Fair and Efficient Resource Allocation with Partial Information

Abstract

We study the fundamental problem of allocating indivisible goods to agents with additive preferences. We consider eliciting from each agent only a ranking of her k most preferred goods instead of her full cardinal valuations. We characterize the value of k needed to achieve envy-freeness up to one good and approximate maximin share guarantee, two widely studied fairness notions. We also analyze the multiplicative loss in social welfare incurred due to the lack of full information with and without the fairness requirements.

Ordinal Maximin Share Approximation for Goods

“…Other fair allocation algorithms with this robustness property are the Decreasing Demands algorithm of Herreiner and Puppe (2002), the Envy Graph algorithm of Lipton, Markakis, Mossel, and Saberi (2004), and the UnderCut algorithm of Brams, Kilgour, and Klamler (2012). Amanatidis, Birmpas, and Markakis (2016), Halpern and Shah (2021) study an even stronger robustness notion, where the agents report only a ranking over the items. Their results imply that, in this setting, the highest attainable multiplicative approximation of MMS is Θ(1/ log n).…”