No worries! Relatedly, Iām hoping to get out a post explaining (part of) the case for indeterminacy in the not-too-distant future, so to some extent Iāll punt to that for more details.
without having such an account itās sort of hard to assess how much of our caring for non-hedonist goods is grounded in themselves, vs in some sense being debunked by the explanation that they are instrumentally good to care about on hedonist grounds
Cool, that makes sense. Iām all for debunking explanations in principle. Extremely briefly, hereās why I think thereās something qualitative that determinate credences fail to capture: If evidence, trustworthy intuitions, and appealing norms like the principle of indifference or Occamās razor donāt uniquely pin down an answer to āhow likely should I consider outcome X?ā, then I think I shouldnāt pin down an answer. Instead I should suspend judgment, and say that there arenāt enough constraints to give an answer that isnāt arbitrary. (This runs deeper than āwait to learn /ā think moreā! Because I find suspending judgment appropriate even in cases where my uncertainty is resilient. Contra Greg Lewis here.)
Is it some analogue of betting odds? Or what?
No, I see credences as representing the degree to which I anticipate some (hypothetical) experiences, or the weight I put on a hypothesis /ā how reasonable I find it. IMO the betting odds framing gets things backwards. Bets are decisions, which are made rational by whether the beliefs theyāre justified by are rational. Iām not sure what would justify the betting odds otherwise.
how youād be inclined to think about indeterminate credences in an example like the digits of pi case
Ah, I should have made clear, I wouldnāt say indeterminate credences are necessary in the pi case, as written. Because I think itās plausible I should apply the principle of indifference here: I know nothing about digits of pi beyond the first 10, except that pi is irrational and I know irrational numbersā digits are wacky. I have no particular reason to think one digit is more or less likely than another, so, since thereās a unique way of splitting my credence impartially across the possibilities, I end up with 50:50.[1]
Instead, hereās a really contrived variant of the pi case I had too much fun writing, analogous to a situation of complex cluelessness, where Iād think indeterminate credences are appropriate:
Suppose that Sally historically has an uncanny ability to guess the parity of digits of (conjectured-to-be) normal numbers with an accuracy of 70%. Somehow, itās verifiable that sheās not cheating. No one quite knows how her guesses are so good.
Her accuracy varies with how happy she is at the time, though. She has an accuracy of ~95% when really ecstatic, ~50% when neutral, and only ~10% when really sad. Also, sheās never guessed parities of Nth digits for any N < 1 million.
Now, Sally also hasnāt seen the digits of pi beyond the first 10, and she guesses the 20th is odd. I donāt know how happy she is at the time, though I know sheās both gotten a well-earned promotion at her job and had an important flight canceled.
What should my credence in āthe 20th digit is oddā be? Seems like there are various considerations floating around:
The principle of indifference seems like a fair baseline.
But thereās also Sallyās really impressive average track record on N ā„ 1 million.
But also I know nothing about what mechanism drives her intuition, so itās pretty unclear if her intuition generalizes to such a small N.
And even setting that aside, since I donāt know how happy she is, should I just go with the base rate of 70%? Or should I apply the principle of indifference to the āhappiness levelā parameter, and assume sheās neutral (so 50%)?
But presumably the evidence about the promotion and canceled flight tell me something about her mood. I guess slightly less than neutral overall (but I have little clue how she personally would react to these two things)? How much less?
I really donāt know a privileged way to weigh all this up, especially since Iāve never thought about how much to defer to a digit-guessing magician before. It seems pretty defensible to have a range of credences between, say, 40% and 75%. These endpoints themselves are kinda arbitrary, but at least seem considerably less arbitrary than pinning down to one number.
I could try modeling all this and computing explicit priors and likelihood ratios, but it seems extremely doubtful thereās gonna be one privileged model and distribution over its parameters.
(I think forming beliefs about the long-term future is analogous in many ways to the above.)
Not sure how much that answers your question? Basically I ask myself what constraints the considerations ought to put on my degree of belief, and try not to needlessly get more precise than those constraints warrant.
