Modeling in Economic and Social Sciences

Hubert Bray, Professor of Mathematics

What is democracy? For example, given a finite number of choices, how does a group of equals choose the option which “best” reflects the will of the group? When there are more than two options, this is an open question in the sense that philosophical notions of “best” are not universally agreed upon. The seminar will also include an introduction to game theory as an essential tool for predicting how intelligent people with agendas behave given carefully defined rules. We will apply game theory, broadly defined, to voting theory, economics, poker, and many other games. Class participation includes discussions, presentations, and experimenting with ideas, including by playing the "Money and Politics" game in class which involves electing a class president, taxation, taking risks, forming alliances, and double crosses in an attempt to  simulate the real world with relatively few rules.

Scott de Marchi, Professor of Political Science and Director of the Decision Science

Our goal as social scientists is to build models of the world and provide advice to policymakers. Given that human actors are often strategic and the games they play are complex, building and testing these models is difficult and distinct from common examples of machine learning. A task that is often used to motivate introductions to machine learning is teaching a model to recognize hand-written characters using MNIST data (https://www.tensorflow.org/datasets/catalog/mnist). Our task is harder: we must build models that involve forecasting human behavior ranging from votes in a legislature to changes in stock prices. Given the complexity of these sorts of problems, we will cover both human decision-making and machine learning in this course. The hope is that our machine learning models will be better when they are informed by theoretical models of behavior.

Alexander Volfovsky, Associate Professor of Statistical Science

This course introduces statistics and probability through their historical development, allowing us to explore not only how statistical methods work, but why they were invented. Students will encounter foundational quantitative ideas (such as uncertainty, averages, variation, and the central limit theorem) as they originally emerged from real scientific and social problems. Starting with small, historically authentic datasets that gave rise to these methods, students will develop quantitative reasoning skills and build toward understanding how these ideas scale to modern settings involving large and complex data. This foundation provides essential preparation for interpreting contemporary applications of statistics, including modern data science and artificial intelligence.

Gregory Joseph Herschlag, Associate Research Professor of Mathematics

In this course, students will learn about statistical modeling, with primary emphasis on developing critical thinking skills. Topics vary, but can include statistical genetics, agent-based modeling, Shannon's theory of communication, game theory, and mathematical models for epidemics and redistricting. After completing this course, students will be able to design and analyze basic statistical studies, to understand and criticize statistical methods in journals and the media, and to appreciate the power and utility of statistical thinking. Examples and methods are drawn primarily from the behavioral, natural, and social sciences and public policy.