The social sciences have been profoundly affected by progress in information technology that has facilitated the collection and processing of vast amounts of data related to human activity. So far, information technology has assisted less with theoretical reasoning of the sort done by Gary Becker or Milton Friedman. There are automatic algebraic simplifiers, but simplicity is often in the eye of the beholder, and such tools are sparingly used by social science theorists. Computers have already been used for generating numerical examples, but approximation quality is a concern, and more thinking is always needed to appreciate the generality of the results from examples.
A process for automated reasoning has emerged from real algebraic geometry and is readily applied to economics, sociology, and political science. It can, among other things, arrive at purely qualitative conclusions about human behavior. For example, we may not be ready to assume, say, how much price reduces quantity demanded, just that the relationship between price and demand is negative. Computers can tell us how markets would operate under that assumption and others.
New technology like this will transform reasoning in the social sciences the way it transformed data processing in the recent past. Much of pencil-and-paper reasoning may someday be as archaic as the mechanics of, say, arithmetic already is.
In this talk, Casey Mulligan, professor of economics in the UChicago Department of Economics, reviewed how technology assists with theoretical reasoning. He discussed the size and complexity of the problems that can be processed this way, and how to check whether “a machine made a mistake.”