I donāt think this is clearly the appropriate response. I think itās kinda defensible to say, āThis doesnāt seem like qualitatively the same kind of epistemic situation as guessing a coin flip. I have at least a rough mechanistic picture of how coin flips work physically, which seems symmetric in a way that warrants a determinate prediction of 50:50. But with digits of pi, thereās not so much a āsymmetryā as an absence of a determinate asymmetry.ā But I donāt think you need to die on that hill to think indeterminacy is warranted in realistic cause prio situations.
IMO the betting odds framing gets things backwards. Bets are decisions, which are made rational by whether the beliefs theyāre justified by are rational. Iām not sure what would justify the betting odds otherwise.
Not sure what I overall think of the better odds framing, but to speak in its defence: I think thereās a sense in which decisions are more real than beliefs. (I originally wrote ādecisions are real and beliefs are notā, but theyāre both ultimately abstractions about whatās going on with a bunch of matter organized into an agent-like system.) I can accept the idea of X as an agent making decisions, and ask what those decisions are and what drives them, without implicitly accepting the idea that X has beliefs. Then āX has beliefsā is kind of a useful model for predicting their behaviour in the decision situations. Or could be used (as you imply) to analyse the rationality of their decisions.
I like your contrived variant of the pi case. But to play on it a bit:
Maybe when I first find out the information on Sally, I quickly eyeball and think that defensible credences probably lie within the range 30% to 90%
Then later when I sit down and think about it more carefully, I think that actually the defensible credences are more like in the range 40% to 75%
If I thought about it even longer, maybe Iād tighten my range a bit further again (45% to 55%? 50% to 70%? I donāt know!)
In this picture, no realistic amount of thinking Iām going to do will bring it down to just a point estimate being defensible, and perhaps even the limit with infinite thinking time would have me maintain an interval of what seems defensible, so some fundamental indeterminacy may well remain.
But to my mind, this kind of behaviour where you can tighten your understanding by thinking more happens all of the time, and is a really important phenomenon to be able to track and think clearly about. So I really want language or formal frameworks which make it easy to track this kind of thing.
Moreover, after you grant this kind of behaviour [do you grant this kind of behaviour?], you may notice that from our epistemic position we canāt even distinguish between:
Cases where weād collapse our estimated range of defensible credences down to a very small range or even a single point with arbitrary thinking time, but where in practice progress is so slow that itās not viable
Cases where even in the limit with infinite thinking time, we would maintain a significant range of defensible credences
Because of this, from my perspective the question of whether credences are ultimately indeterminate is ā¦ not so interesting? Itās enough that in practice a lot of credences will be indeterminate, and that in many cases it may be useful to invest time thinking to shrink our uncertainty, but in many other cases it wonāt be.
I can accept the idea of X as an agent making decisions, and ask what those decisions are and what drives them, without implicitly accepting the idea that X has beliefs. Then āX has beliefsā is kind of a useful model for predicting their behaviour in the decision situations.
I think this is answering a different question, though. When talking about rationality and cause prioritization, what we want to know is what we ought to do, not how to describe our patterns of behavior after the fact. And when asking what we ought to do under uncertainty, I donāt see how we escape the question of what beliefs weāre justified in. E.g. betting on short AI timelines by opting out of your pension is only rational insofar as itās rational to (read: you have good reasons to) believe in short timelines.
from my perspective the question of whether credences are ultimately indeterminate is ā¦ not so interesting? Itās enough that in practice a lot of credences will be indeterminate, and that in many cases it may be useful to invest time thinking to shrink our uncertainty, but in many other cases it wonāt be
Iām not sure what youāre getting at here. My substantive claim is that in some cases, our credences about features of the far future might be sufficiently indeterminate that overall we wonāt be able to determinately say āX is net-good for the far future in expectation.ā If you agree with that, that seems to have serious implications that the EA community isnāt pricing in yet. If you donāt agree with that, Iām not sure if itās because of (1) thorny empirical disagreements over the details of what our credences should be, or (2) something more fundamental about epistemology (which is the level at which I thought we were having this discussion, so far). I think getting into (1) in this thread would be a bit of a rabbit hole (which is better left to some forthcoming posts Iām coauthoring), though Iād be happy to give some quick intuition pumps. Greaves here (the āSuppose thatās my personal uber-analysis...ā paragraph) is a pretty good starting point.
