Reducing Leximin Fairness to Utilitarian Optimization

Two prominent objectives in social choice are utilitarian - maximizing the sum of agents' utilities, and leximin - maximizing the smallest agent's utility, then the second-smallest, etc. Utilitarianism is typically computationally easier to attain but is generally viewed as less fair. This paper presents a general reduction scheme that, given a utilitarian solver, produces a distribution over states (deterministic outcomes) that is leximin in expectation. Importantly, the scheme is robust in the sense that, given an approximate utilitarian solver, it produces a lottery that is approximately-leximin (in expectation) - with the same approximation factor. We apply our scheme to several social choice problems: stochastic allocations of indivisible goods, giveaway lotteries, and fair lotteries for participatory budgeting.

Authors

• Eden Hartman Bar-Ilan University
• Yonatan Aumann Bar-Ilan University
• Avinatan Hassidim Bar-Ilan University, Israel Google, Israel
• Erel Segal-Halevi Ariel University

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