Blog
Math of Choice
A blog series exploring the mathematical foundations of discrete choice.
Based on Alfred Galichon’s forthcoming book, Discrete Choice Models: Mathematical Methods, Econometrics, and Data Science, Princeton University Press, April 2026.
About this series
Discrete choice models are the workhorses of modern applied econometrics, used to predict everything from commuter transport choices to consumer product selection. However, the standard textbook treatment often overlooks the rich mathematical and computational properties that govern these models.
In this series, we follow the roadmap of the book and we start with peeling back the layers of the “Random Utility Model” to reveal its deep connections with convex analysis, information theory, optimal transport, extreme value theory, and generalized linear models.
Still following the book, we then use random utility models as a building block for demand inversion methods, models of trade, dynamic pricing and hedonic models, as well as matching models with and without transfers.
Table of Contents
The role of entropy in discrete choice models, part 1: the logit case
January 5, 2026
We begin with the basics. How does random utility translate into social welfare? We explore the classic logit model and derive the famous result that the “randomness” of the individual aggregates into the “entropy” of the group (Gibbs-Shannon entropy). We introduce the Daly-Zachary-Williams theorem and the concept of the representative consumer along the way.
The role of entropy in discrete choice models, part 2: beyond logit
Coming Soon
What happens when we leave the logit world? We show that every additive random utility model has an associated “Generalized Entropy of Choice.” We explore how different distributions of noise (Probit, etc.) lead to different convex regularization penalties.