Note: I haven’t read the book. Also, based on your other writing, MichaelA, I suspect much of what I write here won’t be helpful to you, but it might be for other readers less familiar with Bayesian reasoning or order of magnitude calculations.
On uncertainty about Bayesian estimates of probabilities (credences), I think the following statement could be rewritten in a way that’s a bit clearer about the nature of these estimates:
There is significant uncertainty remaining in these estimates and they should be treated as representing the right order of magnitude—each could easily be a factor of 3 higher or lower.
But these are Ord’s beliefs, so when he says they could be a factor of 3 higher or lower, I think he means that he think there’s a good chance that he could be convinced that they’re that much higher or lower, with new information, and since he says they “should be treated as representing the right order of magnitude”, he doesn’t think he could be convinced that they should be more than 3x higher or lower.
I don’t think it’s meaningful to say that a belief ”X will happen with probability p” is accurate or not. We could test a set of beliefs and probabilities for calibration, but there are too few events here (many of which are extremely unlikely according to his views and are too far in the future) to test his calibration on them. So it’s basically meaningless to say whether or not he’s accurate about these. We could test his calibration on a different set of events and hope his calibration generalizes to these ones. We could test on multiple sets of events and see how his calibration changes between them to get an idea of the generalization error before we try to generalize.
On the claim, it seems like for many of his estimates, he rounded to the nearest 1 in 10k, on a logarithmic scale, since the halfway point between 10k and 10k+1 on a log scale is 10k+1/2≃3.16×10k, so he can only be off by a factor of √10∼3.16∼3. If he were off by more than a factor of 3, then he would have had to round to a different power of 10. The claim that they represent the right orders of magnitude is equivalent to them being correct to within a factor of about 3. (Or that he thinks he’s unlikely to change his mind about the order of magnitude with new information is equivalent to him believing that new information is unlikely to change his mind about these estimates by more than a factor of 3.)
I’d be curious to know if there are others who have worked as hard on estimating any of these probabilities and how close their estimates are to his.
I’d be curious to know if there are others who have worked as hard on estimating any of these probabilities and how close their estimates are to his.
I definitely share this curiosity. In a footnote, I link to this 2008 “informal survey” that’s the closest thing I’m aware of (in the sense of being somewhat comprehensive). It’s a little hard to compare the estimate, as that was for extinction (or sub-extinction events) rather than existential catastrophe more generally, and was for before 2100 rather than before 2120. But it seems to be overall somewhat more pessimistic than Ord, though in roughly the same ballpark for “overall/total risk”, AI, and engineered pandemics at least.
I don’t off the top of my head know anything comparable in terms of amount of effort, except in the case of individual AI researchers estimating the risks from AI, or specific types of AI catastrophe—nothing broader. Or maybe a couple 80k problem profiles. And I haven’t seen these collected anywhere—I think it could be cool if someone did that (and made sure the collection prominently warned against anchoring etc.).
A related and interesting question would be “If we do find past or future estimates based on as much hard work, and find that they’re similar to Ord’s, what do we make of this observation?” It could be taken as strengthening the case for those estimates being “about right”. But it could also be evidence of anchoring or information cascades. We’d want to know how independent the estimates were. (It’s worth noting that the 2008 survey was from FHI, where Ord works.)
Update: I’m now creating this sort of a collection of estimates, partly inspired by this comment thread (so thanks, MichaelStJules!). I’m not yet sure if I’ll publish them; I think collecting a diversity of views together will reduce rather than exacerbate information cascades and such, but I’m not sure. I’m also not sure when I’d publish, if I do publish.
But I think the answers are “probably” and “within a few weeks”.
If anyone happens to know of something like this that already exists, and/or has thoughts on whether publishing something like this would be valuable or detrimental, please let me know :)
Update #2: This turned into a database of existential estimates, and a post with some broader discussion of the idea of making, using, and collecting such estimates. And it’s now posted.
So thanks for (probably accidentally) prompting this!
Yes, it does seem worth pointing out that these are Bayesian rather than “frequency”/”physical” probabilities. (Though Ord uses them as somewhat connected to frequency probabilities, as he also discusses how long we should expect humanity to last given various probabilities of x-catastrophe per century.)
