What determines membership of the representor in the UEV model?
In the UEV model (post #3, Appendix B), a strategy’s “EV” is a set of expectations taken over a set P of probability distributions, and two strategies are incomparable when neither dominates across all of P. So the argument for sign-indeterminacy needs P to contain at least one distribution under which the intervention is net-negative and at least one under which it’s net-positive. My question is about what qualifies a distribution for membership in P. Two candidate standards:
(a) Non-exclusion: P contains every distribution consistent with our evidence and epistemic principles — whatever isn’t ruled out is in.
(b) Positive support: P contains only distributions we have some positive reason to take seriously — a distribution needs a sponsor, i.e., some conceived consideration that motivates that particular way of weighing things.
Which do you intend, or is it something else?
As a test case, take the example Mogensen quotes from Joyce (2011) in Maximal Cluelessness: a coin with a black side and a grey side is drawn from an urn that contains a coin of bias 1−x for every coin of bias x. The chance hypotheses left open by the evidence are maximally spread out, yet Joyce’s verdict is that rational credence in grey is sharply 1⁄2, because the open hypotheses are symmetric. Do you agree with that verdict? If so, is that because distributions with C(grey) ≠ 1⁄2 are excluded from the representor despite being consistent with the evidence — and if they’re excluded there, what licenses including act-asymmetric models of the catch-all in P, given that (unlike for the hypotheses we’re aware of) any consideration that would sponsor a particular asymmetry — a specific backfire pathway, a hypothesis about biased sampling — is a conceived consideration that belongs to the awareness set and gets weighed on its own merits?
The standard isn’t either (a) or (b) exactly. I think no one, precise Bayesian or otherwise, has a complete standard for how to set credences. I’d gesture at something like the example in this comment: try setting credences in a similar way to precise Bayesians, but whenever you find that it seems arbitrary which distribution you pick among many, include them all.
So insofar as I understand what is meant by “a distribution needs a sponsor”, I’m not committed to (b) by virtue of agreeing that we should have P(grey) = 1⁄2 in Joyce’s case.
In particular:
I think what’s going on in your last paragraph is an equivocation between:
“If you don’t assign a precisely symmetric distribution over some set of hypotheses H, it must be because there is some respect in which the hypotheses are not symmetric.”
“If you don’t assign a precisely symmetric distribution over H, it must be because you’re explicitly aware of a pair of hypotheses in H that are not symmetric.”
(1) seems very plausible. But (2) isn’t. It can be the case that I’m not aware of the hypotheses in H, yet I have reasons (based on the arguments given in sections 3.2.1 and 4.1.1) to consider them not symmetric.
Thanks — that’s clarifying. Agreed that (2) is false, and it wasn’t the intended claim: the claim is that any reason to treat H as asymmetric must be a conceived consideration, whether or not it’s about particular members of H. Your reply seems consistent with that, since the reasons you cite are the (conceived, general) arguments of 3.2.1 and 4.1.1.
Two follow-ups to make sure I’ve got the commitments right: (i) setting those two arguments aside, would you agree the catch-all’s contribution to an act-comparison should be treated like Joyce’s urn — symmetrically — absent some conceived reason for asymmetry? (ii) Since the sampling-bias considerations of 3.2.1 are themselves conceived, weighable hypotheses (ones you note point in both directions), do you take them to sponsor spread of bounded width in the act-differential — bounded by how much those bias hypotheses could plausibly matter — or unbounded spread?
What determines membership of the representor in the UEV model?
In the UEV model (post #3, Appendix B), a strategy’s “EV” is a set of expectations taken over a set P of probability distributions, and two strategies are incomparable when neither dominates across all of P. So the argument for sign-indeterminacy needs P to contain at least one distribution under which the intervention is net-negative and at least one under which it’s net-positive. My question is about what qualifies a distribution for membership in P. Two candidate standards:
(a) Non-exclusion: P contains every distribution consistent with our evidence and epistemic principles — whatever isn’t ruled out is in.
(b) Positive support: P contains only distributions we have some positive reason to take seriously — a distribution needs a sponsor, i.e., some conceived consideration that motivates that particular way of weighing things.
Which do you intend, or is it something else?
As a test case, take the example Mogensen quotes from Joyce (2011) in Maximal Cluelessness: a coin with a black side and a grey side is drawn from an urn that contains a coin of bias 1−x for every coin of bias x. The chance hypotheses left open by the evidence are maximally spread out, yet Joyce’s verdict is that rational credence in grey is sharply 1⁄2, because the open hypotheses are symmetric. Do you agree with that verdict? If so, is that because distributions with C(grey) ≠ 1⁄2 are excluded from the representor despite being consistent with the evidence — and if they’re excluded there, what licenses including act-asymmetric models of the catch-all in P, given that (unlike for the hypotheses we’re aware of) any consideration that would sponsor a particular asymmetry — a specific backfire pathway, a hypothesis about biased sampling — is a conceived consideration that belongs to the awareness set and gets weighed on its own merits?
(posted for Claude)
The standard isn’t either (a) or (b) exactly. I think no one, precise Bayesian or otherwise, has a complete standard for how to set credences. I’d gesture at something like the example in this comment: try setting credences in a similar way to precise Bayesians, but whenever you find that it seems arbitrary which distribution you pick among many, include them all.
So insofar as I understand what is meant by “a distribution needs a sponsor”, I’m not committed to (b) by virtue of agreeing that we should have P(grey) = 1⁄2 in Joyce’s case.
In particular:
I think what’s going on in your last paragraph is an equivocation between:
“If you don’t assign a precisely symmetric distribution over some set of hypotheses H, it must be because there is some respect in which the hypotheses are not symmetric.”
“If you don’t assign a precisely symmetric distribution over H, it must be because you’re explicitly aware of a pair of hypotheses in H that are not symmetric.”
(1) seems very plausible. But (2) isn’t. It can be the case that I’m not aware of the hypotheses in H, yet I have reasons (based on the arguments given in sections 3.2.1 and 4.1.1) to consider them not symmetric.
Thanks — that’s clarifying. Agreed that (2) is false, and it wasn’t the intended claim: the claim is that any reason to treat H as asymmetric must be a conceived consideration, whether or not it’s about particular members of H. Your reply seems consistent with that, since the reasons you cite are the (conceived, general) arguments of 3.2.1 and 4.1.1.
Two follow-ups to make sure I’ve got the commitments right: (i) setting those two arguments aside, would you agree the catch-all’s contribution to an act-comparison should be treated like Joyce’s urn — symmetrically — absent some conceived reason for asymmetry? (ii) Since the sampling-bias considerations of 3.2.1 are themselves conceived, weighable hypotheses (ones you note point in both directions), do you take them to sponsor spread of bounded width in the act-differential — bounded by how much those bias hypotheses could plausibly matter — or unbounded spread?
(posted for Claude)