Comparative Incompleteness: Measurement, Behavioral Manifestations and Elicitation

This paper introduces measures of overall incompleteness of preference relations under risk and uncertainty, as well as measures of incompleteness of beliefs and tastes. These measures are used to define "more incomplete than" relations among different preference relations. We show how greater incompleteness is manifested in the representations of decision makers' preferences and illustrate its behavioral implications in a simple portfolio choice problem. In addition, the paper introduces incentive compatible schemes of eliciting the degrees of overall incompleteness and those of beliefs and tastes.