To be clear, though, that’s what I had in mind when suggesting that being uncertain only within a particular order of magnitude was surprising to me. E.g., I agree with the following statement:
But these are Ord’s beliefs, so when he says they could be a factor of 3 higher or lower, I think he means that he think there’s a good chance that he could be convinced that they’re that much higher or lower, with new information
...but I was surprised to hear that, if Ord does mean that the way it sounds to me, he thinks he could only be convinced to raise or lower his credence by a factor of ~3.
Though it’s possible he instead meant that they could definitely be off by a factor of 3, which that wouldn’t surprise him at all, but it’s also plausible they could be off by even more.
I don’t think it’s meaningful to say that a belief “X will happen with probability p” is accurate or not. We could test a set of beliefs and probabilities for calibration, but there are too few events here (many of which are extremely unlikely according to his views and are too far in the future) to test his calibration on them. So it’s basically meaningless to say whether or not he’s accurate about these.
I think there’s something to this, but I’m not sure I totally agree. Or at least it might depend on what you mean by “accurate”. I’m not an expert here, but Wikipedia says:
Broadly speaking, there are two interpretations on Bayesian probability. For objectivists, interpreting probability as extension of logic, probability quantifies the reasonable expectation everyone (even a “robot”) sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by Cox’s theorem.[2][8] For subjectivists, probability corresponds to a personal belief.
I think a project like Ord’s is probably most useful if it’s at least striving for objectivist Bayesian probabilities. (I think “the epistemic interpretation” is also relevant.) And if it’s doing so, I think the probabilities can be meaningfully critiqued as more or less reasonable or useful.
The claim that they represent the right orders of magnitude is equivalent to them being correct to within a factor of about 3.
I agree that this is at least roughly correct, given that he’s presenting each credence/probability as “1 in [some power of 10]”. I didn’t mean to imply that I was questioning two substantively different claims of his; more just to point out that he reiterates a similar point, weakly suggesting he really does mean that this is roughly the range of uncertainty he considers these probabilities to have.
I’m not sure I totally agree, or at least it depends on what you mean by “accurate”. I’m not an expert here, but Wikipedia says:
Broadly speaking, there are two interpretations on Bayesian probability. For objectivists, interpreting probability as extension of logic, probability quantifies the reasonable expectation everyone (even a “robot”) sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by Cox’s theorem.[2][8] For subjectivists, probability corresponds to a personal belief.
I think a project like Ord’s is probably most useful if it’s at least striving for objetivist Bayesian probabilities. (I think “the epistemic interpretation” is also relevant.)
I’m also not an expert here, but I think we’d have to agree about how to interpret knowledge and build the model, and have the same priors to guarantee this kind of agreement. See some discussion here. The link you sent about probability interpretations also links to the reference class problem.
And if it’s doing so, I think the probabilities can be meaningfully critiqued as more or less reasonable or useful.
I think we can critique probabilities based on how they were estimated, at least, and I think some probabilities we can be pretty confident in because they come from repeated random-ish trials or we otherwise have reliable precedent to base them on (e.g. good reference classes, and the estimates don’t vary too much between the best reference classes). If there’s only really one reasonable model, and all of the probabilities are pretty precise in it (based on precedent), then the final probability should be pretty precise, too.
Just found a quote from the book which I should’ve mentioned earlier (perhaps this should’ve also been a footnote in this post):
any notion of risk must involve some kind of probability. What kind is involved in existential risk? Understanding the probability in terms of objective long-run frequencies won’t work, as the existential catastrophes we are concerned with can only ever happen once, and will always be unprecedented until the moment it is too late. We can’t say the probability of an existential catastrophe is precisely zero just because it hasn’t happened yet.
Situations like these require an evidential sense of probability, which describes the appropriate degree of belief we should have on the basis of the available information. This is the familiar type of probability used in courtrooms, banks and betting shops. When I speak of the probability of an existential catastrophe, I mean the credence humanity should have that it will occur, in light of our best evidence.
And I’m pretty sure there was another quote somewhere about the complexities with this.
As for your comment, I’m not sure if we’re just using language slightly differently or actually have different views. But I think we do have different views on this point:
If there’s only really one reasonable model, and all of the probabilities are pretty precise in it (based on precedent), then the final probability should be pretty precise, too.
