So I see two possible interpretations of traditional Dutch books:
I disagree, I don’t think it’s a simple binary thing. I don’t think Dutch book arguments in general never apply to recursive things, but it’s more just that the recursion needs to be modelled in some way, and since your OP didn’t do that, I ended up finding the argument confusing.
The standard dutch book arguments would apply to the imp. Why should you be in such a different position from the imp?
I don’t think your argument goes through for the imp, since it never needs to decide its action, and therefore the second part of selling the contract back never comes up?
For example, multiply the contract payoff by 0.001.
Hmm, on further reflection, I had an effect in mind which doesn’t necessarily break your argument, but which increases the degree to which other counterarguments such as AlexMennen’s break your argument. This effect isn’t necessarily solved by multiplying the contract payoff (since decisions aren’t necessarily continuous as a function of utilities), but it may under many circumstances be approximately solved by it. So maybe it doesn’t matter so much, at least until AlexMennen’s points are addressed so I can see where it fits in with that.
Hmm, on further reflection, I had an effect in mind which doesn’t necessarily break your argument, but which increases the degree to which other counterarguments such as AlexMennen’s break your argument. This effect isn’t necessarily solved by multiplying the contract payoff (since decisions aren’t necessarily continuous as a function of utilities), but it may under many circumstances be approximately solved by it. So maybe it doesn’t matter so much, at least until AlexMennen’s points are addressed so I can see where it fits in with that.
I disagree, I don’t think it’s a simple binary thing. I don’t think Dutch book arguments in general never apply to recursive things, but it’s more just that the recursion needs to be modelled in some way, and since your OP didn’t do that, I ended up finding the argument confusing.
But what does that look like? How should it make a difference? (This isn’t a rhetorical question; I would be interested in a positive position. My lack of interest is, significantly, due to a lack of positive positions in this direction.)
I don’t think your argument goes through for the imp, since it never needs to decide its action, and therefore the second part of selling the contract back never comes up?
Ah, true, but the imp will necessarily just make EDT-type predictions anyway. So the imp argument reaches a similar conclusion.
But I’m not claiming the imp argument is very strong in any case, it’s just an intuition pump.
I disagree, I don’t think it’s a simple binary thing. I don’t think Dutch book arguments in general never apply to recursive things, but it’s more just that the recursion needs to be modelled in some way, and since your OP didn’t do that, I ended up finding the argument confusing.
I don’t think your argument goes through for the imp, since it never needs to decide its action, and therefore the second part of selling the contract back never comes up?
Hmm, on further reflection, I had an effect in mind which doesn’t necessarily break your argument, but which increases the degree to which other counterarguments such as AlexMennen’s break your argument. This effect isn’t necessarily solved by multiplying the contract payoff (since decisions aren’t necessarily continuous as a function of utilities), but it may under many circumstances be approximately solved by it. So maybe it doesn’t matter so much, at least until AlexMennen’s points are addressed so I can see where it fits in with that.
Replied.
But what does that look like? How should it make a difference? (This isn’t a rhetorical question; I would be interested in a positive position. My lack of interest is, significantly, due to a lack of positive positions in this direction.)
Ah, true, but the imp will necessarily just make EDT-type predictions anyway. So the imp argument reaches a similar conclusion.
But I’m not claiming the imp argument is very strong in any case, it’s just an intuition pump.