27 ms·

The necktie paradox

19 points by strategy 17y ago

CWuestefeld 17y ago
The explanation confuses Price and Value. The scenario that's laid out for us is that initially the men are unsure which tie is more expensive. If neither of them believes that one tie is more expensive, then neither of them value their own tie above the other. Thus, each man has two outcomes: either he will acquire a second tie of the same value to him, or he will be left with no ties. Ignoring the diminished marginal utility of the second tie over the first, it really is 50/50 -- but to an economist, it's not for the reasons explained.
- emmett 17y ago
  No, the reasons explained are perfectly valid. Another way to think about it is: you are risking losing the more expensive tie (50%) and your potential gain is a more expensive tie (50%). Those are obviously of equal and opposite value.
  - CWuestefeld 17y ago
    The prices of the ties are irrelevant. The only thing that matters is how much each party to the transaction values those ties. Imagine that instead of ties, the other guy has a share of GM stock that he bought two years ago for $40. And I've got my wedding ring, which cost roughly the same. By your logic, getting the GM stock would double my aggregate value, and I should be able to shrug off the loss of my ring. But in the real world, the GM stock has little to no value (due to its depreciation), while the ring has huge value to me (sentimental or not, it's still value). The same things that make that true, also make things that had widely differing purchase prices provide equal value (what economists call utility) to someone.
    - roundsquare 17y ago
      Wow, you are really nitpicking here. For the paradox, its assumed that value = price. Yes, in reality, thats not true, but thats not the point. If you don't like ties as an example, feel free to use the original envelope with money or think of some other item where value = price (or is directly proportional to it). In fact, as long as I can say each person might value the other person's tie more than his own, the paradox holds.
forinti 17y ago
If they really enjoy ties or collect them, they would probably be able to tell if their wives gave them cheap ones. If they don't, their wives probably don't really love them. So, given their suspicion, I'd say the most likely outcome is divorce.
kwamenum86 17y ago
How is misapplied probability theory a paradox?
- jerf 17y ago
  As much as I hate to wave the dictionary around in a comment, a paradox is an apparent contradiction that may not actually be one, and usually isn't. You don't need an actual contradiction to have a "paradox". (I'd argue an actual contradiction is simply a contradiction and not a paradox at all, but the dictionary I consulted disagrees.)
jpwagner 17y ago
not really a paradox. learn to play poker.

19 points by strategy 17y ago

The explanation confuses Price and Value. The scenario that's laid out for us is that initially the men are unsure which tie is more expensive. If neither of them believes that one tie is more expensive, then neither of them value their own tie above the other. Thus, each man has two outcomes: either he will acquire a second tie of the same value to him, or he will be left with no ties. Ignoring the diminished marginal utility of the second tie over the first, it really is 50/50 -- but to an economist, it's not for the reasons explained.

emmett 17y ago
No, the reasons explained are perfectly valid. Another way to think about it is: you are risking losing the more expensive tie (50%) and your potential gain is a more expensive tie (50%). Those are obviously of equal and opposite value.
- CWuestefeld 17y ago
  The prices of the ties are irrelevant. The only thing that matters is how much each party to the transaction values those ties. Imagine that instead of ties, the other guy has a share of GM stock that he bought two years ago for $40. And I've got my wedding ring, which cost roughly the same. By your logic, getting the GM stock would double my aggregate value, and I should be able to shrug off the loss of my ring. But in the real world, the GM stock has little to no value (due to its depreciation), while the ring has huge value to me (sentimental or not, it's still value). The same things that make that true, also make things that had widely differing purchase prices provide equal value (what economists call utility) to someone.
  - roundsquare 17y ago
    Wow, you are really nitpicking here. For the paradox, its assumed that value = price. Yes, in reality, thats not true, but thats not the point. If you don't like ties as an example, feel free to use the original envelope with money or think of some other item where value = price (or is directly proportional to it). In fact, as long as I can say each person might value the other person's tie more than his own, the paradox holds.

forinti 17y ago

If they really enjoy ties or collect them, they would probably be able to tell if their wives gave them cheap ones. If they don't, their wives probably don't really love them. So, given their suspicion, I'd say the most likely outcome is divorce.

kwamenum86 17y ago

How is misapplied probability theory a paradox?

jerf 17y ago
As much as I hate to wave the dictionary around in a comment, a paradox is an apparent contradiction that may not actually be one, and usually isn't. You don't need an actual contradiction to have a "paradox". (I'd argue an actual contradiction is simply a contradiction and not a paradox at all, but the dictionary I consulted disagrees.)

jpwagner 17y ago

not really a paradox. learn to play poker.