The key question is whether the revealed preferences are immune to trammelling. This was a major point of confusion for me in discussion with Sami—his proposal involves a set of preferences passed into a decision rule, but those “preferences” are (potentially) different from the revealed preferences. (I’m still unsure whether Sami’s proposal solves the problem.)
I claim that, yes, the revealed preferences in this sense are immune to trammeling. I’m happy to continue the existing discussion thread but here’s a short motivation: what my results about trammelling show is that there will always be multiple (relevant) options between which the agent lacks a preference and the DSM choice rule does not mandate picking one over another. The agent will not try to push probability mass toward one of those options over another.
Yeah, I also want to keep that discussion going. I think the next step is for one or both of us to walk through exactly what the DSM agent does in a case where trammelling-of-the-revealed-preferences could happen. For instance, a case where there are sometimes (probabilistically) opportunities for the sort of A1 → B1 and B1 → A2 transitions in this post, and the agent has the opportunity to precommit (including the opportunity to randomize its own precommitments as-needed).
I claim that, yes, the revealed preferences in this sense are immune to trammeling. I’m happy to continue the existing discussion thread but here’s a short motivation: what my results about trammelling show is that there will always be multiple (relevant) options between which the agent lacks a preference and the DSM choice rule does not mandate picking one over another. The agent will not try to push probability mass toward one of those options over another.
Yeah, I also want to keep that discussion going. I think the next step is for one or both of us to walk through exactly what the DSM agent does in a case where trammelling-of-the-revealed-preferences could happen. For instance, a case where there are sometimes (probabilistically) opportunities for the sort of A1 → B1 and B1 → A2 transitions in this post, and the agent has the opportunity to precommit (including the opportunity to randomize its own precommitments as-needed).