Abstract

This paper presents a formal characterization of a two stage decision rule. This characterization involves three conditions which, together, are satisfied by any choice function that can be represented as a two-tier choice function. And any choice function satisfying these three conditions can be represented as a two-tier choice function. The first condition identifies particular features of two-tier choice functions when they violate Property α. The other two conditions are essentially existence claims, required to ensure that the two tiers of a choice function can be represented as (pseudo-) rationalizable choice functions. My aim is to offer a formal result that provides insight into the nature of two-tier decisions. The more we understand how a particular decision procedure operates, the more we should expect to predict its results accurately, and the more we should be able to understand the circumstances under which its use is (and is not) appropriate