says things like he who hesitates is lost, a stitch in time saves nine, or two heads are better than one, too many cooks spoil the broth. So you've got to hear this really good advice, something that probably made it in the Synopticon, but then you get something that says the exact opposite. Well, how do they adjudicate between those two things? The way we adjudicate between those two things is by constructing models because models give us the conditions under which he who hesitates is lost, and then there's the conditions under which a stitch in time saves nine. So when we talk about the wide diversity and prediction, we'll see why it's the case that two heads is better than one, and we'll see why it's the case that too many cooks spoil the broth. So, ironically, what models do is they tie us to a mast, they tie us to a mast of logic and by tying us to a mast of logic, we figure out which ways of thinking, which ideas in this Are useful to us.'K? So, if you look at almost any discipline, whether its economics, and here what you see in this diagram, is you see a description of sort of, this is a, a utility function for an agent. And what that agent is doing trying to maximize their pay-off, right? So, economists use models all the time. Biologists use models, as well. They, they, you know, have, you know, models of the brain, where they have little axons and dendrites going between the neurons. They have models of gene regulatory networks. They have models species, right? Things like that. Sociology, we have models, as well, right? So, there's models of, sort of. How your identity effects your actions, and your behaviors and things like that. Okay, in political science. We have models. Political science these days, this is a picture of a spatial voting model. So they might say candidates are a little more conservative on certain dimensions and voters are a little more conservative and you say that, well, you're more likely to vote for a candidate who takes positions similar to yourself. So my work at the University of Michigan we have something called the National Election Studies that's run out of there where we sort of gather all this data about where politicians are and where voters are, and that allows us to make sense of who votes for whom and why. Okay? So models help us understand the decisions people make. Linguistics, right? Here's another area, right? So you might think, how can you use models in linguistics? Well, this little model here, you see things where it says you see v's and n and p's in here, if you look closely. Well, v stands for verb, n stands for noun, and well you gotta. And S stands for, you know, subject, let's say, right? So you can do this: you can ask "What is the structure of a language?" You can ask, formally and mathematically, what are the structure of a language is, and whether some languages are more like other languages or not, depending on how people, you know, set up their sentences. So in German, where they may put all the adjectives. At the end of the sentence that looks very different than let's say English. All right. Even the law. This is a graph from one of my graduate students, former graduate student. Now, he's a law professor, Dan Katz. Where he's got sort of a network model of which Supreme Court justices, you know, who they appoint, so who, if someone appoints judges from some other judge. By putting that data that's out there in this sort of model-based form, we can begin to understand how conservative and how liberal certain judges are. All right? So, there's lots of ways to use models, and there's even whole disciplines now, that have evolved, that are based entirely on models. So, game theory, which is what I was really trained in as a graduate student, is all about strategic behavior. Behavior. It's the study of strategic interactions between, you know, individuals, companies, nations. Right? And game theory can also be applied to biology, right? So there's all sorts of stuff, right? When you go to, when you go to, you know, college, you go to college, you'll find that there's game theory models of just about anything. Right? So it's actually a field based entirely just on models. Right? Why, right? Why all these models, right? Why does everything from linguistics, to economics to, you know, political science use models? Well, cuz, they're better, right? They're just better than we are. So, let me show you a graph, here. This is a graph from a book by Phil Tetlock. It's a fabulous book. And in this graph, he, what he's showing is, he's showing the accuracy of, some different, let me pull up a pin here. Different ways of predicting. So, what you see on this axis, this calibration axis, right here. This is asking, sort of how, showing you how accurate a model is. And this axis is saying how discriminating is it, in terms of how particular, how fine of predictions is it making. So, instead of saying is it hot or cold, it might be saying it's gonna be 90 degrees, or 80 degrees, or 70 degrees. So this axis here, this up and down axis, is discriminatoriness, discrimination, and this axis is how accurate. So, what you see here, down here, are hedgehogs. So, these are people who use a single model. Hedgehogs are not very good at predicting. Right? They're terrible at predicting. Up here are people he calls foxes. Now, foxes are people who use lots of models. They have sort of lots of loose models in their head. And, they do much better at, you know, sort of at calibration, a little bit better at discrimination, than individuals. But way up here, better than anybody, are formal models. Formal models just do better than either foxes or