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Aristotle's Conference

T

TheGoldenBlazer

#1
Suppose Aristotle was holding a conference with the 100 most rational philosophers in all of Greece. He explained, ?Each of you will guess a number no more than 100, whoever?s guess is the closest to 2/3 of the average of all of the guesses, will become my apprentice.? If you were one of the 100 men invited to Aristotle?s conference, what number would you guess?
 
#3
Suppose Aristotle was holding a conference with the 100 most rational philosophers in all of Greece. He explained, “Each of you will guess a number no more than 100, whoever’s guess is the closest to 2/3 of the average of all of the guesses, will become my apprentice.” If you were one of the 100 men invited to Aristotle’s conference, what number would you guess?
I'll say 9.

For a chuckle, read the first paragraph of the Wikipedia entry for Aumann's agreement theorem. After I stopped laughing, my head exploded.
 

Ninja

Looking for Reality
Trusted
#7
Yep, it's wordy. I read the wiki article three times, investigated the links and came to this conclusion: I ain't got a darn clue what they be talkin' about.
I've found that folks try to rationalize the world around them by conforming or creating math so that life can be explained by math. It makes the world feel more rational...and in many cases the language of math does give a better ability to understand life situations.

Take "quality" for example. If a part doesn't work in my application, it is poor quality. Improving quality and understanding quality is a large part (the main part) of what this forum is...and we all treasure the statisticians that are sharing...go figure.

How matter works...math (physics)
What matters?...math (stats)
How employees are motivated...math (stats)
how to control a chemical fab process...math (Chemistry & stats)
how to improve customer satisfaction...math (stats)

So I'm not all that surprised that considering how people agree or disagree or try to predict one another's number guessing is treated as math...though it may be considered logic rather than math...but they're the same thing to me when you reduce it to an equation.

Oh, and an apology to GoldenBlazer...I wasn't intending to hijack your thread but it seems I have done so...sorry.
 
T

TheGoldenBlazer

#8
Ninja, I don't mind at all! You solved the riddle quick, and I got a good laugh at the wiki article as well!
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#9
I haven't found the wiki article, but I'd say that this exercise is more of one of game theory rather than math or statistics. Every one has the same set of rules. If you give any number except zero, and everyone else gives zero, you will be above the average of the group. Note if the goal was to be 2/3 above average, everyone would choose 100.
 
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