This, again, seems plausible if the payoff is made sufficiently small.
How do you make the payoff small?
This is actually very similar to traditional Dutch-book arguments, which treat the bets as totally independent of everything.
Isn’t your Dutch-book argument more recursive than standard ones? Your contract only pays out if you act, so the value of the dutch book causally depends on the action you choose.
Isn’t your Dutch-book argument more recursive than standard ones? Your contract only pays out if you act, so the value of the dutch book causally depends on the action you choose.
Sure, do you think that’s a concern? I was noting the similarity in this particular respect (pretending that bets are independent of everything), not in all respects.
Note, in particular, that traditional dutch book arguments make no explicit assumption one way or the other about whether the propositions have to do with actions under the agent’s control. So I see two possible interpretations of traditional Dutch books:
They apply to “recursive” stuff, such as things you have some influence over. For example, I can bet on a presidential election, even though I can also vote in a presidential election. In this case, what we have here is not weirder. This is the position I prefer.
They can’t apply to “recursive” stuff. In this case, presumably we don’t think standard probability theory applies to stuff we have influence over. This could be a respectable position, and I’ve seen it discussed. However, I don’t buy it. I’ve seen philosophers answer this kind of think with the following argument: what if you had a little imp on your shoulder, who didn’t influence you in any way but who watched you and formed predictions? The imp could have probabilistic beliefs about your actions. The standard dutch book arguments would apply to the imp. Why should you be in such a different position from the imp?
How do you make the payoff small?
For example, multiply the contract payoff by 0.001.
Think of it this way. Making bets about your actions (or things influenced by your actions) can change your behavior. But if you keep the bets small enough, then you shouldn’t change your behavior; the bets are less important than other issues. (Unless two actions are exactly tied, in terms of other issues.)
I will concede that this isn’t 100% convincing. Perhaps different laws of probability should apply to actions we can influence. OTOH, I’m not sure what laws those would be.
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.
How do you make the payoff small?
Isn’t your Dutch-book argument more recursive than standard ones? Your contract only pays out if you act, so the value of the dutch book causally depends on the action you choose.
Sure, do you think that’s a concern? I was noting the similarity in this particular respect (pretending that bets are independent of everything), not in all respects.
Note, in particular, that traditional dutch book arguments make no explicit assumption one way or the other about whether the propositions have to do with actions under the agent’s control. So I see two possible interpretations of traditional Dutch books:
They apply to “recursive” stuff, such as things you have some influence over. For example, I can bet on a presidential election, even though I can also vote in a presidential election. In this case, what we have here is not weirder. This is the position I prefer.
They can’t apply to “recursive” stuff. In this case, presumably we don’t think standard probability theory applies to stuff we have influence over. This could be a respectable position, and I’ve seen it discussed. However, I don’t buy it. I’ve seen philosophers answer this kind of think with the following argument: what if you had a little imp on your shoulder, who didn’t influence you in any way but who watched you and formed predictions? The imp could have probabilistic beliefs about your actions. The standard dutch book arguments would apply to the imp. Why should you be in such a different position from the imp?
For example, multiply the contract payoff by 0.001.
Think of it this way. Making bets about your actions (or things influenced by your actions) can change your behavior. But if you keep the bets small enough, then you shouldn’t change your behavior; the bets are less important than other issues. (Unless two actions are exactly tied, in terms of other issues.)
I will concede that this isn’t 100% convincing. Perhaps different laws of probability should apply to actions we can influence. OTOH, I’m not sure what laws those would be.
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.