An algebraic approach to revealed preferences

TL;DR

This paper introduces an algebraic framework for revealed preference theory that eliminates the need for topological assumptions, providing a unified set of axioms for rationalizability.

Contribution

It develops an algebraic approach that generalizes classical revealed preference axioms and introduces new axioms for behavioral theories.

Findings

Data sets are rationalizable if and only if they satisfy an algebraic axiom.

The approach subsumes classical revealed preference axioms.

New axioms for behavioral theories are generated.

Abstract

We propose and develop an algebraic approach to revealed preference. Our approach dispenses with non algebraic structure, such as topological assumptions. We provide algebraic axioms of revealed preference that subsume previous, classical revealed preference axioms, as well as generate new axioms for behavioral theories, and show that a data set is rationalizable if and only if it is consistent with an algebraic axiom.