Research

Decision Theory

Decision theory builds normative and descriptive models of decision making. The starting point of almost all work in decision theory is to find axiomatic foundations for decision models that usually come in the form of a utility maximizing model. In other words, given some assumptions on choice data such as preferences or probability distributions over alternatives, what is a utility model that can generate such data?

One of my works combines the classical von Neumann-Morgenstern expected utility axioms with a slight variation of the Herstein and Milnor mixture set axioms to somewhat surprisingly obtain the Shannon and Tsallis entropies as a representation. In an application to decision times, I show that this provides a foundation for a Hick's law: that decision times should be increasing in the entropy of the decision probabilities. I show that Hick's law should indeed hold whenever decision probabilities follow the Luce/logit model of stochastic choice. This result has won the Jaffray lecture award at RUD 2023.

A philosophical question is whether it is normatively mandatory to maximize expected utility in decisions under uncertainty. Together with coauthors, I found that if you intrinsically care about gaining knowledge about the world, you will violate expected utility. For example, if you only care about the information partition you have at the end of your life, you will violate Savage's axioms and there is no sensible redefinition of outcomes that will allow you to fulfill these axioms!

I have worked with Qin, Wei-zhi on some foundational questions such as when preferences can be represented by additively separable utility functions and quasi-additive utility functions.