Kevin Blackwell (Bristol): “An IP Solution to the Two-Envelopes Problem”

This event will take place online via Zoom.

Everyone is welcome to join using a computer with access to the internet and Zoom. To take part just follow these instructions:

– Download Zoom here: https://zoom.us/download
– Join the event using this link: https://bristol-ac-uk.zoom.us/j/97254257804?pwd=QVpSNnBDcWF2dldsdWpNd2pEUlVlZz09
– When prompted, enter the password “Bristol”

Please note that these events are routinely recorded, with the edited footage being made publicly available on our website and YouTube channel. We will only record the audio, the slides and the speaker and will not include the Q&A section. However, any question asked during the talk itself will feature in the final edit.

Abstract: 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.