I think scope neglect respecting the variation of small factors (like probabilities) results from these very often being subjective guesses. In constrat, methods used to assess large factors are very often scope sensitive. For example, longtermists typically come up with huge amounts of potential benefits (e.g. 10^50 QALY) based on the physical properties of the universe, but then independently guess an increase in the probability of the potential benefits materialising which is only moderately small (e.g. 10^-10), which results in huge expected benefits (e.g. 10^40 QALY). I think this does not work because the small factors are not independent from the large factors. In particulat, I believe the small factors get smaller as the large factors get larger. Solving half of the problem is harder (more costly) for larger problems.
One can see the expected benefits coming from large benefits may be negligible modelling the benefits as a distribution. For example, if the benefits are described by a power law distribution with tail index alpha > 0, their probability will be proportional to ābenefitsā^-(1 + alpha), so the expected benefits linked to a given amount of benefits will be proportional to ābenefitsā*ābenefitsā^-(1 + alpha) = ābenefitsā^-alpha. This decreases with benefits, so the expected benefits coming from astronomically large benefits will be negligible.
Great post, Karthik! Strongly upvoted.
I think scope neglect respecting the variation of small factors (like probabilities) results from these very often being subjective guesses. In constrat, methods used to assess large factors are very often scope sensitive. For example, longtermists typically come up with huge amounts of potential benefits (e.g. 10^50 QALY) based on the physical properties of the universe, but then independently guess an increase in the probability of the potential benefits materialising which is only moderately small (e.g. 10^-10), which results in huge expected benefits (e.g. 10^40 QALY). I think this does not work because the small factors are not independent from the large factors. In particulat, I believe the small factors get smaller as the large factors get larger. Solving half of the problem is harder (more costly) for larger problems.
One can see the expected benefits coming from large benefits may be negligible modelling the benefits as a distribution. For example, if the benefits are described by a power law distribution with tail index alpha > 0, their probability will be proportional to ābenefitsā^-(1 + alpha), so the expected benefits linked to a given amount of benefits will be proportional to ābenefitsā*ābenefitsā^-(1 + alpha) = ābenefitsā^-alpha. This decreases with benefits, so the expected benefits coming from astronomically large benefits will be negligible.