In Chapter 2, it was taken for granted that a subject's state of mind with respect to preferences can be adequately represented by a binary relation. For some purposes – and in particular for studies of changes in preference – a somewhat more sophisticated mode of representation will turn out to be useful. The purpose of this chapter is to introduce a more general format for the representation of preference states. A preference state is an idealized state of mind with respect to value comparisons of a particular set of alternatives.

To see why preference relations are not a fully general representation of preference states, it is sufficient to note that if “A is at least as good as B” is validated by a preference relation, then so is either “A is better than B” or “A and B are of equal value.” (If A≥B holds, then so does either A>B or A≡B.) Furthermore, a preference relation cannot validate a sentence such as A>C ∨ B>C without also validating either A>C or B>C, and it cannot validate A≥B ∨ B≥A (“A and B are comparable”) without validating either A≥B or B≥A. In the models to be introduced in this chapter, these restrictions will be removed.

It is possible to interpret this generalization as representing the subject's lack of knowledge about her own preferences. However, this is not the intended interpretation.