I had a long-ish conversation with John Wentworth and want to make it known that I could probably write up any of the following distillations if I invested lots of time into them (about a day (edit: 3 days seems more likely) of my time and an hour of John’s). Reply if you’re really interested in one of them.
What is the type signature of a utility function?
Utility functions must be defined with respect to an external world-model
Infinite money-pumps are not required for incoherence, and not likely in practice. The actual incoherent behavior is that an agent could get to states A_1 or A_2, identical except that A_1 has more money, and chooses A_2. Implications.
Why VNM is not really a coherence theorem. Other coherence theorems relating to EU maximization simultaneously derive Bayesian probabilities and utilities. VNM requires an external frequentist notion of probabilities.
1 and 2 are the same writeup, I think. Utility function maps contingent future universe-state to a preference ranking (ordinal or cardinal, depending). This requires a world-model because the mentally-projected future states under consideration are always and only results of one’s models.
If you/he are just saying that money pumps are just one way to show incoherence, but not the only way, I’d enjoy a writeup of other ways.
I’d also enjoy a writeup of #4 - I’m curious if it’s just a directionality argument (VNM assumes coherence, rather than being about it), or if there’s more subtle differences.
I had a long-ish conversation with John Wentworth and want to make it known that I could probably write up any of the following distillations if I invested lots of time into them (about a day (edit: 3 days seems more likely) of my time and an hour of John’s). Reply if you’re really interested in one of them.
What is the type signature of a utility function?
Utility functions must be defined with respect to an external world-model
Infinite money-pumps are not required for incoherence, and not likely in practice. The actual incoherent behavior is that an agent could get to states A_1 or A_2, identical except that A_1 has more money, and chooses A_2. Implications.
Why VNM is not really a coherence theorem. Other coherence theorems relating to EU maximization simultaneously derive Bayesian probabilities and utilities. VNM requires an external frequentist notion of probabilities.
I wish we had polling. Anyway if you made four individual comments, one for each, I’d weak upvote the first and last.
1 and 2 are the same writeup, I think. Utility function maps contingent future universe-state to a preference ranking (ordinal or cardinal, depending). This requires a world-model because the mentally-projected future states under consideration are always and only results of one’s models.
If you/he are just saying that money pumps are just one way to show incoherence, but not the only way, I’d enjoy a writeup of other ways.
I’d also enjoy a writeup of #4 - I’m curious if it’s just a directionality argument (VNM assumes coherence, rather than being about it), or if there’s more subtle differences.
Interested in 3.