  When multiple sources of information are available, any decision must take
into account their correlation. If information about this correlation is
lacking, an agent may find it desirable to make a decision that is robust to
possible correlations. Our main results characterize the strategies that are
robust to possible hidden correlations. In particular, with two states and two
actions, the robustly optimal strategy pays attention to a single information
source, ignoring all others. More generally, the robustly optimal strategy may
need to combine multiple information sources, but can be constructed quite
simply by using a decomposition of the original problem into separate decision
problems, each requiring attention to only one information source. An
implication is that an information source generates value to the agent if and
only if it is best for at least one of these decomposed problems.