hedgehogs. Now how much data is this? Tetlock actually had tens of thousands of predictions. So, over a 20-year period, he gathered predictions by people. And compared how those people did to models. And the answer is models do much, much better. Okay. All right, so. What about people, then, who actually make predictions for a living? So, this is a picture of Bruce Bueno de Mesquita, who makes predictions about what's gonna happen in international relationships, and he's very good at it. He's so good at it that they put his picture on the cover of magazines, right? He's at, Stanford and NYU. Chair of the department at NYU. Used to be, anyway. So, Bruce, uses models. He's got a very elaborate model that helps him figure out, based on sort of bargaining position and interest, what different countries are gonna do. But, just like George Box said at the beginning, he doesn't base his decision entirely on that model. What the model does is gives him guidance as to what he then thinks. So, it's a blending of what the formal model tells him, and. Experience tells them so smart people who use models but the models don't tell them what to do. Okay. Another reason models have taken yeah they are better but they're also very fertile. So once you learn a model. It's, you know, for one domain, you can apply to a whole bunch of other domains, which is fascinating. So we're gonna learn something called mark-off processes, which are models about dynamic processes. So they can be used to model things like disease spread and stuff like that, right? We're gonna finally learn though that you can also use them, this is sorta surprising, to figure out who wrote a book. >> And they say, how does that happen? Well that happens because you can think of words, writing a sentence, as an anemic process. So different authors, right, use different sequences of words. Different patterns. So therefore we can use this mathematical model that wasn't developed in any way for this purpose to figure out who wrote what book, okay? Totally cool. All right. Another big reason. Models really make us humble. The reason they make us humble is we just have to lay out sort of all the logic and then we realize holy cow, I had no idea that this was going to happen, right. So often when we construct the model, we're going to get very different predictions than what we thought before, right. So if you look at things, here's a picture of a, the tulip graph, right, from When there's a big, in the six-, seventeenth century, when there's a, you know, this big spike in tulip prices. You can imagine that people thought that prices were gonna continue to go up and up and up. Well, if you had a simple linear model, you might have invested heavily in tulips, and lost a lot of money. So, one reason that models make us humble is, never go back to the George Box code. All models are wrong, right? So, a model is going to be wrong. But the models are humbling to us, because they sort of make us see the full dimensionality of a problem. So, once we try and write down a model of any sort of system, it's a very humbling exercise, because we realize how much we've gotta leave out to try and understand what's going on. All right. Here's another example, right? This is the Case-Shiller Home Price Index, and what you see is, you see prices going up and up an up, right? And then you see this, let me put a pin up here, precipitous crash right here, right? A lot of people had models that just said, look, things are gonna continue this way. There were a few people that had models that said things go down. These people, the ones whose models went down, they made a lotta money. These people thought it was gonna go up, didn't. So, we're always gonna see a lot of diversity in models, and you're really not gonna know, often until after the fact, which one is right. And so, one thing that's gonna be really important is to have many models. So, let's go back to that fox-hedgehog graphite that we, I showed you before. The, the foxes, the people with lots of models, did much better than the hedgehogs, the people with no models. And former models did better than. The foxes. Well, what would do better than formal models? Well, people with lots of formal models. Right? So if we really want to make sense of the world what we want to do is have lots of formal models in our disclosures. So what we're going to do in this class is almost like, remember the old, like, sixteen, 32 box of Crayolas? That's sort of what we're doing here. Right? We're just going to pick up a whole bunch of models. And we're going to have them, right, they're fertile. We're going to plot across a bunch of settings. So when we're confronted with something what we can do is pull out our models. Ask which ones are appropriate, and in doing so, right, be better at what we do. So the essence of Tetlocks's book, right? That's where that graph came from with the foxes and hedgehogs is that, the only people who are really even better than what he. He has a way of classifying what a random choice would be. The only people who are better than random at predicting what's gonna happen are people who use multiple models. And that's the kind of people that we wanna be. Okay, so thats, sort of the big, intelligent citizen of the world logic, right. There is, models, are incredibly fertile, they make us humble, they help, you know really clarify the logic, and they're just better. Okay? So if you wanna be out there, you know, helping to change the world in useful ways, it's really, really helpful to have some understanding of models. Thank you very much.
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