Constant inapproximability for PPA
Argyrios Deligkas, John Fearnley, Alexandros Hollender, Themistoklis Melissourgos · 2022
In the ε-Consensus-Halving problem, we are given n probability measures v1, …, vn on the interval R = [0,1], and the goal is to partition R into two parts R+ and R− using at most n cuts, so that |vi(R+) − vi(R−)| ≤ ε for all i. This fundamental fair division problem was the first natural problem shown to be complete for the class PPA, and all subsequent PPA-completeness results for other natural problems have been obtained by reducing from it.