We study two-stage choice procedures in which the decision maker first preselects the alternatives whose values according to a criterion pass a menu-dependent threshold, and then maximizes a second criterion to narrow the selection further. This framework overlaps with several existing models...

In Tversky's (1969) model of a lexicographic semiorder, preference is generated by the sequential application of numerical criteria, by declaring an alternative x better than an alternative y if the first criterion that distinguishes between x and y ranks x higher than y by an amount exceeding a...