Your utility function can instead be bounded wrt the difference you make relative to some fixed default distribution of outcomes (“doing nothing”, or “business as usual”) or in each pairwise comparison (although I’m not sure this will be well-behaved). For example, take all the differences in welfare between the two random variable outcomes corresponding to two options, apply some bounded function of all of these differences, and finally take the expected value.
Consider the following amended thought experiment: (changes in bold)
Walking home one night from a lecture on astrophysics where you learned about the latest research establishing the massive size of the universe, you come across a child drowning in a pond. The kid is kicking and screaming trying to stay above the water. You can see the terror in his eyes and you know that it’s going to get painful when the water starts filling his lungs. You see is mother, off in the distance, screaming and running. Something just tells you she’ll never get over this. It will wreck her marriage and her career. There’s two buttons near you. Pressing either will trigger an event that adds 101000 really good lives to the universe. (The buttons will create the exact same lives and only function once.) The second also causes a life preserver to be tossed to the child. The second button is slightly further from you, and you’d have to strain to reach it. And there’s a real small chance that solipsism is true, in which case your whims matter much more (we’re not near the bounds) and satisfying them will make a much bigger difference to total value. The altruistic thing to do is to not make the additional effort to react the further button, which could be mildly unpleasant, even though it very likely means the kid will die an agonizing death and his mother will mourn for decades.
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.
Consider the following amended thought experiment: (changes in bold)
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.