This paper introduces the Prince incentive system for measuring preferences. Prince is a variation of the random incentive system that enhances isolation and makes incentive compatibility more transparent to subjects. It allows for the precise and direct elicitation of indifference values as with matching while having the clarity and validity of choice lists. Prince avoids the opaqueness of Becker-DeGroot-Marschak’s mechanism and precludes strategic behavior in adaptive experiments. Using Prince, we shed new light on willingness to accept and the major components of decision under uncertainty: utilities, subjective beliefs, and ambiguity attitudes. Prince outperforms a classical implementation of the random incentive system.