How do people cope with an ambiguous situation when it becomes even more ambiguous?

As illustrated by the famous Ellsberg paradox, many subjects prefer to bet on events with known rather than with unknown probabilities, i.e., they are ambiguity averse. In an experiment, we examine subjects’ choices when there is an additional source of ambiguity, namely, when they do not know how much money they can win. Using a standard independence assumption, we show that ambiguity averse subjects should continue to strictly prefer the urn with known probabilities. In contrast, our results show that many subjects no longer exhibit such a strict preference. This should have important ramifications for modeling ambiguity aversion.