I would say that, even if one model is the most (or only) reasonable one we’re aware of, if we’re not certain about the model, we should account for model uncertainty (or uncertainty about the argument). So (I think) even if we don’t have specific reasons for other precise probabilities, or for decreasing the precision, we should still make our probabilities less precise, because there could be “unknown unknowns”, or mistakes in our reasoning process, or whatever.
If we know that our model might be wrong, and we don’t account for that when thinking about how certain vs uncertain we are, then we’re not using all the evidence and information we have. Thus, we wouldn’t be striving for that “evidential” sense of probability as well as we could. And more importantly, it seems likely we’d predictably do worse in making plans and achieving our goals.
Interestingly, Ord is among the main people I’ve seen making the sort of argument I make in the prior paragraph, both in this book and in two prior papers (one of which I’ve only read the abstract of). This increased my degree of surprise at him appearing to suggest he was fairly confident these estimates were of the right order of magnitude.
I agree that we should consider model uncertainty, including the possibility of unknown unknowns.
I think it’s rare that you can show that only one model is reasonable in practice, because the world is so complex. Mostly only really well-defined problems with known parts and finitely many known unknowns, like certain games, (biased) coin flipping, etc..
Note: I haven’t read the book. Also, based on your other writing, MichaelA, I suspect much of what I write here won’t be helpful to you, but it might be for other readers less familiar with Bayesian reasoning or order of magnitude calculations.
On uncertainty about Bayesian estimates of probabilities (credences), I think the following statement could be rewritten in a way that’s a bit clearer about the nature of these estimates:
But these are Ord’s beliefs, so when he says they could be a factor of 3 higher or lower, I think he means that he think there’s a good chance that he could be convinced that they’re that much higher or lower, with new information, and since he says they “should be treated as representing the right order of magnitude”, he doesn’t think he could be convinced that they should be more than 3x higher or lower.
I don’t think it’s meaningful to say that a belief ”X will happen with probability p” is accurate or not. We could test a set of beliefs and probabilities for calibration, but there are too few events here (many of which are extremely unlikely according to his views and are too far in the future) to test his calibration on them. So it’s basically meaningless to say whether or not he’s accurate about these. We could test his calibration on a different set of events and hope his calibration generalizes to these ones. We could test on multiple sets of events and see how his calibration changes between them to get an idea of the generalization error before we try to generalize.
On the claim, it seems like for many of his estimates, he rounded to the nearest 1 in 10k, on a logarithmic scale, since the halfway point between 10k and 10k+1 on a log scale is 10k+1/2≃3.16×10k, so he can only be off by a factor of √10∼3.16∼3. If he were off by more than a factor of 3, then he would have had to round to a different power of 10. The claim that they represent the right orders of magnitude is equivalent to them being correct to within a factor of about 3. (Or that he thinks he’s unlikely to change his mind about the order of magnitude with new information is equivalent to him believing that new information is unlikely to change his mind about these estimates by more than a factor of 3.)
I’d be curious to know if there are others who have worked as hard on estimating any of these probabilities and how close their estimates are to his.
I definitely share this curiosity. In a footnote, I link to this 2008 “informal survey” that’s the closest thing I’m aware of (in the sense of being somewhat comprehensive). It’s a little hard to compare the estimate, as that was for extinction (or sub-extinction events) rather than existential catastrophe more generally, and was for before 2100 rather than before 2120. But it seems to be overall somewhat more pessimistic than Ord, though in roughly the same ballpark for “overall/total risk”, AI, and engineered pandemics at least.
I don’t off the top of my head know anything comparable in terms of amount of effort, except in the case of individual AI researchers estimating the risks from AI, or specific types of AI catastrophe—nothing broader. Or maybe a couple 80k problem profiles. And I haven’t seen these collected anywhere—I think it could be cool if someone did that (and made sure the collection prominently warned against anchoring etc.).
A related and interesting question would be “If we do find past or future estimates based on as much hard work, and find that they’re similar to Ord’s, what do we make of this observation?” It could be taken as strengthening the case for those estimates being “about right”. But it could also be evidence of anchoring or information cascades. We’d want to know how independent the estimates were. (It’s worth noting that the 2008 survey was from FHI, where Ord works.)
