[extropy-chat] Re: monty hall paradox again: reds and green gorfs

[Eliezer Yudkowsky]

Spike wrote:
> 
> What I want to understand is why women seem to have an 
> uncanny intuition that sticking is at least equivalent 
> to swapping, *even without actually doing a mathematical 
> model*.  What puzzles me even more is the reasoning of
> the gay mathematician, who had no problem with the idea 
> that opening one envelope somehow causes the other
> one to become "probably the smaller one."  How?  I
> asked.  "It doesn't matter how," he calmly replied.
> "Physicists worry about that sort of thing, the crass
> impericists.  Mathematicians do not."
> 
> I must have been wearing a stunned or puzzled countenance.
> "Well," he continued, "It must do it, right?  There
> cannot be any inherent profit to swapping.  You can
> write a quick sim to prove it.  The probability that
> the other envelope is larger must go to 1/3, it doesn't
> matter how it gets there."

Your mathematician friend is flat wrong, and needs to study Bayesian 
probability theory.

-- 
Eliezer S. Yudkowsky                          http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence