On the falsifiability and learnability of decision theories

We study the degree of falsifiability of theories of choice. A theory is easy to falsify if relatively small datasets are enough to guarantee that the theory can be falsified: the VC dimension of a theory is the largest sample size for which the theory is ``never falsifiable.'' VC dimension is motivated strategically. We consider a model with a strategic proponent of a theory, and a skeptical consumer, or user, of theories. The former presents experimental evidence in favor of the theory, and the latter may doubt whether the experiment could ever have falsified the theory. We focus on decision-making under uncertainty, considering the central models of Expected Utility, Choquet Expected Utility and Max-min Expected Utility models. We show that Expected Utility has VC dimension that grows linearly with the number of states while that of Choquet Expected Utility grows exponentially. The Max-min Expected Utility model has infinite VC dimension when there are at least three states of the world. In consequence, Expected Utility is easily falsified, while the more flexible Choquet and Max-min Expected Utility are hard to falsify. Finally, as VC dimension and statistical estimation are related, we study the implications of our results for machine learning approaches to preference recovery.