Model Thinking

Scott Page, University of Michigan

We live in a complex world with diverse people, firms, and governments whose behaviors aggregate to produce novel, unexpected phenomena. We see political uprisings, market crashes, and a never ending array of social trends. How do we make sense of it? Models. Evidence shows that people who think with models consistently outperform those who don't. And, moreover people who think with lots of models outperform people who use only one. Why do models make us better thinkers? Models help us to better organize information - to make sense of that fire hose or hairball of data (choose your metaphor) available on the Internet. Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures. In this class, I present a starter kit of models: I start with models of tipping points. I move on to cover models explain the wisdom of crowds, models that show why some countries are rich and some are poor, and models that help unpack the strategic decisions of firm and politicians. The models covered in this class provide a foundation for future social science classes, whether they be in economics, political science, business, or sociology. Mastering this material will give you a huge leg up in advanced courses. They also help you in life. Here's how the course will work. For each model, I present a short, easily digestible overview lecture. Then, I'll dig deeper. I'll go into the technical details of the model. Those technical lectures won't require calculus but be prepared for some algebra. For all the lectures, I'll offer some questions and we'll have quizzes and even a final exam. If you decide to do the deep dive, and take all the quizzes and the exam, you'll receive a Course Certificate. If you just decide to follow along for the introductory lectures to gain some exposure that's fine too. It's all free. And it's all here to help make you a better thinker!

Why Model & Segregation/Peer Effects

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.

Aggregation & Decision Models

In this section, we explore the mysteries of aggregation, i.e. adding things up. We start by considering how numbers aggregate, focusing on the Central Limit Theorem. We then turn to adding up rules. We consider the Game of Life and one dimensional cellular automata models. Both models show how simple rules can combine to produce interesting phenomena. Last, we consider aggregating preferences. Here we see how individual preferences can be rational, but the aggregates need not be.There exist many great places on the web to read more about the Central Limit Theorem, the Binomial Distribution, Six Sigma, The Game of LIfe, and so on. I've included some links to get you started. The readings for cellular automata and for diverse preferences are short excerpts from my books Complex Adaptive Social Systems and The Difference Respectively.

Thinking Electrons: Modeling People & Categorical and Linear Models

In this section, we study various ways that social scientists model people. We study and contrast three different models. The rational actor approach,behavioral models , and rule based models . These lectures provide context for many of the models that follow. There's no specific reading for these lectures though I mention several books on behavioral economics that you may want to consider. Also, if you find the race to the bottom game interesting just type "Rosemary Nagel Race to the Bottom" into a search engine and you'll get several good links. You can also find good introductions to "Zero Intelligence Traders" by typing that in as well.

Tipping Points & Economic Growth

In this section, we cover tipping points. We focus on two models. A percolation model from physics that we apply to banks and a model of the spread of diseases. The disease model is more complicated so I break that into two parts. The first part focuses on the diffusion. The second part adds recovery. The readings for this section consist of two excerpts from the book I'm writing on models. One covers diffusion. The other covers tips. There is also a technical paper on tipping points that I've included in a link. I wrote it with PJ Lamberson and it will be published in the Quarterly Journal of Political Science. I've included this to provide you a glimpse of what technical social science papers look like. You don't need to read it in full, but I strongly recommend the introduction. It also contains a wonderful reference list.

Diversity and Innovation & Markov Processes

In this section, we cover some models of problem solving to show the role that diversity plays in innovation. We see how diverse perspectives (problem representations) and heuristics enable groups of problem solvers to outperform individuals. We also introduce some new concepts like "rugged landscapes" and "local optima". In the last lecture, we'll see the awesome power of recombination and how it contributes to growth. The readings for this chapters consist on an excerpt from my book The Difference courtesy of Princeton University Press.

Midterm Exam

Lyapunov Functions & Coordination and Culture

Models can help us to determine the nature of outcomes produced by a system: will the system produce an equilibrium, a cycle, randomness, or complexity? In this set of lectures, we cover Lyapunov Functions. These are a technique that will enable us to identify many systems that go to equilibrium. In addition, they enable us to put bounds on how quickly the equilibrium will be attained. In this set of lectures, we learn the formal definition of Lyapunov Functions and see how to apply them in a variety of settings. We also see where they don't apply and even study a problem where no one knows whether or not the system goes to equilibrium or not.

Path Dependence & Networks

In this set of lectures, we cover path dependence. We do so using some very simple urn models. The most famous of which is the Polya Process. These models are very simple but they enable us to unpack the logic of what makes a process path dependent. We also relate path dependence to increasing returns and to tipping points. The reading for this lecture is a paper that I wrote that is published in the Quarterly Journal of Political Science

Randomness and Random Walks & Colonel Blotto

In this section, we first discuss randomness and its various sources. We then discuss how performance can depend on skill and luck, where luck is modeled as randomness. We then learn a basic random walk model, which we apply to the Efficient Market Hypothesis, the ideas that market prices contain all relevant information so that what's left is randomness. We conclude by discussing finite memory random walk model that can be used to model competition. The reading for this section is a paper on distinguishing skill from luck by Michael Mauboussin.

Prisoners' Dilemma and Collective Action & Mechanism Design

In this section, we cover the Prisoners' Dilemma, Collective Action Problems and Common Pool Resource Problems. We begin by discussion the Prisoners' Dilemma and showing how individual incentives can produce undesirable social outcomes. We then cover seven ways to produce cooperation. Five of these will be covered in the paper by Nowak and Sigmund listed below. We conclude by talking about collective action and common pool resource problems and how they require deep careful thinking to solve. There's a wonderful piece to read on this by the Nobel Prize winner Elinor Ostrom.

Learning Models: Replicator Dynamics & Prediction and the Many Model Thinker

In this section, we cover replicator dynamics and Fisher's fundamental theorem. Replicator dynamics have been used to explain learning as well as evolution. Fisher's theorem demonstrates how the rate of adaptation increases with the amount of variation. We conclude by describing how to make sense of both Fisher's theorem and our results on six sigma and variation reduction. The readings for this section are very short. The second reading on Fisher's theorem is rather technical. Both are excerpts from Diversity and Complexity.

Final Exam

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