  We give a simple deterministic $O(\log K / \log\log K)$ approximation
algorithm for the Min-Max Selecting Items problem, where $K$ is the number of
scenarios. While our main goal is simplicity, this result also improves over
the previous best approximation ratio of $O(\log K)$ due to Kasperski, Kurpisz,
and Zieli\'nski (Information Processing Letters (2013)). Despite using the
method of pessimistic estimators, the algorithm has a polynomial runtime also
in the RAM model of computation. We also show that the LP formulation for this
problem by Kasperski and Zieli\'nski (Annals of Operations Research (2009)),
which is the basis for the previous work and ours, has an integrality gap of at
least $\Omega(\log K / \log\log K)$.
