Single-crossing dominance: A preference lattice

Most comparisons of preferences are instances of single-crossing dominance. We examine the lattice structure of single-crossing dominance, proving characterisation, existence and uniqueness results for minimum upper bounds of arbitrary sets of preferences. We apply these theorems to derive new comparative statics theorems for collective choice and under analyst uncertainty, and to characterise a general ‘maxmin’ class of uncertainty-averse preferences over Savage acts.