Best of Both Worlds Guarantees for Equitable Allocations
Umang Bhaskar, Vishwa Prakash HV, Aditi Sethia, Rakshitha

TL;DR
This paper investigates the existence and computation of randomized fair allocations that are equitable in expectation and satisfy a fairness condition in every deterministic outcome, providing comprehensive theoretical and algorithmic results.
Contribution
It characterizes the conditions for existence of 'Best of Both Worlds' equitable allocations and offers algorithms for their computation, especially for two agents and binary valuations.
Findings
Ex ante EQ and ex post EQ1 allocations always exist for two agents.
Deciding existence of such allocations is NP-complete for three or more agents.
Efficient algorithms exist for binary valuations and a fixed number of agents.
Abstract
Equitability is a well-studied fairness notion in fair division, where an allocation is equitable if all agents receive equal utility from their allocation. For indivisible items, an exactly equitable allocation may not exist, and a natural relaxation is EQ1, which stipulates that any inequitability should be resolved by the removal of a single item. In this paper, we study equitability in the context of randomized allocations. Specifically, we aim to achieve equitability in expectation (ex ante EQ) and require that each deterministic outcome in the support satisfies ex post EQ1. Such an allocation is commonly known as a `Best of Both Worlds' allocation, and has been studied, e.g., for envy-freeness and MMS. We characterize the existence of such allocations using a geometric condition on linear combinations of EQ1 allocations, and use this to give comprehensive results on both…
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications · Ethics and Social Impacts of AI
