A steelman could be to just set it up like a hypothetical sequential choice problem consistent with Dasguptaâs approach:
Choose between A and B
If you chose B in 1, choose between B and C.
or
Choose between A and (B or C).
If you chose B or C in 1, choose between B and C.
In either case, âpicking Bâ (including âpicking B or Câ) in 1 means actually picking C, if you know youâd pick C in 2, and then use backwards induction.
The fact that A is at least as good as (or not worse than and incomparable to) B could follow because B actually just becomes C, which is equivalent to A once weâve ruled out B. Itâs not just facts about direct binary choices that decide rankings (âbetternessâ), but the reasoning process as a whole and how we interpret the steps.
At any rate, I donât think itâs that important whether we interpret the rankings as âbetternessâ, as usually understood, with its usual sensitivities and only those. I think youâve set up a kind of false dichotomy between permissibility and betterness as usually understood. A third option is rankings not intended to be interpeted as betterness as usual. Or, we could interpret betterness more broadly.
Having separate rankings of options apart from or instead of strict permissibility facts can still be useful, say because we want to adopt something like a scalar consequentialist view over those rankings. I still want to say that C is âbetterâ than B, which is consistent with Dasguptaâs approach. There could be other options like A, with the same 100 people, but everyone gets 39 utility instead of 40, and another where everyone gets 20 utility instead. I still want to say 39 is better than 20, and ending up with 39 instead of 40 is not so bad, compared to ending up with 20, which would be a lot worse.
A steelman could be to just set it up like a hypothetical sequential choice problem consistent with Dasguptaâs approach:
Choose between A and B
If you chose B in 1, choose between B and C.
or
Choose between A and (B or C).
If you chose B or C in 1, choose between B and C.
In either case, âpicking Bâ (including âpicking B or Câ) in 1 means actually picking C, if you know youâd pick C in 2, and then use backwards induction.
The fact that A is at least as good as (or not worse than and incomparable to) B could follow because B actually just becomes C, which is equivalent to A once weâve ruled out B. Itâs not just facts about direct binary choices that decide rankings (âbetternessâ), but the reasoning process as a whole and how we interpret the steps.
At any rate, I donât think itâs that important whether we interpret the rankings as âbetternessâ, as usually understood, with its usual sensitivities and only those. I think youâve set up a kind of false dichotomy between permissibility and betterness as usually understood. A third option is rankings not intended to be interpeted as betterness as usual. Or, we could interpret betterness more broadly.
Having separate rankings of options apart from or instead of strict permissibility facts can still be useful, say because we want to adopt something like a scalar consequentialist view over those rankings. I still want to say that C is âbetterâ than B, which is consistent with Dasguptaâs approach. There could be other options like A, with the same 100 people, but everyone gets 39 utility instead of 40, and another where everyone gets 20 utility instead. I still want to say 39 is better than 20, and ending up with 39 instead of 40 is not so bad, compared to ending up with 20, which would be a lot worse.