It’s quite true that my estimate of 3/2048 is (to say the least) more likely to be too low by 1⁄512 than to be too high by 1⁄512 :-). The error is probably something-like-lognormally distributed, being the result of multiplying a bunch of hopefully-kinda-independent errors.
But:
Suppose (for simplicity) that the probability we seek is the product of several independent probabilities, each of which I have independently estimated. Then Pr_actual(win) = Pr_actual(win1) Pr_actual(win2) … , and likewise Pr_est(win) = Pr_est(win1) Pr_est(win2) … . If I haven’t goofed in estimating the individual probabilities, then Pr_est(win1) = E_subjective(Pr_actual(win1)) etc. Hence:
In other words, even taking my unreliability in probability-estimating into account, and despite the asymmetry you noted, once I’ve estimated the individual probabilities my best estimate of the overall probability is what I get by using those individual estimates. I should not increase my probability estimate merely because there are uncertainties in the individual probability estimates.
For sure, my estimates could be wrong. For sure, they can be too high by much more than they can be too low. But they are very unlikely to be too high, and it turns out that (subject to the assumptions above) my overall estimate is unbiased provided my individual estimates are.
There’s something wrong with an analysis that biases the outcome in a particular direction as you add more details. In this case, the more different kinds of things that might go wrong or have to go right, the more fractions you have to multiply your result by. I don’t know how to get out of this trap, but it seems a failure mode with any attempt to predict the future by multiplying lists of probabilities, each generated by a handwave.
The only one of your numbers that I think can be estimated based on current experience is #2. Alcor publishes details regularly about how their cryopreservations go, and numbers for how many members quit or die in circumstances that make their preservation hopeless. Your 80% number sounds like it’s in the right ballpark. (*)
My other complaint is that your numbers are connected by a more complicated web of conditional likelihoods and interactions than simple multiplication shows. If civilization survives, the likelihood of particular technologies being developed increases, and if organizations like Alcor persist, that ought to raise those odds as well. In many of the bad societal outcomes, you won’t get revived. This reduces your downside almost as much as it reduces your upside. You’ve still paid for suspension, but it doesn’t count as a hell scenario.
I don’t think “Shut up and Multiply” should be taken literally here.
(*) ETA: simpleton’s reference to Alcor’s numbers says I’m wrong about this.
It’s perfectly correct that your estimate of P(cryonics will work for me) should go down as you think of more things that all have to happen for it to work. When something depends on many things all working right, it’s less likely to work out than intuition suggests; that’s one reason why project time estimates are almost always much too short, and why many projects fail.
Of course my probability estimates are only rough guesses. I don’t trust estimates derived in this way very much; but I trust an estimate derived by breaking the problem down into smallish bits and handwaving all the bits better than I trust one derived by handwaving the whole thing. (And there’s nothing about the breaking-it-down approach that necessitates a pessimistic answer; Robin Hanson did a similar handwavy calculation over on OB a little while ago and came up with a very different result.)
The estimate of 80% for #2 was not mine but Roko’s. My estimate for that one is 25%. I’m not in the US, which I gather makes a substantial difference, but in any case, as your later edit points out, it looks like my number may be better than Roko’s anyway.
Yes, the relationship between all those factors is not as simple as a bunch of independent events. That would be why, in the comment you’re replying to, I said “Suppose (for simplicity) that the probability we seek is the product of several independent probabilities, each of which I have independently estimated.” And also why some of my original estimates were explicitly made conditional on their predecessors.
“Shut up and multiply” was never meant to be taken literally, and as it happens I am not so stupid as to think that because someone once said “Shut up and multiply” I should therefore treat all probability calculations as chains of independent events. “Shut up and calculate” would be more accurate, but in the particular cases for which SUAM was (I think) coined the key calculations were very simple.
It’s quite true that my estimate of 3/2048 is (to say the least) more likely to be too low by 1⁄512 than to be too high by 1⁄512 :-). The error is probably something-like-lognormally distributed, being the result of multiplying a bunch of hopefully-kinda-independent errors.
