More powerful multiple testing under dependence via randomization

We show that two procedures for false discovery rate (FDR) control -- the Benjamini-Yekutieli procedure for dependent p-values, and the e-Benjamini-Hochberg procedure for dependent e-values -- can both be made more powerful by a simple randomization involving one independent uniform random variable. As a corollary, the Hommel test under arbitrary dependence is also improved. Importantly, our randomized improvements are never worse than the originals, and they are typically strictly more powerful, with marked improvements in simulations. The same technique also improves essentially every other multiple testing procedure based on e-values.