Good example! At least this isn’t solipsistic egoism, but I agree the results seem too egoistic.
What you could do is rearrange the two probability distributions of aggregate welfares statewise in non-decreasing order (or in a way that minimizes some distance between the two distributions), take the difference between the two resulting random variables, apply a bounded monotonically increasing function to the difference, and then take the expected value.
Unfortunately, I suspect this pairwise comparison approach won’t even be transitive.
Given an intransitive relation over options (distributions over outcomes), you can use voting methods like beatpath to define a similar transitive relation or choose among options even when there’s intransitivity in a choice set. Using beatpath on the specific actual option sets you face in particular will mean violating the independence of irrelevant alternatives, which I’m pretty okay with giving up, personally.
You could apply beatpath to the set of all conceivable options, even those not actually available to you in a given choice situation, but I imagine you’ll get too much indifference or incomparability.
Good example! At least this isn’t solipsistic egoism, but I agree the results seem too egoistic.
What you could do is rearrange the two probability distributions of aggregate welfares statewise in non-decreasing order (or in a way that minimizes some distance between the two distributions), take the difference between the two resulting random variables, apply a bounded monotonically increasing function to the difference, and then take the expected value.
Unfortunately, I suspect this pairwise comparison approach won’t even be transitive.
Given an intransitive relation over options (distributions over outcomes), you can use voting methods like beatpath to define a similar transitive relation or choose among options even when there’s intransitivity in a choice set. Using beatpath on the specific actual option sets you face in particular will mean violating the independence of irrelevant alternatives, which I’m pretty okay with giving up, personally.
This is done in this paper:
https://globalprioritiesinstitute.org/teruji-thomas-the-asymmetry-uncertainty-and-the-long-term/
You could apply beatpath to the set of all conceivable options, even those not actually available to you in a given choice situation, but I imagine you’ll get too much indifference or incomparability.