# Cutting the Cake: A Language for Fair Division

arXiv: https://arxiv.org/abs/2304.04642 · HTML: https://mlsanity.com/paper/2304.04642/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [Pact: A Choreographic Language for Agentic Ecosystems](https://mlsanity.com/paper/2605.03143/) (2026)

## Abstract (arXiv)

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.