Revealed preferences under uncertainty: Incomplete preferences and preferences for randomization

We present a set of experiments testing for incomplete preferences due to uncertainty. In a first experiment, we observe that approximately half of the participants exhibit a choice pattern inconsistent with models assuming complete preferences and Certainty Independence (CI). To understand these participants' behavior, in a second experiment, we design a decision task that distinguishes between models assuming complete preferences and relaxing CI and models of incomplete preferences under uncertainty. We find that about half of the participants in question exhibit behavior consistent with incomplete preferences, about one third shows behavior consistent with a preference for randomization between risky and ambiguous prospects, and the remaining participants' behavior is consistent with both types of preferences. In further experiments we find that the observed choice pattern cannot be attributed to probability weighting, choice mistakes, regret aversion or intransitive indifference under risk and certainty. We also show that the observed behavior is robust to a prize variation in the ambiguous prospect.