The other day I went to get some productivity-enhancement M&Ms from the candy machine at work. When I opened my wallet, I didn't immediately see a $1 bill. Then I looked some more and I found one, and I was happy! But of course that doesn't make any sense. If that bill hadn't been a $1, then it would have had to be a $5 or more, with an expected value of $5+, which is an amount that I certainly would not have paid for a bag of M&Ms, most excellent though they may be. This means that I preferred a bag of M&Ms to $1 (that's why I went to the candy machine in the first place), $1 to $5+ (I was happy when the bill turned out to be a $1), and $5+ to a bag of M&Ms (I wouldn't have bought them at that price). Not too surprising I guess, but still kind of weird.

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If hypothetically you went to the machine and your wallet was unexpectedly empty, and you noticed the corner of a bill poking out from under the machine, would you rather it be a $1 bill (and you get to buy M&Ms) or it be a $5 bill (and you don't get M&Ms)?

"Would you rather it be a $1 bill (and you get to buy M&Ms) or it be a $5 bill (and you don't get M&Ms)?"

Depends on the person and how they value money/M&Ms.

I do feel confident saying that ANY person in that situation would be less happy finding that $5 then latter finding $5 under there couch while vacuuming.

Well put.

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:

  1. Do I get to eat M&Ms or not?
  2. 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?

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?

*Omega darkly shook his head*

I don't get it.

No meaning intended.

Okay, I've got it. You're a selflessly devoted altruist, and you know that money in your hands doesn't matter any more than money elsewhere - but with a $1 bill, you could generate gains from trade and thereby make the whole world a slightly better place!

Nice. Steven Landsburg once wrote something similar (I think in The Armchair Economist) about how it is wasteful to bend down to pick up a $50 bill off the sidewalk, because the money is a pure transfer and the effort of bending down is a pure social loss.

The problem is that I pretty clearly don't value a random person having the $4 as much as me having it, as evidenced by the fact that a lot of my income I keep, and the part of it that I give away (which is pretty substantial but the Peter Singer argument is always working on me that it should be higher) I give away to really poor people abroad, not to random Americans.

You wanted M&Ms. If you had not had a $1 bill you would not have gotten them.

Right. You're motivated by the prospect of making a good exchange ($1 for some M&Ms) not having a high net worth ($4 more happening to be in your pocket).

I've done the same thing!

Perhaps you were assuming that your net wealth was a certain fixed amount, and that if the bill had been a $5 instead of a $1, it would have meant that there was $4 less at home or in the bank.

In that case, you're rooting only for having the right change on you, rather than having less money overall.

Since most people get things they want when they spend money, the information you got from looking in your wallet is about configuration, not amount. You were happy because you had correct change, not because you had a $1 bill instead of a $5 bill.

The M&Ms are worth $5 to you at that instant, but you would feel bad spending it.

Your emotions are more wired to produce actions that benefit you, not necessarily to reflect absolute state of utility in the form of happiness. You would not desire to trade $5 to receive $1, your wealth is not affected in any way by what you discover and your instrumental goal was in finding a $1 bill. Nothing is amiss.

Don't your vending machines over there give change? (You can't generally put notes(/bills) in ours over here, but they do generally give change for your coins.)

They take $1 bills but usually nothing larger than that. Where are you?

The vending machines in Melbourne seem to accept bills up to $20, sometimes $10, giving change. Older models are limited to coins, usually excluding $0.05 ones.

Does this change comprise of a mixture of bills and coins, or coins alone? One handicap in the States is that dollar coins are not widely circulated.

Edit: A datum, for example, is that I recall only one vending machine of the many (hundreds? possibly only dozens) I've encountered in the DC area accepting fives and offering change in dollar coins, and that (a) doesn't always and (b) is selling ice cream treats for US$1.75 each.

Does this change comprise of a mixture of bills and coins, or coins alone?

I have never used a higher denomination bill than $5 (our smallest note). However, the dispensers do not usually have a mechanism for dispensing notes at all. I recall seeing warning signs specifying a limit to how much change will be given (up to $10 so probably $2 coins) but this may have been at a machine dispensing transportation tickets rather than candy.

ETA: Do you guys over there seriously still not have notes that are colour coded? (Also, my friendly spell checker just picked up that I was trying to spell colour as 'color' which I found rather ironic. A pox on popular programming languages.)


Did you have few enough bills in your wallet that you could immediately and accurately apprehend how many there were? If not, then there were enough that you didn't know how many there were, and that $1 was one that might as well have not been there according to your initial coarse perception.

I think this works if the $1 represents an extra bill that you didn't know was in there, but not if you looked more closely at a specific bill and were happy to realize that it was a $1.

How about this, then: if I don't have any ones in my purse, this is because I have spent them on things already (since in the past, my purse has contained singles, and that is the typical method by which they depart). Assuming I really want the M&Ms, I might resent the fact that I made other spending choices in the past that caused the lack of ones. Finding the one is news that I did not make (all of) those resented choices.

It seems to me that the problem is self-contained, and doesn't depend on past purchases. Am I missing something?

Hah. Your software for assessing "the proper prices of things" is separate from your preferences. In a nearby hypothetical world where $5 were the normal price for M&Ms, I think you would've bought them at that price. Because in our world, when the universe took $4 away from you as a fait accompli but allowed you to enjoy the M&Ms for $1 in return, you liked it! In effect, you were deprived of the chance to notice the "unfairly high" price of $5, so the blame/propriety circuit was stopped from interfering with your actual preference =) If the sole bill in your wallet had been a $100 but then "luckily" morphed into $1, I guess you wouldn't have been as happy!


The circumstances you describe are pretty weird. When I search my wallet for a single, I don't think, "There are twelve bills in my wallet. I hope one of them is a single." I think, "That a single? Nope. That one? Nope. That one? There we go!" The question isn't, "What's the value of each bill in my possession," but, "Do I have a single in my possession?" Discovering that I have a single simply does not entail discovering that I don't have a bill of greater value.

But I think you may be missing the meaning of that happiness you experienced. Your immediate goal was buying M&M's. You thought you couldn't accomplish this. Then, you found out you could, and this made you happy. That happiness was not comparative; you simply experienced a kick of satisfaction because something you hoped for turned out to be true. Your happiness is not an indicator of your general preferences, it is a result of your hope being fulfilled. Concluding that experience indicates you preferred having $1 to having $5 may be inappropriate.