[extropy-chat] Mature rationality

[The Avantguardian]

--- Eliezer Yudkowsky <sentience at pobox.com> wrote:
> 
> There is no God.  Thank you for asking.  Now get on
> with your lives, 
> knowing that you alone are in charge.
> 

      Allow me to play the Devil's advocate, Eliezer.
Actually I will be representing God too and many of
the other denizens of the spirit world so consider
this a class action suit. So if you could, as judge
and jury of the court of Bayes, indulge me by solving
a socratic homework problem indirectly pertaining to
the issue at hand.

       The problem is simple lets say you and I decide
to play a very simple game. the rules are:

1. You and I stake a dollar each on the outcome of the
draw of a single card from a deck (normal 52 cards no
jokers).
2. I get to draw the card and if it comes up an ace of
spades, I win and I get your dollar.
3. If it come up as any other card, you get a dollar.
4. We only play it once- that is to say there is only
one draw from the deck.

     Next, I send you a picture in an email showing a
deck of cards and next to it is the ace of spades. I
demand my dollar. Your problem is this:

      Use Bayes Theorem to determine:
a. The probability that I cheated.
b. The probabilities that an ace of spades would show
up if I was cheating.
c. The probability of an ace of spades if I was not.
d. Should you send me your dollar.

      Please exposite this by showing the math.
Listing your probabilities and/or distributions
including posteriors, assumed priors- even if they are
assumed as they would have to be since you don't know
me well enough to know how honest I am.







=====
The Avantguardian 


"He stands like some sort of pagan god or deposed tyrant. Staring out over the city he's sworn to . . .to stare out over and it's evident just by looking at him that he's got some pretty heavy things on his mind."


		
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