I think you at least get an edge on the problem from this (related to the point you make about factual uncertainty—familiarity with humans means we have more factual uncertainty about insect experience). But I wouldn’t want to rest the whole of my argument on this edge.
I agree that “I assign probability p that humans are 10^3 times as important as insects and probability q that humans are 10^10 times as important as insects” is logically equivalent to “I assign probability p that insects are 10^-3 times as important as humans and probability q that insects are 10^-10 times as important as humans”. However, when people turn these into the argument that “you should care about insects/humans much more than about humans/insects”, they’re implicitly doing an expected utility calculation.
In one version of the calculation, you’re saying that insect lives have utility 1, and human lives have utility 10^3 with probability p and 10^10 with probability q. When you take the expectation (for certain values of p and q), you end up with the human population being more important than the insect population.
In another version of the calculation, you’re saying that human lives have utility 1, and insect lives have utility 10^-3 with probability p and 10^-10 with probability q. Then, when you take the expectation (for values of p and q compatible with the pro-human conclusion above), you end up with the insect population being more important than the human population.
My point is that although both these probability assignments are compatible with the description “humans are 10^3 times as important with probability p and 10^10 times as important with probability q”, they are not equivalent distributions over utilities. Furthermore, I think my probability distribution looks more like the second than the first.
I don’t think you can avoid the problem that way, since it’s logically equivalent to re-cast your statement in terms of insect value units?
I think you at least get an edge on the problem from this (related to the point you make about factual uncertainty—familiarity with humans means we have more factual uncertainty about insect experience). But I wouldn’t want to rest the whole of my argument on this edge.
I agree that “I assign probability p that humans are 10^3 times as important as insects and probability q that humans are 10^10 times as important as insects” is logically equivalent to “I assign probability p that insects are 10^-3 times as important as humans and probability q that insects are 10^-10 times as important as humans”. However, when people turn these into the argument that “you should care about insects/humans much more than about humans/insects”, they’re implicitly doing an expected utility calculation.
In one version of the calculation, you’re saying that insect lives have utility 1, and human lives have utility 10^3 with probability p and 10^10 with probability q. When you take the expectation (for certain values of p and q), you end up with the human population being more important than the insect population.
In another version of the calculation, you’re saying that human lives have utility 1, and insect lives have utility 10^-3 with probability p and 10^-10 with probability q. Then, when you take the expectation (for values of p and q compatible with the pro-human conclusion above), you end up with the insect population being more important than the human population.
My point is that although both these probability assignments are compatible with the description “humans are 10^3 times as important with probability p and 10^10 times as important with probability q”, they are not equivalent distributions over utilities. Furthermore, I think my probability distribution looks more like the second than the first.