Efficiency Adjustments Break the Logarithmic Rank Barrier
This study addresses the limitations of the traditional Deferred Acceptance (DA) mechanism, which achieves only logarithmic expected average rank in i.i.d. matching markets. Focusing on the Efficiency-adjusted Deferred Acceptance (EADA) mechanism, the paper establishes the first asymptotic upper bound on the expected average rank for EADA and a broader class of Pareto-efficient improvement mechanisms. By integrating probabilistic analysis with mechanism design theory and leveraging Pareto efficiency along with weak Pareto dominance conditions, the authors prove that EADA attains an expected average rank of at most \(4 \log \log n + O(1)\), substantially surpassing DA’s logarithmic barrier. These results extend to many-to-one matching settings and random markets with correlated preferences.