These results are super interesting! Thanks for writing and sharing! (I happened to have already read a bunch of the original papers you’re summarizing, and some of your work, too.)
By the way, I think you can capture common intuitions against fanaticism and dependence on unaffected things with a multi-step procedure:
Ignore anything unaffected between your options,[1] and keep only the remaining differences between options.
Use some method that’s not fanatical with respect to the remaining differences between options, e.g. the expected value of a bounded function of the differences.
However, this means violating stochastic dominance with respect to outcomes, and the approach might seem ad hoc. While these do count against the approach in my mind, I don’t think they rule it out decisively, because the approach seems to match other intuitions of mine so well otherwise. So, I give a decent amount of weight to something like this approach under normative uncertainty. I also give some weight to fanatical views, of course, too.
I discuss these ideas a bit in this post, but kind of scattered across the subsections of this section.
These results are super interesting! Thanks for writing and sharing! (I happened to have already read a bunch of the original papers you’re summarizing, and some of your work, too.)
By the way, I think you can capture common intuitions against fanaticism and dependence on unaffected things with a multi-step procedure:
Ignore anything unaffected between your options,[1] and keep only the remaining differences between options.
Use some method that’s not fanatical with respect to the remaining differences between options, e.g. the expected value of a bounded function of the differences.
However, this means violating stochastic dominance with respect to outcomes, and the approach might seem ad hoc. While these do count against the approach in my mind, I don’t think they rule it out decisively, because the approach seems to match other intuitions of mine so well otherwise. So, I give a decent amount of weight to something like this approach under normative uncertainty. I also give some weight to fanatical views, of course, too.
I discuss these ideas a bit in this post, but kind of scattered across the subsections of this section.
Either just pairwise, dealing with pairwise comparisons first, or across all of them together at the same time.