The Two-Envelope Paradox Resolved with Imprecise Probabilities

Although there have been many attempts at solving the famous two-envelopes problem, I think there is an obvious aspect of the case that has been overlooked: the problem is most naturally resolved with imprecise beliefs/partial preferences. I briefly present a solution to the problem in terms of imprecise probabilities, represented by sets of probabilities consistent with the evidence given; I analyse the decisions in the formalism of sets of desirable gambles. An imprecise credal response to the two-envelopes problem is evidentially well-motivated, validates the common-sense position that the agent should initially regard the two envelopes with indifference, and captures other features of the case that no precise credence function can.