  We propose a model of incomplete \textit{twofold multiprior preferences}, in
which an act $f$ is ranked above an act $g$ only when $f$ provides higher
utility in a worst-case scenario than what $g$ provides in a best-case
scenario. The model explains failures of contingent reasoning, captured through
a weakening of the state-by-state monotonicity (or dominance) axiom. Our model
gives rise to rich comparative statics results, as well as extension exercises,
and connections to choice theory. We present an application to second-price
auctions.
