Luke says in the post you linked that the numbers in the graphic are not usable as expected moral weights, since ratios of expectations are not the same as expectations of ratios.
Let me try to restate your point, and suggest why one may disagree. If one puts weight w on the welfare range (WR) of humans relative to that of chickens being N, and 1 - w on it being n, the expected welfare range of:
Humans relative to that of chickens is E(“WR of humans”/”WR of chickens”) = w*N + (1 - w)*n.
Chickens relative to that of humans is E(“WR of chickens”/”WR of humans”) = w/N + (1 - w)/n.
You are arguing that N can plausibly be much larger than n. For the sake of illustration, we can say N = 389 (ratio between the 86 billion neurons of a humans and 221 M of a chicken), n = 3.01 (reciprocal of RP’s median welfare range of chickens relative to humans of 0.332), and w = 1⁄12 (since the neuron count model was one of the 12 RP considered, and all of them were weighted equally). Having the welfare range of:
Chickens as the reference, E(“WR of humans”/”WR of chickens”) = 35.2. So 1/E(“WR of humans”/”WR of chickens”) = 0.0284.
Humans as the reference (as RP did), E(“WR of chickens”/”WR of humans”) = 0.305.
So, as you said, determining welfare ranges relative to humans results in animals being weighted more heavily. However, I think the difference is much smaller than the suggested above. Since N and n are quite different, I guess we should combine them using a weighted geometric mean, not the weighted mean as I did above. If so, both approaches output exactly the same result:
E(“WR of humans”/”WR of chickens”) = N^w*n^(1 - w) = 4.49. So 1/E(“WR of humans”/”WR of chickens”) = (N^w*n^(1 - w))^-1 = 0.223.
E(“WR of chickens”/”WR of humans”) = (1/N)^w*(1/n)^(1 - w) = 0.223.
The reciprocal of the expected value is not the expected value of the reciprocal, so using the mean leads to different results. However, I think we should be using the geometric mean, and the reciprocal of the geometric mean is the geometric mean of the reciprocal. So the 2 approaches (using humans or chickens as the reference) will output the same ratios regardless of N, n and w as long as we aggregate N and n with the geometric mean. If N and n are similar, it no longer makes sense to use the geometric mean, but then both approaches will output similar results anyway, so RP’s approach looks fine to me as a 1st pass. Does this make any sense?
Of course, it would still be good to do further research (which OP could fund) to adjudicate how much weight should be given to each model RP considered.
I had argued for many years that insects met a lot of the functional standards one could use to identify the presence of well-being, and that even after taking two-envelopes issues and nervous system scale into account expected welfare at stake for small wild animals looked much larger than for FAW.
I’m not planning on continuing a long thread here, I mostly wanted to help address the questions about my previous comment, so I’ll be moving on after this. But I will say two things regarding the above. First, this effect (computational scale) is smaller for chickens but progressively enormous for e.g. shrimp or lobster or flies. Second, this is a huge move and one really needs to wrestle with intertheoretic comparisons to justify it:
I guess we should combine them using a weighted geometric mean, not the weighted mean as I did above.
Suppose we compared the mass of the human population of Earth with the mass of an individual human. We could compare them on 12 metrics, like per capita mass, per capita square root mass, per capita foot mass… and aggregate mass. If we use the equal-weighted geometric mean, we will conclude the individual has a mass within an order of magnitude of the total Earth population, instead of billions of times less.
I’m not planning on continuing a long thread here, I mostly wanted to help address the questions about my previous comment, so I’ll be moving on after this.
Fair, as this is outside of the scope of the original post. I noticed you did not comment on RP’s neuron counts post. I think it would be valuable if you commented there about the concerns you expressed here, or did you already express them elsewhere in another post of RP’s moral weight project sequence?
First, this effect (computational scale) is smaller for chickens but progressively enormous for e.g. shrimp or lobster or flies.
I agree that is the case if one combines the 2 wildly different estimates for the welfare range (e.g. one based on the number of neurons, and another corresponding to RP’s median welfare ranges) with a weighted mean. However, as I commented above, using the geometric mean would cancel the effect.
Suppose we compared the mass of the human population of Earth with the mass of an individual human. We could compare them on 12 metrics, like per capita mass, per capita square root mass, per capita foot mass… and aggregate mass. If we use the equal-weighted geometric mean, we will conclude the individual has a mass within an order of magnitude of the total Earth population, instead of billions of times less.
Is this a good analogy? Maybe not:
Broadly speaking, giving the same weight to multiple estimates only makes sense if there is wide uncertainty with respect to which one is more reliable. In the example above, it would make sense to give negligible weight to all metrics except for the aggregate mass. In contrast, there is arguably wide uncertainty with respect to what are the best models to measure welfare ranges, and therefore distributing weights evenly is more appropriate.
