Preferences With Grades of Indecisiveness

Departing from the traditional approach to modeling an agent who finds it difficult to make clear-cut comparisons between alternatives, we introduce the notion of graded preferences: Given two alternatives, the agent reports a number between 0 and 1, which reflects her inclination to prefer the first option over the second or, put differently, how confident she is about the superiority of the first one. In the classical framework of uncertainty, we derive a representation of a graded preference by a measure of the set of beliefs that rank one option better than the other. Our model is a refinement of Bewley’s (1986) model of Knightian uncertainty: It is based on the same object of representation — the set of beliefs — but provides more information about how the agent compares alternatives. We also define and characterize, in terms of the representation, the notion of one agent being "more decisive" than another.