An Axiomatic Characterization of the Equal Division Rule in the Random Assignment Problem

Abstract

In the random assignment problem, the equal division rule recommends all agents to get the same random allocation. Although it is inefficient, many of its benefits still make it an important rule in the random assignment problem: simple and practical, extremely fair, and robust to strategic manipulations. Therefore, this paper aims to study the equal division rule by an axiomatic approach. It turns out that the rule is the only rule that satisfies rank symmetry and strategy-proofness when the number of agents and objects are equal to three or equal to four, where rank symmetry implies that the probability that an agent gets his r-th best object is the same with the probability that other agents get their r-th best objects.