Exact Envy-Free Cake Cutting with Polynomial Expected Queries
Simon Mackenzie, Mashbat Suzuki · arXiv: 2610.28535v1 · Summary page
Why cover this story this week?
Fair division gets a randomized route to exactness
Cake cutting is the mathematical problem of dividing a resource so that nobody prefers another person’s share. The difficulty is not merely finding a fair allocation, but doing so with a manageable number of questions about people’s preferences. This theoretical preprint establishes a polynomial expected query bound for a randomized protocol, without assuming that preferences come from any particular distribution.
The protocol draws its randomness only from uniformly sampled points on the cake. It terminates with probability one, and every allocation it returns is complete and exactly envy-free for the valuation assumptions in the paper. Randomness therefore changes the known query-efficiency picture without making fairness approximate. The qualification matters: an expected polynomial bound is not a polynomial worst-case guarantee, nor does a query bound alone establish a practical allocation tool.
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