Choice Group

I argue that extant, precise analyses of the two-envelopes problem are not fully satisfactory. Although it is true that concerns about conditionally convergent series block the argument from conditional expected value to unconditional expected value, this is only a partial resolution. I think the standard analysis (John Norton, Arntzenius and McCarthy, David Chalmers) leaves the version of the problem where a prize is revealed unresolved. There are other intuitive features of the case that no precise probability analysis can correctly capture. I also discuss Ned Markosian’s “simple solution”; while not correct, I think his argument contains a compelling insight to the effect that we should really want an analysis on which the agent is required to be determinately indifferent about switching (in the versions of the problem I discuss). I provide two new solutions to the problem which model the agent’s beliefs with imprecise probabilities. The first is very simple, evidentially well-motivated, and captures more of the intuitive judgments about the case than the standard line. However, it doesn’t achieve the desideratum of indifference about switching; so, I provide a second solution which does. It is very slightly less simple than the first, and I’m not yet quite sure what the most compelling evidential justification is.