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.
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.