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arXiv · 2304.04642

Cutting the Cake: A Language for Fair Division

Noah Bertram·Alex Levinson·Justin Hsu
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Abstract

The fair division literature in economics considers how to divide resources between multiple agents such that the allocation is envy-free: each agent receives their favorite piece. Researchers have developed a variety of fair division protocols for the most standard setting, where the agents want to split a single item, however, the protocols are highly intricate and the proofs of envy-freeness involve tedious case analysis. We propose Slice, a domain specific language for fair-division. Programs in our language can be converted to logical formulas encoding envy-freeness and other target properties. Then, the constraints can be dispatched to automated solvers. We prove that our constraint generation procedure is sound and complete. We also report on a prototype implementation of Slice, which we have used to automatically check envy-freeness for several protocols from the fair division literature.

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Noah Bertram, Alex Levinson, Justin Hsu. 2023-04-10. Cutting the Cake: A Language for Fair Division. https://doi.org/10.1145/3591293

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