Rank-Envy-Freeness in Roommate Matchings

Baptistin Coutance, Prasanna Maddila, Anaëlle Wilczynski

Abstract: In the roommate problem, pairs of agents must be formed, based on ordinal preferences of the agents over each other. In this article, we examine fair roommate matchings by relaxing envy-freeness to account for justified envy based on the rank in the agents’ preferences. A rank-envy-free matching prevents that an agent prefers the partner of another agent whereas she has ranked it better. Although this requirement is pretty weak in house allocation [9], we show that it is more demanding in the roommate setting. We study parameterizations of rank-envy-freeness, as well as further natural relaxations of this concept. We also investigate the connections between the family of rank-based fairness criteria and known optimality or stability concepts.