Economic decisions often involve maximising an objective whose value is itself
the outcome of another optimisation problem. This decision structure arises in
multi-output production and choice under uncertainty with multi-prior beliefs. To analyse comparative statics in these models, we introduce a theory of supermodular correspondences. In particular, we employ this theory to generalise the notion of first order stochastic dominance to multi-prior beliefs, allowing us to characterise conditions under which greater optimism leads to higher action.