Fair! I didn’t work out the details of the particular case, partly for space and partly from my own limited bandwidth in writing the post. I’m actually having more trouble writing it out now that I sit down with it, in part because of the choice-dependent nature of how your values change.
Here’s how we’d normally money-pump you when you have a predictable change in values. Suppose at t1 you value X at $1 and at t2 you predictably will come to value it at $2. Suppose at t1 you have X; since you value it at $1, you’ll trade it to me for $1, so now you’re at +$1; then I wait for t2 to come around, and now you value X more, so I offer to trade you $X for $2, so you happily trade and end up with X - $1. Which is worse than you started.
The trouble is that this seems like precisely a case where you WOULDN’T rationalize, since you traded X away. I think there will still be some way to do it, but haven’t figured it out yet. It’d be interesting if not (it’s MAYBE possible that the money-pump argument for fixed preferences I had in mind presupposed that how they change wouldn’t be sensitive to which trades you make. But I kinda doubt it).
Let me know if you have thoughts! I’ll write back if I have the chance to sit down and figure it out properly.
I think I got it. Right after the person buys X for $1, you offer to buy it off them for $2, but with a delay, so they keep X for another month before the sale goes through. After the month passes, they now value X at $3 so they are willing to pay $3 to buy it back from you, and you end up with +$1.
Nice.
This also matches my earlier observation that the epestemic failure is of not anticipating one’s change in value. If you do anticipate it, you won’t agree to this money pump.
Fair! I didn’t work out the details of the particular case, partly for space and partly from my own limited bandwidth in writing the post. I’m actually having more trouble writing it out now that I sit down with it, in part because of the choice-dependent nature of how your values change.
Here’s how we’d normally money-pump you when you have a predictable change in values. Suppose at t1 you value X at $1 and at t2 you predictably will come to value it at $2. Suppose at t1 you have X; since you value it at $1, you’ll trade it to me for $1, so now you’re at +$1; then I wait for t2 to come around, and now you value X more, so I offer to trade you $X for $2, so you happily trade and end up with X - $1. Which is worse than you started.
The trouble is that this seems like precisely a case where you WOULDN’T rationalize, since you traded X away. I think there will still be some way to do it, but haven’t figured it out yet. It’d be interesting if not (it’s MAYBE possible that the money-pump argument for fixed preferences I had in mind presupposed that how they change wouldn’t be sensitive to which trades you make. But I kinda doubt it).
Let me know if you have thoughts! I’ll write back if I have the chance to sit down and figure it out properly.
I think I got it. Right after the person buys X for $1, you offer to buy it off them for $2, but with a delay, so they keep X for another month before the sale goes through. After the month passes, they now value X at $3 so they are willing to pay $3 to buy it back from you, and you end up with +$1.
Nice. This also matches my earlier observation that the epestemic failure is of not anticipating one’s change in value. If you do anticipate it, you won’t agree to this money pump.
Yeah, that looks right! Nice. Thanks!