No worries! Relatedly, Iām hoping to get out a post explaining (part of) the case for indeterminacy in the not-too-distant future, so to some extent Iāll punt to that for more details.
Cool, that makes sense. Iām all for debunking explanations in principle. Extremely briefly, hereās why I think thereās something qualitative that determinate credences fail to capture: If evidence, trustworthy intuitions, and appealing norms like the principle of indifference or Occamās razor donāt uniquely pin down an answer to āhow likely should I consider outcome X?ā, then I think I shouldnāt pin down an answer. Instead I should suspend judgment, and say that there arenāt enough constraints to give an answer that isnāt arbitrary. (This runs deeper than āwait to learn /ā think moreā! Because I find suspending judgment appropriate even in cases where my uncertainty is resilient. Contra Greg Lewis here.)
No, I see credences as representing the degree to which I anticipate some (hypothetical) experiences, or the weight I put on a hypothesis /ā how reasonable I find it. IMO the betting odds framing gets things backwards. Bets are decisions, which are made rational by whether the beliefs theyāre justified by are rational. Iām not sure what would justify the betting odds otherwise.
Ah, I should have made clear, I wouldnāt say indeterminate credences are necessary in the pi case, as written. Because I think itās plausible I should apply the principle of indifference here: I know nothing about digits of pi beyond the first 10, except that pi is irrational and I know irrational numbersā digits are wacky. I have no particular reason to think one digit is more or less likely than another, so, since thereās a unique way of splitting my credence impartially across the possibilities, I end up with 50:50.[1]
Instead, hereās a really contrived variant of the pi case I had too much fun writing, analogous to a situation of complex cluelessness, where Iād think indeterminate credences are appropriate:
Suppose that Sally historically has an uncanny ability to guess the parity of digits of (conjectured-to-be) normal numbers with an accuracy of 70%. Somehow, itās verifiable that sheās not cheating. No one quite knows how her guesses are so good.
Her accuracy varies with how happy she is at the time, though. She has an accuracy of ~95% when really ecstatic, ~50% when neutral, and only ~10% when really sad. Also, sheās never guessed parities of Nth digits for any N < 1 million.
Now, Sally also hasnāt seen the digits of pi beyond the first 10, and she guesses the 20th is odd. I donāt know how happy she is at the time, though I know sheās both gotten a well-earned promotion at her job and had an important flight canceled.
What should my credence in āthe 20th digit is oddā be? Seems like there are various considerations floating around:
The principle of indifference seems like a fair baseline.
But thereās also Sallyās really impressive average track record on N ā„ 1 million.
But also I know nothing about what mechanism drives her intuition, so itās pretty unclear if her intuition generalizes to such a small N.
And even setting that aside, since I donāt know how happy she is, should I just go with the base rate of 70%? Or should I apply the principle of indifference to the āhappiness levelā parameter, and assume sheās neutral (so 50%)?
But presumably the evidence about the promotion and canceled flight tell me something about her mood. I guess slightly less than neutral overall (but I have little clue how she personally would react to these two things)? How much less?
I really donāt know a privileged way to weigh all this up, especially since Iāve never thought about how much to defer to a digit-guessing magician before. It seems pretty defensible to have a range of credences between, say, 40% and 75%. These endpoints themselves are kinda arbitrary, but at least seem considerably less arbitrary than pinning down to one number.
I could try modeling all this and computing explicit priors and likelihood ratios, but it seems extremely doubtful thereās gonna be one privileged model and distribution over its parameters.
