The Revealed Preference Theory of Aggregate Object Allocations

TL;DR

This paper introduces a revealed preference framework to test Pareto efficiency and individual rationality of aggregate object allocations without individual preference data, using graph acyclicity and a new measure called CEI.

Contribution

It provides the first complete revealed preference analysis for Pareto efficiency and individual rationality in matching markets, with necessary and sufficient conditions and practical tools.

Findings

Allocation graph is acyclic if and only if the allocation is PI-rationalizable.

Removing minimal subsets to restore PI-rationalizability is NP-complete.

Critical Exchange Index quantifies the extent of inefficiency in allocations.

Abstract

I develop a revealed preference framework to test whether an aggregate allocation of indivisible objects satisfies Pareto efficiency and individual rationality (PI) without observing individual preferences. Exploiting the type-based preferences of Echenique et. al. (2013), I derive necessary and sufficient conditions for PI-rationalizability. I show that an allocation is PI-rationalizable if and only if its allocation graph is acyclic. Next, I analyse non-PI-rationalizable allocations. First, I study the three respective problems: removal of a minimum size of subset of individuals/types/objects to restore PI-rationalizability. I prove that these three problems are NP-complete. Then, I provide an alternative goodness-of-fit measure, namely Critical Exchange Index (CEI). The CEI assess the highest portion of individuals who can involve exchanging their final objects to reach PI. This measure shows the extent of inefficiencies. The results yield the first complete revealed preference analysis for Pareto efficiency and individual rationality in matching markets and provide an implementable tool for empirical applications.