The Alice and Bob example isn’t a good argument against the independence axiom. The combined agent can be represented using a fact-conditional utility function. Include the event “get job offer” in the outcome space, so that the combined utility function is a function of that fact.
This is a far more natural way to combine agents. We can avoid the ontologically weird mixing of probabilities and preference implied by having preference (pC+(1−p)B≺pC+(1−p)A) and also C≺B. Like… what does a geometrically rational agent actually care about, and why does it’s preferences change depending on its own beliefs and priors? A fact-conditional utility function is ontologically cleaner. Agents care about events in the world (potentially in different ways across branches of possibility, but it’s still fundamentally caring about events).
This removes all the appeal of geometric rationality for me. The remaining intuitive appeal comes from humans having preferences that are logarithmic in most resources, which is more simply represented as one utility function rather than as a geometric average of many.
The Alice and Bob example isn’t a good argument against the independence axiom. The combined agent can be represented using a fact-conditional utility function. Include the event “get job offer” in the outcome space, so that the combined utility function is a function of that fact.
E.g.
Bob {A: 0, B: 0.5, C: 1}
Alice {A: 0.3, B: 0, C: 0}
Should merge to become
AliceBob {Ao: 0, Bo: 0.5, Co: 1, A¬o: 0, B¬o: 0, C¬o: 0.3}, where o=”get job offer”.
This is a far more natural way to combine agents. We can avoid the ontologically weird mixing of probabilities and preference implied by having preference (pC+(1−p)B≺pC+(1−p)A) and also C≺B. Like… what does a geometrically rational agent actually care about, and why does it’s preferences change depending on its own beliefs and priors? A fact-conditional utility function is ontologically cleaner. Agents care about events in the world (potentially in different ways across branches of possibility, but it’s still fundamentally caring about events).
This removes all the appeal of geometric rationality for me. The remaining intuitive appeal comes from humans having preferences that are logarithmic in most resources, which is more simply represented as one utility function rather than as a geometric average of many.