On the falsifiability and learnability of decision theories

Abstract

We study the degree of falsifiability of theories of choice. A theory is easy to falsify if relatively small data sets are enough to guarantee that the theory can be falsified: the Vapnik–Chervonenkis (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; 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.

Recovering Preferences From Finite Data

“…Below in Sections 4 and 5, we apply Theorem 3 in different environments. Basu and Echenique (2020) compute the VC dimension of some common models of choice, they show, in particular, that the class of expected utility, Choquet expected utility, and two‐state max‐min preferences have finite VC dimension.…”

“…More closely related to our paper, Matzkin (2003) and Blundell, Kristensen, and Matzkin (2010) considered identification in an econometric model of stochastic demand data (see Matzkin (2007), for a general discussion). Recently, Basu and Echenique (2020) investigated the learnability of four standard models of choice under uncertainty using the notion of Probably Approximately Correct (PAC) learning from computational learning theory. Basu (2019) applied several other measures of model complexity to a study of stochastic choice.…”

Summarized distributions of mass: a statistical approach to consumers’ consumption spaces

“…In this paper, the real nature of the objects of consumer choice has been identified (see also [5], where decision-making under conditions of uncertainty is considered). We have defined two consumer's demand functions connected with two contingent consumption plans.…”

How Flexible is that Functional Form? Quantifying the Restrictiveness of Theories

“…For example, theHarless and Camerer (1994) exercise would be much harder on larger menus of binary lotteries, on 3-outcome lotteries, or if subjects had been asked to report real-valued certainty equivalents.4 This paper has a different goal than the extensive econometric literature that studies how the "restrictiveness" of an econometric model may affect the identification of parameters and the efficiency of estimators.5 The VC dimension is known for very few economic models. A recent exception is the work ofBasu and Echenique (2020) for various models of decision-making under uncertainty.…”