# The Theory of Weak Revealed Preference

## TL;DR

This paper develops a new theoretical framework called maximin rationalization to explain consumer choices under the weak generalized axiom of revealed preference, especially when consumers are not utility maximizers.

## Contribution

It introduces maximin rationalization for weak revealed preference, providing new bounds and insights into consumer preferences beyond traditional utility maximization assumptions.

## Key findings

- Maximin rationalization explains choices under WGARP.
- Preference recoverability may be limited when consumers are not utility maximizers.
- New bounds improve understanding of true consumer preferences.

## Abstract

We offer a rationalization of the weak generalized axiom of revealed preference (WGARP) for both finite and infinite data sets of consumer choice. We call it maximin rationalization, in which each pairwise choice is associated with a "local" utility function. We develop its associated weak revealed-preference theory. We show that preference recoverability and welfare analysis \`a la Varian (1982) may not be informative enough, when the weak axiom holds, but when consumers are not utility maximizers. We clarify the reasons for this failure and provide new informative bounds for the consumer's true preferences.