Talk:Necktie paradox

From Wikipedia, the free encyclopedia

As the user who submitted the article for deletion had no idea as to the paradoxical portion of the puzzle... there is none. It's a form of misrepresentation, because both men are assuming the wrong thing and making a wager on it. It's simply a form of gambling, NOT A PARADOX. Ikki the Fox Breeder 03:31, 15 December 2006 (UTC)

I totally disagree. ALL paradoxes by their very nature involve a certan amount of misrepresentation and that is what makes them often a paradox. If you care to look at many of the other examples of paradoxes in wikipedia, you will see they are not significantly different.

I also take offence at "as the user .. had no idea .." perhaps you would like to explain that to the mathematicians who describe the necktie paradox in the book "mathematical puzzles and diversions". They clearly see it fit as a paradox. PS I have a university degree in mathematics, so I should think I have SOME idea as to what constitutes a mathematical paradox. xs935

Can this "paradox" be referenced to a reliable source? If it cannot, it should go as WP:OR. L'omo del batocio (talk) 15:35, 20 January 2008 (UTC)

[edit] Clarification

I don't believe the paradox was correctly stated:

The first man considers this : The probability of me winning or losing is 50:50. If I lose my necktie, then I lose the value of the cheaper necktie. If I win, then I win the value of a more expensive necktie. By winning, I more than double the value of my neckties. In other words, I can bet x and have a 50% chance of winning more than x. Therefore it is definitely in my interest to make the wager.

Specifically, the statement "If I lose my necktie, then I lose the value of the cheaper necktie" was incorrect. Also, the statement "By winning, I more than double the value of my neckties" is only true if he currently owns excactly one necktie, and in any case it is irrelevant to the paradox.

I rewrote the third paragraph thus:

The first man considers this: The probability of me winning or losing is 50:50. If I lose, then I lose the value of my necktie. If I win, then I win more than the value of my necktie. In other words, I can bet x and have a 50% chance of winning more than x. Therefore it is definitely in my interest to make the wager.

Nasorenga 14:32, 1 February 2007 (UTC)

I fail to see the paradox here. Apparently it is that "it is in both men's interest to wager their neckties!" but isn't it in both men's interest to wager their ties? I mean, isn't that how every standard wager works -- both parties anty up and only one wins the combined booty? 71.117.109.47 07:07, 4 April 2007 (UTC)

The paradox lies in the fact that it is assumed that there is a 50% chance that your tie is worth more, meaning you should be indifferent to the wager (50% you have more expensive tie vs. 50% you have less expensive tie). However, due to the expectation calcualation (the heart of the paradox), you always want to wager (as does your opponent) To your comment, in most "real-life" wagers, the wager comes about due to differing expected values (sort of like the probability an event will occur, only with payoffs factored in).

In retrospect, that may be the answer to the paradox. From our perspective, we see a 50/50 game, whereas they see the expected value from their perspective. However, we don't know any more than them, so I don't know why this would matter Akshayaj 18:46, 17 July 2007 (UTC)

[edit] Related to exchange paradox?

This seems to be related to the envelope (exchange) paradox, probably worth a mention and would further clarify the description. Petersburg 21:16, 12 August 2007 (UTC)