  We study the recently introduced idea of worst-case sensitivity for monotone
submodular maximization with cardinality constraint $k$, which captures the
degree to which the output argument changes on deletion of an element in the
input. We find that for large classes of algorithms that non-trivial
sensitivity of $o(k)$ is not possible, even with bounded curvature, and that
these results also hold in the distributed framework. However, we also show
that in the regime $k = \Omega(n)$ that we can obtain $O(1)$ sensitivity for
sufficiently low curvature.
