Thanks, Derek. What do you think about what I proposed here?
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(âWR of humansâ/ââWR of chickensâ) = w*N + (1 - w)*n.
Chickens relative to that of humans is E(âWR of chickensâ/ââWR of humansâ) = w/âN + (1 - w)/ân.
You [Carl Shulman] 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 RPâs [Rethink Prioritiesâ] median welfare range of chickens relative to humans of 0.332), and w = 1â12 (since the neuron count model was one of the 12 RP considered, and all of them were weighted equally [I think RP only used 7 or 8 models for the final welfare ranges, and not neuron counts, but my point does not depend on the weight]). Having the welfare range of:
Chickens as the reference, E(âWR of humansâ/ââWR of chickensâ) = 35.2. So 1/âE(âWR of humansâ/ââWR of chickensâ) = 0.0284.
Humans as the reference (as RP did), E(âWR of chickensâ/ââWR of humansâ) = 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(âWR of humansâ/ââWR of chickensâ) = N^w*n^(1 - w) = 4.49. So 1/âE(âWR of humansâ/ââWR of chickensâ) = (N^w*n^(1 - w))^-1 = 0.223.
E(âWR of chickensâ/ââWR of humansâ) = (1/âN)^w*(1/ân)^(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 RPâs approach looks fine to me as a 1st pass. Does this make any sense?
I forgot to say OPISâ survey did not look into the types of pain defined by the Welfare Footprint Project.