Next weekend at EAGx Australia I'll be doing a live 80,000 Hours Podcast recording with philosopher Alan Hájek, who has spent his life studying the nature of probability, counterfactuals, Bayesianism, expected value and more.
What should I ask him?
He's he author of among other papers:
- Waging war on Pascal's wager
- The reference class problem is your problem too
- Interpretations of probability
- Arguments for—or against—Probabilism?
- Most counterfactuals are false
- The nature of uncertainty
Topics he'd likely be able to comment on include:
- problems with orthodox expected utility theory, especially involving infinite and undefined utilities or expectations
- risk aversion, whether it’s justified, and how best to spell it out
- how to set base rate priors for unknown quantities
- his heuristics for doing good philosophy (about which he has lots to say) / how to spot bad philosophical arguments
See more about Professor Hájek here: https://philosophy.cass.anu.edu.au/people/professor-alan-h-jek
Harsanyi's theorem doesn't start from any axiom I would call "separability". See this post for non-technical summary. It also doesn't imply separability in different number cases. For example, average utilitarianism is consistent with Harsanyi's theorem, but the average welfare level of unaffected individuals matters when choosing between options with different numbers of individuals. Under average utilitarianism, it's good to create an individual with higher than the average welfare without them and bad to create individuals with lower than the average welfare without them, assuming no one else is affected, but the average welfare without them is exactly the average welfare of the unaffected.
One axiom (quoting from the summary post) seems close to separability:
This axiom rules out preferences for and against ex post equality, which is often non-separable. In particular, it means you have to be indifferent between these two options, which should conflict with your intuition about a backup planet:
Prioritarianism, just ∑ni=1f(ui) (with the ui matching the utilities from the vNM theorem for each individual), satisfies separability but not this other axiom. Average utilitarianism and other functions of the form an×∑ni=1ui satisfy this other axiom (in fixed population cases) but not separability in different population size cases.