We propose a model of preferences in which the effect of randomization on ambiguity depends on how the unknown probability law is determined. We adopt the framework of Anscombe and Aumann (1963) and relax the axioms. In the resulting representation of the individual's preference, the individual has a collection of sets of priors <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="script">M</a:mi> </a:math>. She believes that before she moves, nature has chosen an unknown scenario (a set of priors) from <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi mathvariant="script">M</d:mi> </d:math>, and from that scenario, nature will choose a prior after she moves. The representation illustrates how randomization may partially eliminate the effect of ambiguity.

We introduce a high quality proxy for bank misconduct that is constructed from Consumer Financial Protection Bureau (CFPB) complaint data. We employ this proxy to measure the impact of bank misconduct on the expansion of online lending in the United States. Using nearly complete loan and application data from the online lending market, we demonstrate that bank misconduct is associated with a statistically and economically significant increase in online lending demand at the state and county levels. This result is robust to the inclusion of bank credit supply shocks and holds for both broader and more narrowly-defined bank misconduct measures. Furthermore, we show that this effect is strongest for lower rated borrowers and weakest in states with high levels of generalized trust.