One particular model on which we can put lots of weight on is that mass is straightforwardly additive (at least at the macro scale). So we can say the mass of all humans equals the number of humans times the mass per human, and then just estimate this for a typical human. In contrast, it is arguably unclear whether one can obtain the welfare range of an animal by e.g. just adding up the welfare range of its individual neurons.
Thanks for elaborating, Carl!
Let me try to restate your point, and suggest why one may disagree. If one puts weight w on the welfare range (WR) of humans relative to that of chickens being N, and 1 - w on it being n, the expected welfare range of:
Humans relative to that of chickens is E(“WR of humans”/”WR of chickens”) = w*N + (1 - w)*n.
Chickens relative to that of humans is E(“WR of chickens”/”WR of humans”) = w/N + (1 - w)/n.
You are arguing that N can plausibly be much larger than n. For the sake of illustration, we can say N = 389 (ratio between the 86 billion neurons of a humans and 221 M of a chicken), n = 3.01 (reciprocal of RP’s median welfare range of chickens relative to humans of 0.332), and w = 1⁄12 (since the neuron count model was one of the 12 RP considered, and all of them were weighted equally). Having the welfare range of:
Chickens as the reference, E(“WR of humans”/”WR of chickens”) = 35.2. So 1/E(“WR of humans”/”WR of chickens”) = 0.0284.
Humans as the reference (as RP did), E(“WR of chickens”/”WR of humans”) = 0.305.
So, as you said, determining welfare ranges relative to humans results in animals being weighted more heavily. However, I think the difference is much smaller than the suggested above. Since N and n are quite different, I guess we should combine them using a weighted geometric mean, not the weighted mean as I did above. If so, both approaches output exactly the same result:
E(“WR of humans”/”WR of chickens”) = N^w*n^(1 - w) = 4.49. So 1/E(“WR of humans”/”WR of chickens”) = (N^w*n^(1 - w))^-1 = 0.223.
E(“WR of chickens”/”WR of humans”) = (1/N)^w*(1/n)^(1 - w) = 0.223.
The reciprocal of the expected value is not the expected value of the reciprocal, so using the mean leads to different results. However, I think we should be using the geometric mean, and the reciprocal of the geometric mean is the geometric mean of the reciprocal. So the 2 approaches (using humans or chickens as the reference) will output the same ratios regardless of N, n and w as long as we aggregate N and n with the geometric mean. If N and n are similar, it no longer makes sense to use the geometric mean, but then both approaches will output similar results anyway, so RP’s approach looks fine to me as a 1st pass. Does this make any sense?
Of course, it would still be good to do further research (which OP could fund) to adjudicate how much weight should be given to each model RP considered.
True!
Thanks for sharing your views!
I’m not planning on continuing a long thread here, I mostly wanted to help address the questions about my previous comment, so I’ll be moving on after this. But I will say two things regarding the above. First, this effect (computational scale) is smaller for chickens but progressively enormous for e.g. shrimp or lobster or flies. Second, this is a huge move and one really needs to wrestle with intertheoretic comparisons to justify it:
Suppose we compared the mass of the human population of Earth with the mass of an individual human. We could compare them on 12 metrics, like per capita mass, per capita square root mass, per capita foot mass… and aggregate mass. If we use the equal-weighted geometric mean, we will conclude the individual has a mass within an order of magnitude of the total Earth population, instead of billions of times less.
Fair, as this is outside of the scope of the original post. I noticed you did not comment on RP’s neuron counts post. I think it would be valuable if you commented there about the concerns you expressed here, or did you already express them elsewhere in another post of RP’s moral weight project sequence?
I agree that is the case if one combines the 2 wildly different estimates for the welfare range (e.g. one based on the number of neurons, and another corresponding to RP’s median welfare ranges) with a weighted mean. However, as I commented above, using the geometric mean would cancel the effect.
Is this a good analogy? Maybe not:
Broadly speaking, giving the same weight to multiple estimates only makes sense if there is wide uncertainty with respect to which one is more reliable. In the example above, it would make sense to give negligible weight to all metrics except for the aggregate mass. In contrast, there is arguably wide uncertainty with respect to what are the best models to measure welfare ranges, and therefore distributing weights evenly is more appropriate.
One particular model on which we can put lots of weight on is that mass is straightforwardly additive (at least at the macro scale). So we can say the mass of all humans equals the number of humans times the mass per human, and then just estimate this for a typical human. In contrast, it is arguably unclear whether one can obtain the welfare range of an animal by e.g. just adding up the welfare range of its individual neurons.