(I think forming beliefs about the long-term future is analogous in many ways to the above.)
Not sure how much that answers your question? Basically I ask myself what constraints the considerations ought to put on my degree of belief, and try not to needlessly get more precise than those constraints warrant.
I donāt think this is clearly the appropriate response. I think itās kinda defensible to say, āThis doesnāt seem like qualitatively the same kind of epistemic situation as guessing a coin flip. I have at least a rough mechanistic picture of how coin flips work physically, which seems symmetric in a way that warrants a determinate prediction of 50:50. But with digits of pi, thereās not so much a āsymmetryā as an absence of a determinate asymmetry.ā But I donāt think you need to die on that hill to think indeterminacy is warranted in realistic cause prio situations.
Not sure what I overall think of the better odds framing, but to speak in its defence: I think thereās a sense in which decisions are more real than beliefs. (I originally wrote ādecisions are real and beliefs are notā, but theyāre both ultimately abstractions about whatās going on with a bunch of matter organized into an agent-like system.) I can accept the idea of X as an agent making decisions, and ask what those decisions are and what drives them, without implicitly accepting the idea that X has beliefs. Then āX has beliefsā is kind of a useful model for predicting their behaviour in the decision situations. Or could be used (as you imply) to analyse the rationality of their decisions.
I like your contrived variant of the pi case. But to play on it a bit:
Maybe when I first find out the information on Sally, I quickly eyeball and think that defensible credences probably lie within the range 30% to 90%
Then later when I sit down and think about it more carefully, I think that actually the defensible credences are more like in the range 40% to 75%
If I thought about it even longer, maybe Iād tighten my range a bit further again (45% to 55%? 50% to 70%? I donāt know!)
In this picture, no realistic amount of thinking Iām going to do will bring it down to just a point estimate being defensible, and perhaps even the limit with infinite thinking time would have me maintain an interval of what seems defensible, so some fundamental indeterminacy may well remain.
But to my mind, this kind of behaviour where you can tighten your understanding by thinking more happens all of the time, and is a really important phenomenon to be able to track and think clearly about. So I really want language or formal frameworks which make it easy to track this kind of thing.
Moreover, after you grant this kind of behaviour [do you grant this kind of behaviour?], you may notice that from our epistemic position we canāt even distinguish between:
Cases where weād collapse our estimated range of defensible credences down to a very small range or even a single point with arbitrary thinking time, but where in practice progress is so slow that itās not viable
Cases where even in the limit with infinite thinking time, we would maintain a significant range of defensible credences
Because of this, from my perspective the question of whether credences are ultimately indeterminate is ā¦ not so interesting? Itās enough that in practice a lot of credences will be indeterminate, and that in many cases it may be useful to invest time thinking to shrink our uncertainty, but in many other cases it wonāt be.
I think this is answering a different question, though. When talking about rationality and cause prioritization, what we want to know is what we ought to do, not how to describe our patterns of behavior after the fact. And when asking what we ought to do under uncertainty, I donāt see how we escape the question of what beliefs weāre justified in. E.g. betting on short AI timelines by opting out of your pension is only rational insofar as itās rational to (read: you have good reasons to) believe in short timelines.
Iām not sure what youāre getting at here. My substantive claim is that in some cases, our credences about features of the far future might be sufficiently indeterminate that overall we wonāt be able to determinately say āX is net-good for the far future in expectation.ā If you agree with that, that seems to have serious implications that the EA community isnāt pricing in yet. If you donāt agree with that, Iām not sure if itās because of (1) thorny empirical disagreements over the details of what our credences should be, or (2) something more fundamental about epistemology (which is the level at which I thought we were having this discussion, so far). I think getting into (1) in this thread would be a bit of a rabbit hole (which is better left to some forthcoming posts Iām coauthoring), though Iād be happy to give some quick intuition pumps. Greaves here (the āSuppose thatās my personal uber-analysis...ā paragraph) is a pretty good starting point.