In EJT’s post, I remember that the main concrete point was that being stubborn, in this sense:
if I previously turned down some option X, I will not choose any option that I strictly disprefer to X
To my understanding that was a good counter to the idea that anything that is not a utility maximisation is vulnerable to money pumps in a specific kind of games.
But that is restricted to “decision tree” games in which in every turn but the first you have an “active outcome” which you know you can keep until the end if you wish. Every turn you can decide to change that active outcome or to keep it. These games are interesting to discuss dutch book vulnerability but they are still quite specific. Most games are not like that.
On a related note:
a non-dominated strategy for a preference tree compact enough compared to the world it applies to will be approximately a utility maximizer
I think I didn’t understand what you mean by “preference tree” here. Is it just a partial order relation (preference) on outcomes?
If you mean “for a case in which the complexity of the preference ordering is small compared to that of the rest of the game” , then I disagree.
The counterexample could certainly scale to high complexity of the rules without any change to the (very simple) preference ordering.
The closest I could come to your statement in my vocabulary above is:
For some value k, if the ratio “complexity of the outcome preference” / “complexity of the total game” is inferior to k then any nondominated strategy is (approximately) a utility maximisation.
To my understanding that was a good counter to the idea that anything that is not a utility maximisation is vulnerable to money pumps in a specific kind of games. But that is restricted to “decision tree” games in which in every turn but the first you have an “active outcome” which you know you can keep until the end if you wish. Every turn you can decide to change that active outcome or to keep it. These games are interesting to discuss dutch book vulnerability but they are still quite specific. Most games are not like that.
On a related note:
I think I didn’t understand what you mean by “preference tree” here. Is it just a partial order relation (preference) on outcomes? If you mean “for a case in which the complexity of the preference ordering is small compared to that of the rest of the game” , then I disagree. The counterexample could certainly scale to high complexity of the rules without any change to the (very simple) preference ordering.
The closest I could come to your statement in my vocabulary above is:
Is this faithful enough?
Yes, I mean that.
Yup.