(ETA: The parent comment contains several important misunderstandings of my views, so I figured I should clarify here. Hence my long comments â sorry about that.)
Thanks for this, Ryan! Iâll reply to your main points here, and clear up some less central yet important points in another comment.
Hereâs what I think youâre saying (sorry the numbering clashes with the numbering in your comment, couldnât figure out how to change this):
The best representations of our actual degrees of belief given our evidence, intuitions, etc. â what you call the âterminally correctâ credences â should be precise.[1]
In practice, the strategy that maximizes EV w.r.t. our terminally correct credences wonât be âmake decisions by actually writing down a precise distribution and trying to maximize EV w.r.t. that distributionâ. This is because there are empirical features of our situation that hinder us from executing that strategy ideally.
I (Anthony) am mistakenly inferring from (2) that (1) is false.
(In particular, any argument against (1) that relies on premises about the âempirical aspects of the current situationâ must be making that mistake.)
Is that right? If so:
I do disagree with (1), but for reasons that have nothing to do with (2). My case for imprecise credences is: âIn our empirical situation, any particular precise credence [or expected value] we might pick would be highly arbitraryâ (argued for in detail here). (So Iâm also not just saying âyou can have imprecise credences without getting money pumpedâ.)
Iâm not saying that âheuristicsâ based on imprecise credences âoutperformâ explicit EV max. I donât think that principles for belief formation can bottom out in âperformanceâ but should instead bottom out in non-pragmatic principles â one of which is (roughly) âif our available information is so ambiguous that picking one precise credence over another seems arbitrary, our credences should be impreciseâ.
However, when we use non-pragmatic principles to derive our beliefs, the appropriate beliefs (not the principles themselves) can and should depend on empirical features of our situation that directly bear on our epistemic state: E.g., we face lots of considerations about the plausibility of a given hypothesis, and we seem to have too little evidence (+ too weak constraints from e.g. indifference principles or Occamâs razor) to justify any particular precise weighing of these considerations.[2] Contra (3.a), I donât see how/âwhy the structure of our credences could/âshould be independent of very relevant empirical information like this.
Intuition pump: Even an âidealâ precise Bayesian doesnât actually terminally care about EV, they terminally care about the ex post value. But their empirical situation makes them uncertain what the ex post value of their action will be, so they represent their epistemic state with precise credences, and derive their preferences over actions from EV. This doesnât imply theyâre conflating terminal goals with empirical facts about how best to achieve them.
Separately, I havenât yet seen convincing positive cases for (1). What are the âreasonably compelling argumentsâ for precise credences + EV maximization? And (if applicable to you) what are your replies to my counterarguments to the usual arguments here[3] (also here and here, though in fairness to you, those were buried in a comment thread)?
So in particular, I think youâre not saying the terminally correct credences for us are the credences that our computationally unbounded counterparts would have. If you are saying that, please let me know and I can reply to that â FWIW, as argued here, itâs not clear a computationally unbounded agent would be justified in precise credences either.
This is true of pretty much any hypothesis we consider, not just hypotheses about especially distant stuff. This ~adds up to normality /â doesnât collapse into radical skepticism, because we have reasons to have varying degrees of imprecision in our credences, and our credences about mundane stuff will only have a small degree of imprecision (more here and here).
Quote: â[L]etâs revisit why we care about EV in the first place. A common answer: âCoherence theorems! If you canât be modeled as maximizing EU, youâre shooting yourself in the foot.â For our purposes, the biggest problem with this answer is: Suppose we act as if we maximize the expectation of some utility function. This doesnât imply we make our decisions by following the procedure âuse our impartial altruistic valuefunction to (somehow) assign a number to each hypothesis, and maximize the expectationâ.â (In that context, I was taking about assigning precise values to coarse-grained hypotheses, but the same applies to assigning precise credences to any hypothesis.)
(ETA: The parent comment contains several important misunderstandings of my views, so I figured I should clarify here. Hence my long comments â sorry about that.)
Thanks for this, Ryan! Iâll reply to your main points here, and clear up some less central yet important points in another comment.
Hereâs what I think youâre saying (sorry the numbering clashes with the numbering in your comment, couldnât figure out how to change this):
The best representations of our actual degrees of belief given our evidence, intuitions, etc. â what you call the âterminally correctâ credences â should be precise.[1]
In practice, the strategy that maximizes EV w.r.t. our terminally correct credences wonât be âmake decisions by actually writing down a precise distribution and trying to maximize EV w.r.t. that distributionâ. This is because there are empirical features of our situation that hinder us from executing that strategy ideally.
I (Anthony) am mistakenly inferring from (2) that (1) is false.
(In particular, any argument against (1) that relies on premises about the âempirical aspects of the current situationâ must be making that mistake.)
Is that right? If so:
I do disagree with (1), but for reasons that have nothing to do with (2). My case for imprecise credences is: âIn our empirical situation, any particular precise credence [or expected value] we might pick would be highly arbitraryâ (argued for in detail here). (So Iâm also not just saying âyou can have imprecise credences without getting money pumpedâ.)
Iâm not saying that âheuristicsâ based on imprecise credences âoutperformâ explicit EV max. I donât think that principles for belief formation can bottom out in âperformanceâ but should instead bottom out in non-pragmatic principles â one of which is (roughly) âif our available information is so ambiguous that picking one precise credence over another seems arbitrary, our credences should be impreciseâ.
However, when we use non-pragmatic principles to derive our beliefs, the appropriate beliefs (not the principles themselves) can and should depend on empirical features of our situation that directly bear on our epistemic state: E.g., we face lots of considerations about the plausibility of a given hypothesis, and we seem to have too little evidence (+ too weak constraints from e.g. indifference principles or Occamâs razor) to justify any particular precise weighing of these considerations.[2] Contra (3.a), I donât see how/âwhy the structure of our credences could/âshould be independent of very relevant empirical information like this.
Intuition pump: Even an âidealâ precise Bayesian doesnât actually terminally care about EV, they terminally care about the ex post value. But their empirical situation makes them uncertain what the ex post value of their action will be, so they represent their epistemic state with precise credences, and derive their preferences over actions from EV. This doesnât imply theyâre conflating terminal goals with empirical facts about how best to achieve them.
Separately, I havenât yet seen convincing positive cases for (1). What are the âreasonably compelling argumentsâ for precise credences + EV maximization? And (if applicable to you) what are your replies to my counterarguments to the usual arguments here[3] (also here and here, though in fairness to you, those were buried in a comment thread)?
So in particular, I think youâre not saying the terminally correct credences for us are the credences that our computationally unbounded counterparts would have. If you are saying that, please let me know and I can reply to that â FWIW, as argued here, itâs not clear a computationally unbounded agent would be justified in precise credences either.
This is true of pretty much any hypothesis we consider, not just hypotheses about especially distant stuff. This ~adds up to normality /â doesnât collapse into radical skepticism, because we have reasons to have varying degrees of imprecision in our credences, and our credences about mundane stuff will only have a small degree of imprecision (more here and here).
Quote: â[L]etâs revisit why we care about EV in the first place. A common answer: âCoherence theorems! If you canât be modeled as maximizing EU, youâre shooting yourself in the foot.â For our purposes, the biggest problem with this answer is: Suppose we act as if we maximize the expectation of some utility function. This doesnât imply we make our decisions by following the procedure âuse our impartial altruistic value function to (somehow) assign a number to each hypothesis, and maximize the expectationâ.â (In that context, I was taking about assigning precise values to coarse-grained hypotheses, but the same applies to assigning precise credences to any hypothesis.)