First-Choice Maximality Meets Ex-ante and Ex-post Fairness
Abstract
For the assignment problem where multiple indivisible items are allocated to a group of agents given their ordinal preferences, we design randomized mechanisms that satisfy first-choice maximality (FCM), i.e., maximizing the number of agents assigned their first choices, together with Pareto efficiency (PE). Our mechanisms also provide guarantees of ex-ante and ex-post fairness. The generalized eager Boston mechanism is ex-ante envy-free, and ex-post envy-free up to one item (EF1). The generalized probabilistic Boston mechanism is also ex-post EF1, and satisfies ex-ante efficiency instead of fairness. We also show that no strategyproof mechanism satisfies ex-post PE, EF1, and FCM simultaneously. In doing so, we expand the frontiers of simultaneously providing efficiency and both ex-ante and ex-post fairness guarantees for the assignment problem.
Keywords
Cite
@article{arxiv.2305.04589,
title = {First-Choice Maximality Meets Ex-ante and Ex-post Fairness},
author = {Xiaoxi Guo and Sujoy Sikdar and Lirong Xia and Yongzhi Cao and Hanpin Wang},
journal= {arXiv preprint arXiv:2305.04589},
year = {2023}
}