Iâm one of the judges of the competition. My comments shouldnât be taken as a full review of a post. And, unfortunately, I wonât have capacity to comment on every post or engage with all replies. Thanks so much to everyone who entered!
Thanks for this. I have some sympathy to the critique of maximality as far as it goes. (Though personally Iâm not that compelled by the symmetry arguments for your proposed alternative, the midpoint rule.)
My worry is that the threat of indeterminacy recurs, at the level of vague degrees of ex ante betterness. When I try to weigh up the reasons in favor of any A vs. B w.r.t. their total consequences, fully accounting for unawareness, I really donât see why I should consider the âupper endpointâ larger or smaller in absolute value than the âlower endpointâ. I think the arguments in posts #3 and #4 of the sequence support this worry, though I didnât explicitly frame them in such terms and used the precise-endpoints formalism. You acknowledge that this is possible here:
Just as we can admit vagueness in the endpoints of our imprecise credences, we can admit corresponding vagueness in the value yielded by D. This makes it difficult to say whether a given option is better than the null action when D is close to 0, which seems quite plausible: cases where D â 0 are exactly the kinds of cases where betterness or comparative justification may be too unclear or too vague to discriminate either way.
But I would like to see more of an argument that this isnât our situation, perhaps building on what you say in your appendix about low-footprint capacity-building.
(If we are indeed in a situation where even the âendpointsâ are hopelessly vague, then I donât think your defense of first-order wagering goes through either. You can have insensitivity to mild sweetening under vague degrees of betterness; it doesnât assume maximality.)
Iâm one of the judges of the competition. My comments shouldnât be taken as a full review of a post. And, unfortunately, I wonât have capacity to comment on every post or engage with all replies. Thanks so much to everyone who entered!
Thanks for this. I have some sympathy to the critique of maximality as far as it goes. (Though personally Iâm not that compelled by the symmetry arguments for your proposed alternative, the midpoint rule.)
My worry is that the threat of indeterminacy recurs, at the level of vague degrees of ex ante betterness. When I try to weigh up the reasons in favor of any A vs. B w.r.t. their total consequences, fully accounting for unawareness, I really donât see why I should consider the âupper endpointâ larger or smaller in absolute value than the âlower endpointâ. I think the arguments in posts #3 and #4 of the sequence support this worry, though I didnât explicitly frame them in such terms and used the precise-endpoints formalism. You acknowledge that this is possible here:
But I would like to see more of an argument that this isnât our situation, perhaps building on what you say in your appendix about low-footprint capacity-building.
(If we are indeed in a situation where even the âendpointsâ are hopelessly vague, then I donât think your defense of first-order wagering goes through either. You can have insensitivity to mild sweetening under vague degrees of betterness; it doesnât assume maximality.)