Now, I’m not saying this is that likely (though it does have surprisingly good arguments in its favor). But if this theory is true, it implies that brains which have about 86 billion neurons would contain around 2^86 billion conscious subsystems. It implies that a single African elephant with about 257 billion neurons has orders of magnitude more moral worth than all humans on Earth, on account of its staggeringly large number of conscious subsystems.
You seem to be using your intuition to assess the plausibility of different ways of comparing welfare across species, but this can easily lead to conclusions which strongly contradict empirical evidence. The gravitational force between 2 masses is proportional to “distance”^-2. An exponent like 0 instead of −2 may seem plausible to people who are not informed, but its probability in reality is practically 0. An exponent of 0 would imply there is no gravitational force.
I think individual welfare per animal-year proportional to 2^”number of neurons” would imply energy mattering implausibly little to produce welfare. A human with 1 k more neurons, or 1.16*10^-6 % (= 1*10^3/(86*10^9)) more, would have basically the same energy consumption, but their welfare per human-year would be 2^(1*10^3) = 10^(log10(2)*10^3) = 10^301 times as large.
Here is an illustration of how one can easily be much more confident than that. If welfare per animal-year was proportional to f(x) = 2^x, where x is the number of neurons, its elasticity would be x*f’(x)/f(x) = x*ln(2)*2^x/2^x = ln(2)*x. Even for the 302 neurons of adult nematodes, which are the animals with the fewest neurons, the elasticity would be 209 (= ln(2)*302). For my assumption that welfare per animal-year is proportional to g(x) = x^a, its elasticity is x*a*x^(a − 1)/x^a = a. So, for a number of neurons close to that of adult nematodes, I think welfare per animal-year being proportional to 2^x is roughly as plausible as it being proportional to x^302. For a number of neurons close to that of humans, I believe welfare per animal-year being proportional to 2^x is roughly as plausible as it being proportional to x^(86*10^9). If the elasticity y follows a normal distribution with mean m, and standard deviation s, the probability p(y) of a given elasticity is proportional to e^(-(y—m)^2/(2*s^2))/s. Given 2 values for the elasticity y1 and y2, the ratio between their probabilities is p(y2)/p(y1) = e^((-(y2 - m)^2 + (y1 - m)^2)/(2*s^2)). For m = 0.5, s = 0.25, y1 = 0.5 (equal the expected elasticity m), and y2 = 302 (the value I am arguing is very unlikely), p(y2)/p(y1) = e^((-(302 − 0.5)^2 + (0.5 − 0.5)^2)/(2*0.25^2)) = e^(-727*10^3) = 10^(-log10(e)*727*10^3) = 10^(-316*10^3).
The above does not show that the welfare of animals with the fewest neurons dominates. However, it illustrate one can not only get astronomical stakes, but also astronomically low probabilities of such stakes holding. For any probability distribution describing real world phenomena, the probability and stakes are not independent. So one cannot just come up with a function implying astronomical stakes, and then independently guess a probability of such stakes holding.
Production functions usually have elasticities from 0 to 1, which is part of why my speculative best guess is that welfare per animal-year is proportional to “number of neurons”^0.5 (0.5 is the mean between 0 and 1). Doubling inputs (which could be energy) usually results in doubling the output (which could be welfare) at most. As far as I know, it would be unthinkable to have a function supposed to model the production of something in the real world with an elasticity of 302 or 86 billion. Here is a related chat I had with Gemini.
You seem to be using your intuition to assess the plausibility of different ways of comparing welfare across species, but this can easily lead to conclusions which strongly contradict empirical evidence. The gravitational force between 2 masses is proportional to “distance”^-2. An exponent like 0 instead of −2 may seem plausible to people who are not informed, but its probability in reality is practically 0. An exponent of 0 would imply there is no gravitational force.
I think individual welfare per animal-year proportional to 2^”number of neurons” would imply energy mattering implausibly little to produce welfare. A human with 1 k more neurons, or 1.16*10^-6 % (= 1*10^3/(86*10^9)) more, would have basically the same energy consumption, but their welfare per human-year would be 2^(1*10^3) = 10^(log10(2)*10^3) = 10^301 times as large.
Yes it would imply that a bit of extra energy can vastly increase consciousness. But so what? Why be 99.9999% confident that it can’t?
Here is an illustration of how one can easily be much more confident than that. If welfare per animal-year was proportional to f(x) = 2^x, where x is the number of neurons, its elasticity would be x*f’(x)/f(x) = x*ln(2)*2^x/2^x = ln(2)*x. Even for the 302 neurons of adult nematodes, which are the animals with the fewest neurons, the elasticity would be 209 (= ln(2)*302). For my assumption that welfare per animal-year is proportional to g(x) = x^a, its elasticity is x*a*x^(a − 1)/x^a = a. So, for a number of neurons close to that of adult nematodes, I think welfare per animal-year being proportional to 2^x is roughly as plausible as it being proportional to x^302. For a number of neurons close to that of humans, I believe welfare per animal-year being proportional to 2^x is roughly as plausible as it being proportional to x^(86*10^9). If the elasticity y follows a normal distribution with mean m, and standard deviation s, the probability p(y) of a given elasticity is proportional to e^(-(y—m)^2/(2*s^2))/s. Given 2 values for the elasticity y1 and y2, the ratio between their probabilities is p(y2)/p(y1) = e^((-(y2 - m)^2 + (y1 - m)^2)/(2*s^2)). For m = 0.5, s = 0.25, y1 = 0.5 (equal the expected elasticity m), and y2 = 302 (the value I am arguing is very unlikely), p(y2)/p(y1) = e^((-(302 − 0.5)^2 + (0.5 − 0.5)^2)/(2*0.25^2)) = e^(-727*10^3) = 10^(-log10(e)*727*10^3) = 10^(-316*10^3).
The above does not show that the welfare of animals with the fewest neurons dominates. However, it illustrate one can not only get astronomical stakes, but also astronomically low probabilities of such stakes holding. For any probability distribution describing real world phenomena, the probability and stakes are not independent. So one cannot just come up with a function implying astronomical stakes, and then independently guess a probability of such stakes holding.
Production functions usually have elasticities from 0 to 1, which is part of why my speculative best guess is that welfare per animal-year is proportional to “number of neurons”^0.5 (0.5 is the mean between 0 and 1). Doubling inputs (which could be energy) usually results in doubling the output (which could be welfare) at most. As far as I know, it would be unthinkable to have a function supposed to model the production of something in the real world with an elasticity of 302 or 86 billion. Here is a related chat I had with Gemini.