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The strange non-transitivity of random variables (2014)

26 points| throwaway000002 | 10 years ago |andreasleiser.com | reply

17 comments

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[+] brudgers|10 years ago|reply
[+] lifeformed|10 years ago|reply
I like the stories about Warren Buffett's fascination with the dice:

> Buffett once attempted to win a game of dice with Bill Gates using nontransitive dice. "Buffett suggested that each of them choose one of the dice, then discard the other two. They would bet on who would roll the highest number most often. Buffett offered to let Gates pick his die first. This suggestion instantly aroused Gates's curiosity. He asked to examine the dice, after which he demanded that Buffett choose first."[1]

> In 2010, Wall Street Journal magazine quoted Sharon Osberg, Buffett's bridge partner, saying that when she first visited his office 20 years earlier, he tricked her into playing a game with nontransitive dice that could not be won and "thought it was hilarious".[2]

[+] mtdewcmu|10 years ago|reply
That is neat and a lot easier to understand than the original link. All the notation made my eyes glaze over.
[+] danharaj|10 years ago|reply
> Examples of binary relations are binary operations (like +,–,⋅,/) on N,Z,Q,R,C,Rn, … etc. (where defined), since functions are special cases of relations, or, the order relations <,≤,>,≥ on R, for instance.

A function of two variables is a ternary relation, not a binary relation. /pedant

[+] x3n0ph3n3|10 years ago|reply
Last I checked, binary implies 2 and ternary implies 3. There are 2 inputs, therefore it's a binary relation or operator.
[+] quietplatypus|10 years ago|reply
this isnt paradoxical at all, it's just you are looking at only 2 dice at a time not the full joint probability of a < b < c. i can come up with similarly retarded "paradoxical conclusions" if i took enough samples of different tiny slices of things.

dude is just trying to sound smart with yet another "counterintuitive probability post"

[+] jeffsco|10 years ago|reply
Imagine a tournament to choose the best tennis player. If you imagine these dice as a simple model of a tennis player, there can be no best tennis player. So tennis tournaments make no sense. This is paradoxical if you believe in tennis rankings.