It’s true that if I knew my total wealth exactly, then finding out that what I thought was a $5 was really a $1 would only tell me something about how much of that wealth was in my wallet and how much wasn’t. But in fact I don’t know my wealth to within anything like $4. Given the state of my knowledge, if what I thought was a $5 turned out to be a $1, it really does mean that I was (paradoxically happily) finding out that I was $4 poorer than I thought I was. Doesn’t it?
You could think that the probability of a given bill being $1 or $5 was largely independent with respect to total [delete: “bank account”] wealth differences in the region of $4, in which case the bill difference provided you with almost no bad news about total wealth, but did provide you with good news about an available gain from trade.
It’s a minor point and probably not worth much more effort, but I’m still confused. If I’m ignorant enough about my total wealth that a finding that a bill turns out to be a $1 instead of a $5 doesn’t cause me change my best estimate of my non-wallet wealth, then why isn’t it $4 worth of bad news? I don’t see the flaw in that reasoning.
Oops, the above should be, “total wealth differences in the region of $4”, not “total bank account wealth differences”. Hm. This is an interesting problem in approximate rationality—if your estimate of “bank account + wallet” and “bank account” is pretty much the same total number, and you learn how much money is in your wallet, what have you learned?
if your estimate of “bank account + wallet” and “bank account” is pretty much the same total number, and you learn how much money is in your wallet, what have you learned?
Hopefully that your bank balance is such that whatever you carry in your wallet pales into insignificance.
It seems to me like you’ve learned only how much what’s actually in your wallet deviated from your best guess about what was in there. If non-wallet wealth effects can be safely ignored, then learning of an $X dollar deviation can be taken as a shock of that size to your total wealth.
Given the state of my knowledge, if what I thought was a $5 turned out to be a $1, it really does mean that I was (paradoxically happily) finding out that I was $4 poorer than I thought I was. Doesn’t it?
Eliezer and 10phil,
It’s true that if I knew my total wealth exactly, then finding out that what I thought was a $5 was really a $1 would only tell me something about how much of that wealth was in my wallet and how much wasn’t. But in fact I don’t know my wealth to within anything like $4. Given the state of my knowledge, if what I thought was a $5 turned out to be a $1, it really does mean that I was (paradoxically happily) finding out that I was $4 poorer than I thought I was. Doesn’t it?
You could think that the probability of a given bill being $1 or $5 was largely independent with respect to total [delete: “bank account”] wealth differences in the region of $4, in which case the bill difference provided you with almost no bad news about total wealth, but did provide you with good news about an available gain from trade.
It’s a minor point and probably not worth much more effort, but I’m still confused. If I’m ignorant enough about my total wealth that a finding that a bill turns out to be a $1 instead of a $5 doesn’t cause me change my best estimate of my non-wallet wealth, then why isn’t it $4 worth of bad news? I don’t see the flaw in that reasoning.
Oops, the above should be, “total wealth differences in the region of $4”, not “total bank account wealth differences”. Hm. This is an interesting problem in approximate rationality—if your estimate of “bank account + wallet” and “bank account” is pretty much the same total number, and you learn how much money is in your wallet, what have you learned?
Hopefully that your bank balance is such that whatever you carry in your wallet pales into insignificance.
It seems to me like you’ve learned only how much what’s actually in your wallet deviated from your best guess about what was in there. If non-wallet wealth effects can be safely ignored, then learning of an $X dollar deviation can be taken as a shock of that size to your total wealth.
*Omega darkly shook his head*
I don’t get it.
No meaning intended.