Thanks! Yeah, good question. The view I’ve sketched will say that A is c-impermissible, but we can still say that A is all-things-considered permissible after taking moral uncertainty into account. As an analogy, declining to push someone in front of a trolley to save 5 people is c-impermissible, but can be all-things-considered permissible after taking moral uncertainty into account.
On your second point, I think the thing I wrote in reply to Jim Buhler applies:
Basically I think the ‘flanking variants’ test will rule out a lot of actions but not all of them. In general, if our set of available actions is finite, then for each probability function there must be some action that has highest EV (and the same holds for infinite action sets modulo some small complications).
In practice, I think the easiest ones to identify will be extreme actions, like donating all your money to charity. Then we have some reason to think that the action is higher EV than its flanking variants, e.g. it’s higher EV than giving less money, and it’s impossible to give any more.
Of course, if we start individuating actions finely enough, then the flanking variants test might start ruling out even extreme actions. For example, it might be implausible that ideal reflection on your current evidence could lead you to judge that donating all your money at time X is higher EV than both (i) donating all your money one millisecond earlier and (ii) donating all your money one millisecond later. That would suggest donating all your money at time X is nowhere-optimal, in which case it’s dominated by some mixed action, in which case it’s c-impermissible.
But note that acting c-impermissibly in this way seems like an inevitable product of our cognitive limitations. So acting c-impermissibly in this way seems at least more forgiveable than choosing actions that are nowhere-optimal (and hence dominated) even on a coarse-grained individuation of our action space.
On your third point, I agree it seems kinda implausible to think you’re required to strictly c-prefer the AB mixture to C even though neither A nor B is strictly c-preferred to C, but as you say denying it will have costs. We can read off one cost from my argument: you’ll have to deny Dissent, Unanimity, or Justification.
> We can read off one cost from my argument: you’ll have to deny Dissent, Unanimity, or Justification.
I haven’t thought about this much at all, but: One idea is that you could avoid the kinds of reflection principle violations involved in preferring mixtures by “rectangularising” the representor (cf. this). I.e., enlarge the representor such that your current expectations match your expectations of your future expectations.
This would violate Unanimity (relative to your original representor), but I’m not sure that’s so bad on its own. I think I’m more worried that it has other bad properties, e.g., maybe we can’t do this without creating “too much” imprecision.
Yeah, that seems like a pretty good way to go. I think creating too much imprecision might be a concern, and that there’s also a concern about motivation. As I understand it, rectangularising in this case means adding probability functions to your representor on which, e.g., Pr(X | Heads)<0.01. But that seems incompatible with characterizing your representor as the set of probability functions you could settle on after ideal reflection on your current evidence, because (we can stipulate that X is such that) ideal reflection won’t lead you to believe that X and Heads are so tightly anti-correlated. And given that, it seems maybe hard to justify including probability functions on which Pr(X | Heads)<0.01 in your representor (and thereby letting those probability functions affect what’s permissible/impermissible for you).
Right, you might want to say that the distributions added to the representor should not have an epistemic interpretation, but should be thought of as a choice-theoretic representation. That is, we have a choice-theoretic reflection principle (something like, if I know that I’ll in future judge A and B to be permissible, I should judge them to both be permissible now), which along with other constraints forces choice behaviour that is representable by the larger representor.
one should never be required to strictly c-prefer a mixture of A and B to C whenever neither A nor B is c-preferred to C
There are candidate counterexamples to this claim. For example, imagine A is giving a benefit to Amy, and B and C each designate the same action of giving a benefit to Bobby. Then if you’re impartial, you won’t strictly c-prefer either of A or B to C, but you might strictly c-prefer the 50:50 mixture AB to C on the basis that it’s fairer to randomize who gets the benefit.
Also, imprecise consequentialism (plus Dissent, Unanimity, and Justification) has an even more counterintuitive implication than ‘you can be required to strictly c-prefer a mixture of AB to C even though neither A nor B is c-preferred to C.’ It implies:
You can be required to strictly c-prefer a mixture of A, B, and C to D, even though (i) neither A nor B is c-preferred to D, (ii) C is c-dispreferred to D, and (iii) the mixture has an arbitrarily high probability of resulting in C.
Here’s an example to illustrate:
I made the mixture have a 60% chance of C just to avoid the diagram being all bunched up. But the steeper you make the diagonals A and B, the higher you can push the probability of C and yet still have the mixture dominate D.
Thanks! Yeah, good question. The view I’ve sketched will say that A is c-impermissible, but we can still say that A is all-things-considered permissible after taking moral uncertainty into account. As an analogy, declining to push someone in front of a trolley to save 5 people is c-impermissible, but can be all-things-considered permissible after taking moral uncertainty into account.
On your second point, I think the thing I wrote in reply to Jim Buhler applies:
On your third point, I agree it seems kinda implausible to think you’re required to strictly c-prefer the AB mixture to C even though neither A nor B is strictly c-preferred to C, but as you say denying it will have costs. We can read off one cost from my argument: you’ll have to deny Dissent, Unanimity, or Justification.
> We can read off one cost from my argument: you’ll have to deny Dissent, Unanimity, or Justification.
I haven’t thought about this much at all, but: One idea is that you could avoid the kinds of reflection principle violations involved in preferring mixtures by “rectangularising” the representor (cf. this). I.e., enlarge the representor such that your current expectations match your expectations of your future expectations.
This would violate Unanimity (relative to your original representor), but I’m not sure that’s so bad on its own. I think I’m more worried that it has other bad properties, e.g., maybe we can’t do this without creating “too much” imprecision.
Yeah, that seems like a pretty good way to go. I think creating too much imprecision might be a concern, and that there’s also a concern about motivation. As I understand it, rectangularising in this case means adding probability functions to your representor on which, e.g., Pr(X | Heads)<0.01. But that seems incompatible with characterizing your representor as the set of probability functions you could settle on after ideal reflection on your current evidence, because (we can stipulate that X is such that) ideal reflection won’t lead you to believe that X and Heads are so tightly anti-correlated. And given that, it seems maybe hard to justify including probability functions on which Pr(X | Heads)<0.01 in your representor (and thereby letting those probability functions affect what’s permissible/impermissible for you).
Right, you might want to say that the distributions added to the representor should not have an epistemic interpretation, but should be thought of as a choice-theoretic representation. That is, we have a choice-theoretic reflection principle (something like, if I know that I’ll in future judge A and B to be permissible, I should judge them to both be permissible now), which along with other constraints forces choice behaviour that is representable by the larger representor.
Extra stuff:
There are candidate counterexamples to this claim. For example, imagine A is giving a benefit to Amy, and B and C each designate the same action of giving a benefit to Bobby. Then if you’re impartial, you won’t strictly c-prefer either of A or B to C, but you might strictly c-prefer the 50:50 mixture AB to C on the basis that it’s fairer to randomize who gets the benefit.
Also, imprecise consequentialism (plus Dissent, Unanimity, and Justification) has an even more counterintuitive implication than ‘you can be required to strictly c-prefer a mixture of AB to C even though neither A nor B is c-preferred to C.’ It implies:
You can be required to strictly c-prefer a mixture of A, B, and C to D, even though (i) neither A nor B is c-preferred to D, (ii) C is c-dispreferred to D, and (iii) the mixture has an arbitrarily high probability of resulting in C.
Here’s an example to illustrate:
I made the mixture have a 60% chance of C just to avoid the diagram being all bunched up. But the steeper you make the diagonals A and B, the higher you can push the probability of C and yet still have the mixture dominate D.