English

Cutting the Cake: A Language for Fair Division

Programming Languages 2023-04-11 v1

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.

Keywords

Cite

@article{arxiv.2304.04642,
  title  = {Cutting the Cake: A Language for Fair Division},
  author = {Noah Bertram and Alex Levinson and Justin Hsu},
  journal= {arXiv preprint arXiv:2304.04642},
  year   = {2023}
}

Comments

31 pages, 15 figures, PLDI 2023

R2 v1 2026-06-28T09:57:34.124Z