Eliciting and distinguishing between weak and incomplete preferences: Theory, experiment and computation

We propose an experimental design and data-analytic method for eliciting and distinguishing the strict-preference, indifference, and indecisiveness components of individual preferences in general choice environments. The design combines a forced-choice treatment with a free-choice treatment. In both treatments, subjects may select multiple alternatives from a menu. In the free-choice treatment, subjects may also avoid or delay choice at a small expected cost. To analyze such data, we extend a standard non-parametric goodness-of-fit criterion to accommodate multi-valued choices. We apply it to evaluate the consistency of subjects’ 50 decisions with utility maximization and two models of incomplete-preference maximization. Around 55% of subjects are well explained by one of these models, with 33% and 22% best explained by utility and incomplete-preference maximization, respectively. Revealed preferences typically feature non-trivial indifferences, and those that are incomplete often exhibit the predicted theoretical distinctions between indifference and indecisiveness, which are documented empirically for the first time.