Revealed preferences under uncertainty: Incomplete preferences and preferences for randomization

The completeness axiom of choice has been questioned for long and theoretical models of decision making allowing for incomplete preferences have been developed. So far the theoretical accomplishments have not been paired with empirical evidence on the actual existence of incomplete preferences under uncertainty. We provide empirical evidence in support of the existence of incomplete preferences due to multiple priors over an ambiguous event, i.e.
Bewley preferences. We design experimental decision tasks where specific choice patterns are consistent with Bewley preferences but inconsistent with models assuming completeness. We find that approximately half of the subjects behave consistent with variational Bewley preferences and that the observed behavioral pattern cannot be attributed to probability weighting, choice mistakes, or intransitive indifference. In a robustness test we show that the
observed behavior is robust to a prize variation in the ambiguous prospect and consistent with comparative statics predictions based on variational Bewley preferences.