Notes on My Conversation With Aaron
Twas a fun chat--here are our remaining disagreements and agreements
Having completed a second chat with Aaron Bergman over our agreements, we now agree on the following claims.
1 the vnm formula implies that we have a cardinal utility function over ranges of events for which the axioms hold
2 they don't over all possible ranges of events (I'd say only with literally infinite pain, Aaron would say differently, holding that finite but immense pain, say torture, is infinitely more undesirable than a papercut.) So I’d say that there’s no probability of infinite torture that can be traded off against a papercut, but there is for any finite torture, Aaron would deny that this would hold for any finite torture.
3 The vnm formula implies that where the axioms hold there is a fact of the matter about x being n times worse than y iff by x being n times worse than y we mean that we should be indifferent between a 1/n chance of x and certainty of y.
4 This semantic thesis about what most people would endorse upon reflection is correct, namely, most people would endorse upon reflection that x is n times worse than y iff we should be indifferent between a 1/n chance of x and certainty of y. We have slight disagreements about whether that is a good account of the meanings of words.