We provide characterizations of four new rules for individual decision-maki
ng under complete uncertainty. They are what we call the min-max rule, the
max-min rule, the lexicographic min-max rule and the lexicographic max-min
rule. These rules provide orderings of the sets of possible outcomes associ
ated with uncertain prospects. They provide significant alternatives to com
monly-used rules that focus on worst outcomes or best outcomes only, and le
xicographic versions of those rules.