I think it would’ve been better to just elicit point estimates of the grants’ expected value, rather than distributions. Using distributions adds complexity, for not much benefit, and it’s somewhat unclear what the distributions even represent.
Added complexity: for researchers giving their elicitations, for the data analysis, for readers trying to interpret the results. This can make the process slower, lead to errors, and lead to different people interpreting things differently. e.g., For including both positive & negative numbers in the distributions.
Not much benefit: at least, when I read this report I mostly looked at the point estimates, except for the section showing that researchers’ confidence intervals for the two elicitation methods didn’t overlap.
Unclear what the distribution represents: The distribution is basically a probability distribution over a probability (p(x-risk)), and it’s not obvious which uncertainties should be represented in the distribution and which are part of p(x-risk). e.g., If someone thinks that there’s an 80% chance that a research direction is misguided & useless and a 20% chance that it’s meaningful & relevant, should they just multiply their distribution by 0.2 (relative to research that is definitely in a meaningful & relevant direction), or should this give a more spread-out distribution with most of the probability mass near zero, or something in between?
Unclear what the distribution represents: The distribution is basically a probability distribution over a probability (p(x-risk)), and it’s not obvious which uncertainties should be represented in the distribution and which are part of p(x-risk). e.g., If someone thinks that there’s an 80% chance that a research direction is misguided & useless and a 20% chance that it’s meaningful & relevant, should they just multiply their distribution by 0.2 (relative to research that is definitely in a meaningful & relevant direction), or should this give a more spread-out distribution with most of the probability mass near zero, or something in between?
Yeah, you can use a mixture distribution if you are thinking about the distribution of impact, like so, or you can take the mean of that mixture if you want to estimate the expected value, like so. Depends of what you are after.
My intuitions point the other way with regards to point estimates vs distributions. Distributions seem like the correct format here, and they could allow for value of information calculations, sensitivity, to highlight disagreements which people wouldn’t notice with point estimates, to better combine. The bottom line could also change when using estimates, e.g., as in here.
That said, they do have a learning curve and I agree with you that they add additional complexity/upfront cost.
Agreed that there are some contexts where there’s more value in getting distributions, like with the Fermi paradox.
Or, before the grants are given out, you could ask people to give an ex ante distribution for “what will be your ex post point estimate of the value of this grant?” That feeds directly into VOI calculations, and it is clearly defined what the distribution represents. But note that it requires focusing on point estimates ex post.
> Or, before the grants are given out, you could ask people to give an ex ante distribution for “what will be your ex post point estimate of the value of this grant?” That feeds directly into VOI calculations, and it is clearly defined what the distribution represents. But note that it requires focusing on point estimates ex post.
Aha, but you can also do this when the final answer is also a distribution. In particular, you can look at the KL-divergence between the initial distribution and the answer, and this is also a proper scoring rule.
More generally, I think there is a difference between what would have been best for this analysis, and you might be right that point estimates would have been better, and what EA/longtermism should be aiming to have, which I think are more uncertain estimates in the shape of distributions.
I think it would’ve been better to just elicit point estimates of the grants’ expected value, rather than distributions. Using distributions adds complexity, for not much benefit, and it’s somewhat unclear what the distributions even represent.
Added complexity: for researchers giving their elicitations, for the data analysis, for readers trying to interpret the results. This can make the process slower, lead to errors, and lead to different people interpreting things differently. e.g., For including both positive & negative numbers in the distributions.
Not much benefit: at least, when I read this report I mostly looked at the point estimates, except for the section showing that researchers’ confidence intervals for the two elicitation methods didn’t overlap.
Unclear what the distribution represents: The distribution is basically a probability distribution over a probability (p(x-risk)), and it’s not obvious which uncertainties should be represented in the distribution and which are part of p(x-risk). e.g., If someone thinks that there’s an 80% chance that a research direction is misguided & useless and a 20% chance that it’s meaningful & relevant, should they just multiply their distribution by 0.2 (relative to research that is definitely in a meaningful & relevant direction), or should this give a more spread-out distribution with most of the probability mass near zero, or something in between?
Yeah, you can use a mixture distribution if you are thinking about the distribution of impact, like so, or you can take the mean of that mixture if you want to estimate the expected value, like so. Depends of what you are after.
My intuitions point the other way with regards to point estimates vs distributions. Distributions seem like the correct format here, and they could allow for value of information calculations, sensitivity, to highlight disagreements which people wouldn’t notice with point estimates, to better combine. The bottom line could also change when using estimates, e.g., as in here.
That said, they do have a learning curve and I agree with you that they add additional complexity/upfront cost.
Agreed that there are some contexts where there’s more value in getting distributions, like with the Fermi paradox.
Or, before the grants are given out, you could ask people to give an ex ante distribution for “what will be your ex post point estimate of the value of this grant?” That feeds directly into VOI calculations, and it is clearly defined what the distribution represents. But note that it requires focusing on point estimates ex post.
> Or, before the grants are given out, you could ask people to give an ex ante distribution for “what will be your ex post point estimate of the value of this grant?” That feeds directly into VOI calculations, and it is clearly defined what the distribution represents. But note that it requires focusing on point estimates ex post.
Aha, but you can also do this when the final answer is also a distribution. In particular, you can look at the KL-divergence between the initial distribution and the answer, and this is also a proper scoring rule.
More generally, I think there is a difference between what would have been best for this analysis, and you might be right that point estimates would have been better, and what EA/longtermism should be aiming to have, which I think are more uncertain estimates in the shape of distributions.