  The OSSS inequality [O'Donnell, Saks, Schramm and Servedio, 46th Annual IEEE
Symposium on Foundations of Computer Science (FOCS'05), Pittsburgh (2005)]
gives an upper bound for the variance of a function f of independent 0-1 valued
random variables, in terms of the influences of these random variables and the
computational complexity of a (randomised) algorithm for determining the value
of f. Duminil-Copin, Raoufi and Tassion [Annals of Mathematics 189, 75-99
(2019)] obtained a generalization to monotonic measures and used it to prove
new results for Potts models and random-cluster models. Their generalization of
the OSSS inequality raises the question if there are still other measures for
which a version of that inequality holds. We derive a version of the OSSS
inequality for a family of measures that are far from monotonic, namely the
k-out-of-n measures (these measures correspond with drawing k elements from a
set of size n uniformly). We illustrate the inequality by studying the event
that there is an occupied horizontal crossing of an R times R box on the
triangular lattice in the site percolation model where exactly half of the
vertices in the box are occupied.
