  Consider Myerson's optimal auction with respect to an inaccurate prior, e.g.,
estimated from data, which is an underestimation of the true value
distribution. Can the auctioneer expect getting at least the optimal revenue
w.r.t. the inaccurate prior since the true value distribution is larger? This
so-called strong revenue monotonicity is known to be true for single-parameter
auctions when the feasible allocations form a matroid. We find that strong
revenue monotonicity fails to generalize beyond the matroid setting, and
further show that auctions in the matroid setting are the only downward-closed
auctions that satisfy strong revenue monotonicity. On the flip side, we recover
an approximate version of strong revenue monotonicity that holds for all
single-parameter auctions, even without downward-closedness. As applications,
we get sample complexity upper bounds for single-parameter auctions under
matroid constraints, downward-closed constraints, and general constraints. They
improve the state-of-the-art upper bounds and are tight up to logarithmic
factors.
