If we had started with 1000 f1 rather than f1 in the first place, then switching it to f1 would seem to give f1 (or 1000 f1, or whatever) too little weight relative to f2, right?
Right, for f3 = 1000 f1, we would need some kind of information to change the weight of f3 from 50% (= 1/​(1 + 1)) to 0.1% (= 0.001/​(0.001 + 1)).
Note that I do not think the starting functions are arbitrary. For the analysis of this post, for example, each function would represent a distribution for the moral weight of poultry birds relative to humans in QALY/​pQALY, under a given theory.
In addition, to determine an overall moral weight given 2 distributions for the moral weight, MWA and MWB, I would weight them by the reciprocal of their variances (based on this analysis from by Dario Amodei):
In my view, the weights of f1 and f2 depend on how much we trust f1 and f2, and therefore they are not arbitrary:
If we had absolutely no idea about in which function to trust more, giving the same weight to each of the functions (i.e. 50%) would seem intuitive.
In order to increase the weight of f1 from 50% to 99.9%, we would need to have new information updating us towards trusting much more in f1 over f2.
If we had started with 1000 f1 rather than f1 in the first place, then switching it to f1 would seem to give f1 (or 1000 f1, or whatever) too little weight relative to f2, right?
Right, for f3 = 1000 f1, we would need some kind of information to change the weight of f3 from 50% (= 1/​(1 + 1)) to 0.1% (= 0.001/​(0.001 + 1)).
Note that I do not think the starting functions are arbitrary. For the analysis of this post, for example, each function would represent a distribution for the moral weight of poultry birds relative to humans in QALY/​pQALY, under a given theory.
In addition, to determine an overall moral weight given 2 distributions for the moral weight, MWA and MWB, I would weight them by the reciprocal of their variances (based on this analysis from by Dario Amodei):
MW = (MWA/​V(MWA) + MWB/​V(MWB))/​(1/​V(MWA) + 1/​V(MWB)).
Having this in mind, the higher is the uncertainty of MWA relative to that of MWB, the larger is the weight of MWA.