Preference Identification

TL;DR

This paper investigates the conditions under which an experimenter can accurately learn a subject's preference relation from finite choice data, highlighting the challenges and providing sufficient criteria for successful identification.

Contribution

It introduces sufficient conditions for preference identification from finite data and discusses the difficulty of utility function recovery, with applications to various models.

Findings

Finite data may not approximate preferences well without specific conditions.

Preferences can be identified under certain conditions, but utility functions are harder to recover.

Examples include consumer choice, expected utility, and Anscombe-Aumann preferences.

Abstract

An experimenter seeks to learn a subject's preference relation. The experimenter produces pairs of alternatives. For each pair, the subject is asked to choose. We argue that, in general, large but finite data do not give close approximations of the subject's preference, even when the limiting (countably infinite) data are enough to infer the preference perfectly. We provide sufficient conditions on the set of alternatives, preferences, and sequences of pairs so that the observation of finitely many choices allows the experimenter to learn the subject's preference with arbitrary precision. While preferences can be identified under our sufficient conditions, we show that it is harder to identify utility functions. We illustrate our results with several examples, including consumer choice, expected utility, and preferences in the Anscombe-Aumann model.