There exists a universal constant c>0 such that the c-thinned e^{-c}-quantile share is unconditionally universally feasible for fair division of indivisible goods, and this parameter choice is tight.
Narayan,Fair division via quantile shares, Proceedings of the 56th Annual ACM Symposium on Theory of Computing (STOC), ACM, 2024, pp
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Thinned Quantile Shares are Universally Feasible
There exists a universal constant c>0 such that the c-thinned e^{-c}-quantile share is unconditionally universally feasible for fair division of indivisible goods, and this parameter choice is tight.