Update: I’m now creating this sort of a collection of estimates, partly inspired by this comment thread (so thanks, MichaelStJules!). I’m not yet sure if I’ll publish them; I think collecting a diversity of views together will reduce rather than exacerbate information cascades and such, but I’m not sure. I’m also not sure when I’d publish, if I do publish.
But I think the answers are “probably” and “within a few weeks”.
If anyone happens to know of something like this that already exists, and/or has thoughts on whether publishing something like this would be valuable or detrimental, please let me know :)
Update #2: This turned into a database of existential estimates, and a post with some broader discussion of the idea of making, using, and collecting such estimates. And it’s now posted.
So thanks for (probably accidentally) prompting this!
Thanks for the comment!
Yes, it does seem worth pointing out that these are Bayesian rather than “frequency”/”physical” probabilities. (Though Ord uses them as somewhat connected to frequency probabilities, as he also discusses how long we should expect humanity to last given various probabilities of x-catastrophe per century.)
To be clear, though, that’s what I had in mind when suggesting that being uncertain only within a particular order of magnitude was surprising to me. E.g., I agree with the following statement:
...but I was surprised to hear that, if Ord does mean that the way it sounds to me, he thinks he could only be convinced to raise or lower his credence by a factor of ~3.
Though it’s possible he instead meant that they could definitely be off by a factor of 3, which that wouldn’t surprise him at all, but it’s also plausible they could be off by even more.
I think there’s something to this, but I’m not sure I totally agree. Or at least it might depend on what you mean by “accurate”. I’m not an expert here, but Wikipedia says:
I think a project like Ord’s is probably most useful if it’s at least striving for objectivist Bayesian probabilities. (I think “the epistemic interpretation” is also relevant.) And if it’s doing so, I think the probabilities can be meaningfully critiqued as more or less reasonable or useful.
I agree that this is at least roughly correct, given that he’s presenting each credence/probability as “1 in [some power of 10]”. I didn’t mean to imply that I was questioning two substantively different claims of his; more just to point out that he reiterates a similar point, weakly suggesting he really does mean that this is roughly the range of uncertainty he considers these probabilities to have.
I’m also not an expert here, but I think we’d have to agree about how to interpret knowledge and build the model, and have the same priors to guarantee this kind of agreement. See some discussion here. The link you sent about probability interpretations also links to the reference class problem.
I think we can critique probabilities based on how they were estimated, at least, and I think some probabilities we can be pretty confident in because they come from repeated random-ish trials or we otherwise have reliable precedent to base them on (e.g. good reference classes, and the estimates don’t vary too much between the best reference classes). If there’s only really one reasonable model, and all of the probabilities are pretty precise in it (based on precedent), then the final probability should be pretty precise, too.
Just found a quote from the book which I should’ve mentioned earlier (perhaps this should’ve also been a footnote in this post):
And I’m pretty sure there was another quote somewhere about the complexities with this.
As for your comment, I’m not sure if we’re just using language slightly differently or actually have different views. But I think we do have different views on this point:
I would say that, even if one model is the most (or only) reasonable one we’re aware of, if we’re not certain about the model, we should account for model uncertainty (or uncertainty about the argument). So (I think) even if we don’t have specific reasons for other precise probabilities, or for decreasing the precision, we should still make our probabilities less precise, because there could be “unknown unknowns”, or mistakes in our reasoning process, or whatever.
If we know that our model might be wrong, and we don’t account for that when thinking about how certain vs uncertain we are, then we’re not using all the evidence and information we have. Thus, we wouldn’t be striving for that “evidential” sense of probability as well as we could. And more importantly, it seems likely we’d predictably do worse in making plans and achieving our goals.
Interestingly, Ord is among the main people I’ve seen making the sort of argument I make in the prior paragraph, both in this book and in two prior papers (one of which I’ve only read the abstract of). This increased my degree of surprise at him appearing to suggest he was fairly confident these estimates were of the right order of magnitude.
I agree that we should consider model uncertainty, including the possibility of unknown unknowns.
I think it’s rare that you can show that only one model is reasonable in practice, because the world is so complex. Mostly only really well-defined problems with known parts and finitely many known unknowns, like certain games, (biased) coin flipping, etc..