I notice I am confused. How do you violate an axiom (completeness) without behaving in a way that violates completeness? I don’t think you need an internal representation.
Elaborating more, I am not sure how you even display a behavior that violates completeness. If you’re given a choice between only universe-histories a and b, and your preferences are imcomplete over them, what do you do? As soon as you reliably act to choose one over the other, for any such pair, you have algorithmically-revealed complete preferences.
If you don’t reliably choose one over the other, what do you do then?
Choose randomly? But then I’d guess you are again Dutch-bookable. And according to which distribution?
Your choice is undefined? That seems both kinda bad and also Dutch-bookable to me tbh. Alwo don’t see the difference between this and random choice (shodt of going up in flames, which would constigute a third, hitherto unassumed option).
Go away/refuse the trade &c? But this is denying the premise! You only have universe-histories a and b tp choose between! I think what happens with humans is that they are often incomplete over very low-ranking worlds and are instead searching for policies to find high-ranking worlds while not choosing. I think incomplwteness might be fine if there are two options you can guarantee to avoid, but with adversarial dynamics that becomes more and more difficult.
I notice I am confused. How do you violate an axiom (completeness) without behaving in a way that violates completeness? I don’t think you need an internal representation.
Elaborating more, I am not sure how you even display a behavior that violates completeness. If you’re given a choice between only universe-histories a and b, and your preferences are imcomplete over them, what do you do? As soon as you reliably act to choose one over the other, for any such pair, you have algorithmically-revealed complete preferences.
If you don’t reliably choose one over the other, what do you do then?
Choose randomly? But then I’d guess you are again Dutch-bookable. And according to which distribution?
Your choice is undefined? That seems both kinda bad and also Dutch-bookable to me tbh. Alwo don’t see the difference between this and random choice (shodt of going up in flames, which would constigute a third, hitherto unassumed option).
Go away/refuse the trade &c? But this is denying the premise! You only have universe-histories a and b tp choose between! I think what happens with humans is that they are often incomplete over very low-ranking worlds and are instead searching for policies to find high-ranking worlds while not choosing. I think incomplwteness might be fine if there are two options you can guarantee to avoid, but with adversarial dynamics that becomes more and more difficult.
If you define your utility function over histories, then every behaviour is maximising an expected utility function no?
Even behaviour that is money pumped?
I mean you can’t money pump any preference over histories anyway without time travel.
The Dutchbook arguments apply when your utility function is defined over your current state with respect to some resource?
I feel like once you define utility function over histories, you lose the force of the coherence arguments?
What would it look like to not behave as if maximising an expected utility function for a utility function defined over histories.