Delegation in decision making under uncertainty. Are preferences incomplete?

In this paper we experimentally document the existence of an unexplored violation of rationality in decision making under uncertainty. In a series of incentivized decision tasks subjects have to choose between risky and ambiguous prospects or state to be indifferent, where the last option effectively means delegating the choice to a fair chance device. We observe that half of the subjects delegate several choices and show that behavior can not be reconciled with theories assuming completeness of preferences. In a second experiment we show that delegation is robust to a prize variation and verify that the observed behavior is consistent with recent models of incomplete preferences. We also find a strong gender effect: female subjects are much more likely to delegate choices then male subjects. First draft: comments highly welcome. Please do not circulate without permission of the authors.