But:
Suppose (for simplicity) that the probability we seek is the product of several independent probabilities, each of which I have independently estimated. Then Pr_actual(win) = Pr_actual(win1) Pr_actual(win2) … , and likewise Pr_est(win) = Pr_est(win1) Pr_est(win2) … . If I haven’t goofed in estimating the individual probabilities, then Pr_est(win1) = E_subjective(Pr_actual(win1)) etc. Hence:
E_subjective(Pr_actual(win)) = {by (objective) independence} E_subjective(product Pr_actual(win_j)) = {by (subjective) independence} product E_subjective(Pr_actual(win_j)) = {my individual estimates are OK, by assumption} product Pr_est(win_j) = {by (subjective) independence} Pr_est(win)
In other words, even taking my unreliability in probability-estimating into account, and despite the asymmetry you noted, once I’ve estimated the individual probabilities my best estimate of the overall probability is what I get by using those individual estimates. I should not increase my probability estimate merely because there are uncertainties in the individual probability estimates.
For sure, my estimates could be wrong. For sure, they can be too high by much more than they can be too low. But they are very unlikely to be too high, and it turns out that (subject to the assumptions above) my overall estimate is unbiased provided my individual estimates are.
There’s something wrong with an analysis that biases the outcome in a particular direction as you add more details. In this case, the more different kinds of things that might go wrong or have to go right, the more fractions you have to multiply your result by. I don’t know how to get out of this trap, but it seems a failure mode with any attempt to predict the future by multiplying lists of probabilities, each generated by a handwave.
The only one of your numbers that I think can be estimated based on current experience is #2. Alcor publishes details regularly about how their cryopreservations go, and numbers for how many members quit or die in circumstances that make their preservation hopeless. Your 80% number sounds like it’s in the right ballpark. (*)
My other complaint is that your numbers are connected by a more complicated web of conditional likelihoods and interactions than simple multiplication shows. If civilization survives, the likelihood of particular technologies being developed increases, and if organizations like Alcor persist, that ought to raise those odds as well. In many of the bad societal outcomes, you won’t get revived. This reduces your downside almost as much as it reduces your upside. You’ve still paid for suspension, but it doesn’t count as a hell scenario.
I don’t think “Shut up and Multiply” should be taken literally here.
(*) ETA: simpleton’s reference to Alcor’s numbers says I’m wrong about this.
It’s perfectly correct that your estimate of P(cryonics will work for me) should go down as you think of more things that all have to happen for it to work. When something depends on many things all working right, it’s less likely to work out than intuition suggests; that’s one reason why project time estimates are almost always much too short, and why many projects fail.
Of course my probability estimates are only rough guesses. I don’t trust estimates derived in this way very much; but I trust an estimate derived by breaking the problem down into smallish bits and handwaving all the bits better than I trust one derived by handwaving the whole thing. (And there’s nothing about the breaking-it-down approach that necessitates a pessimistic answer; Robin Hanson did a similar handwavy calculation over on OB a little while ago and came up with a very different result.)
The estimate of 80% for #2 was not mine but Roko’s. My estimate for that one is 25%. I’m not in the US, which I gather makes a substantial difference, but in any case, as your later edit points out, it looks like my number may be better than Roko’s anyway.
Yes, the relationship between all those factors is not as simple as a bunch of independent events. That would be why, in the comment you’re replying to, I said “Suppose (for simplicity) that the probability we seek is the product of several independent probabilities, each of which I have independently estimated.” And also why some of my original estimates were explicitly made conditional on their predecessors.
“Shut up and multiply” was never meant to be taken literally, and as it happens I am not so stupid as to think that because someone once said “Shut up and multiply” I should therefore treat all probability calculations as chains of independent events. “Shut up and calculate” would be more accurate, but in the particular cases for which SUAM was (I think) coined the key calculations were very simple.