An Axiomatization of the Random Priority Rule

TL;DR

This paper provides an axiomatic foundation for the Random Priority rule in assigning indivisible objects fairly without monetary exchange, emphasizing properties like monotonicity and efficiency.

Contribution

It offers a new axiomatization of the Random Priority rule, linking probabilistic monotonicity with strategy-proofness and extending understanding of fair random assignment.

Findings

Probabilistic monotonicity implies strategy-proofness.

Axiomatization characterizes Random Priority uniquely.

Connections between deterministic and stochastic rules are established.

Abstract

We study the problem of assigning indivisible objects to agents where each is to receive at most one. To ensure fairness in the absence of monetary compensation, we consider random assignments. Random Priority, also known as Random Serial Dictatorship, is characterized by equal-treatment-of-equals, ex-post efficiency and probabilistic (Maskin) monotonicity -- whenever preferences change so that a given deterministic assignment is ranked weakly higher by all agents, the probability of that assignment arising should be weakly larger. Probabilistic monotonicity implies strategy-proofness (in a stochastic dominance sense) for random assignment problems and is equivalent to it on the universal domain of strict preferences; for deterministic rules it coincides with Maskin monotonicity.