We develop a theory of measurement scales for utility functions, based on a generalization of the notion of numeraire commodity. Every sufficiently well-behaved utility is denominated in some scale of this form, and conversely, the choice of a compatible scale unit uniquely identifies utilities up to an additive constant. We define a profile of utilities to be interpersonally comparable precisely when they are denominated in a common measurement unit. We study when profiles of comparable utilities exist, as well as how a planner ought to aggregate them, and provide applications to social choice and welfare economics.
Cycles in revealed preference data are often regarded as fundamental units of choice-theoretic inconsistency. Contrary to this, we show that in nearly any environment, cyclic choices over some menus necessarily force further cyclic choices elsewhere. In many cases, the entirety of a subject’s inconsistency can be explained by only a handful of cycles. We characterize such dependencies, and show that every set of `independent’ cycles capable of explaining all others is necessarily of the same size. This quantity provides a simple, transparent measure of irrationality that accounts for the dependencies introduced by the structure of the choice environment or experiment.
We characterize those ex-ante restrictions on the random utility model which lead to identification. We first identify a simple class of perturbations which transfer mass from a suitable pair of preferences to the pair formed by swapping certain compatible lower contour sets. We show that two distributions over preferences are behaviorally equivalent if and only if they can be obtained from each other by a finite sequence of such transformations. Using this, we obtain specialized characterizations of which restrictions on the support of a random utility model yield identification, as well as of the extreme points of the set of distributions rationalizing a given data set. Finally, when a model depends smoothly on some set of parameters, we show that under mild topological assumptions, identification is characterized by a straightforward, local test.
We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces, constant relative/absolute risk and ambiguity aversion axioms, stationarity for dated rewards or consumption streams, separability, and many others. We provide necessary and sufficient conditions for invariant rationalizability via a novel approach which relies on tools from the theoretical computer science literature on automated theorem proving. We also establish a generalization of the Dushnik-Miller theorem, which we use to give a complete description of the out-of-sample predictions generated by the data under any such collection of axioms.
We develop a least squares theory for the empirical study of models of preference and individual decision-making. Our approach utilizes common invariance properties of various models to obtain cardinal measurements of preference intensity. Our theory is widely applicable, and provides richer, more granular insights into the drivers of a model’s predictive success or failure than traditional revealed preference methods, while simultaneously remaining computationally simple. We illustrate our methodology on common models of preferences over consumption bundles, dated rewards, lotteries, consumption streams, and Anscombe-Aumann acts.
