On the contrary—if the bill had been $5 instead of $1, then your bank account would have had $4 less in it, and you couldn’t have generated the gains from trade.
Paradox cleverly resolved!
(Actually, I suspect the real answer is that you have a “warm” preference for M&Ms over $1 and a “cold” preference for $5 over $1. System 1 vs. System 2.)
I think the answer in the parenthetical is probably closer to the mark. But it’s still the case that even in the “warm” moment I wouldn’t have paid $5+ for a bag of M&Ms, so it doesn’t totally work.
Your happiness was strictly a result of answering YES to question 1, and it was a System 1 judgment that happened before you had time to think about question 2. The subsequent realization that YES on #1 implies having $4 less than NO (via question 2) is a System 2 judgment, so it didn’t occur until (much) after the happiness had occurred, and because it is System 2 rather than System 1, the feeling that it would have been better if it were a $5 doesn’t feel anywhere near as strong as the feeling that you can get M&Ms.
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?
On the contrary—if the bill had been $5 instead of $1, then your bank account would have had $4 less in it, and you couldn’t have generated the gains from trade.
Paradox cleverly resolved!
(Actually, I suspect the real answer is that you have a “warm” preference for M&Ms over $1 and a “cold” preference for $5 over $1. System 1 vs. System 2.)
I think the answer in the parenthetical is probably closer to the mark. But it’s still the case that even in the “warm” moment I wouldn’t have paid $5+ for a bag of M&Ms, so it doesn’t totally work.
I think there are two questions being resolved:
Do I get to eat M&Ms or not?
Is the bill a $1 or something higher?
Your happiness was strictly a result of answering YES to question 1, and it was a System 1 judgment that happened before you had time to think about question 2. The subsequent realization that YES on #1 implies having $4 less than NO (via question 2) is a System 2 judgment, so it didn’t occur until (much) after the happiness had occurred, and because it is System 2 rather than System 1, the feeling that it would have been better if it were a $5 doesn’t feel anywhere near as strong as the feeling that you can get M&Ms.
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.