**Next message:**Eliezer S. Yudkowsky: "Re: Iconoclasm"**Previous message:**Damien Broderick: "Re: Iconoclasm"**In reply to:**Spike Jones: "Re: I strongly disagree with Lee's answer"**Next in thread:**Lee Corbin: "Primes and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Spike Jones wrote:

*>
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*> "Eliezer S. Yudkowsky" wrote:
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*>
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*> > For example, suppose that you're on a game show called "ExtroQuiz" and
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*> > there are three doors: A, B, and C. One door has a prize behind it. You
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*> > pick door C. The game show host opens up door A, and shows you that it's
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*> > empty. What is the probability that the prize is behind door B? Answer:
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*> > 0%. Why? Because the game show host *knows* the standard answer to this
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*> > riddle, *knows* that most Extropians will switch to B, and he opens A *if
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*> > and only if* the prize is actually behind C.
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*>
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*> Another way to illustrate why it is best to switch doors after Monte
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*> opens one is by restating the game thus: Monte offers you one of the
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*> three doors, but before you choose, he writes a letter on a card and
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*> places it face down. This is the letter of a door that he knows has a
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*> goat behind it. He says that after you choose a door, which might be
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*> the one he wrote, he will reveal the door written on the card. That
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*> illustration may help some to understand why its best to switch, assuming
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*> one prize and two zonks.
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In this instance, where Monte's actions are fixed, *and the door he

reveals is predetermined*, the problem is equivalent to the

lightning-strike riddle that Lee asked. The card he turns over may have

'C' written on it. In this case, if he reveals 'A', there is no reason to

switch.

*> Eliezer's contention is incorrect methinks. If you choose C and it is a
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*> zonk, Monte must open A, for he knows B is the prize. If you choose
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*> C and it has the prize, Monte can open either A or B, and then you
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*> switch and get zonked. So assuming Mr. Hall wishes to zonk you,
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*> he can do so only if you originally chose the prize door, 1/3 chance.
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Who says that Monte *must* open a door? If I choose C and it's a failure,

Monte can simply not open any doors at all. He only has a logical

motivation to open a door, possibly causing a change in my actions, if he

wants me to switch; he only wants me to switch if C actually has the

prize. Of course, if Monte realizes that I know this, and I have

correctly picked C, he will fake me out by showing me B. This is why

Bayesian reasoners should never play zero-sum-games with each other.

-- -- -- -- --

Eliezer S. Yudkowsky http://singinst.org/

Research Fellow, Singularity Institute for Artificial Intelligence

**Next message:**Eliezer S. Yudkowsky: "Re: Iconoclasm"**Previous message:**Damien Broderick: "Re: Iconoclasm"**In reply to:**Spike Jones: "Re: I strongly disagree with Lee's answer"**Next in thread:**Lee Corbin: "Primes and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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