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Author Topic: CoinCube Highlights  (Read 1380 times)
CoinCube
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August 11, 2016, 01:19:26 AM
Last edit: August 11, 2019, 01:26:52 AM by CoinCube
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CoinCube Highlights

Areas of Interest:
Health and Religion
How Do We Make Society Better?
Man or Rabbit? by CS Lewis
Freedom and Moral Self-Control
The Abolition of Man
An Argument for God
Understand Everything Fundamentally
Finance: Part 1, 2, 3
Awake In The Night Land (Book Review)
Intervention Theory
Debate on Nihilism
Kurt Gödel
Sustaining Cultural Integrity
Way of God
Does God Send People to Hell?
The Platonia Dilemma


Solution to the Platonia Dilemma:
(By Douglas Hofstadter)

"And what about the Platonia Dilemma? There, two things are very clear: (1) if you decide not to send a telegram, your chances of winning are zero; (2) if everyone sends a telegram, your chances of winning are zero. If you believe that what you choose will be the same as what everyone else chooses because you are all superrational, then neither of these alternatives is very appealing. With dice, however, a new option presents itself to roll a die with probability p of coming up “good” and then to send in your name if and only if “good” comes up.

Now imagine twenty people all doing this, and figure out what value of p maximizes the likelihood of exactly one person getting the go-ahead. It turns out that it is p=120, or more generally, p=1N where N is the number of participants. In the limit where N approaches infinity, the chance that exactly one person will get the go-ahead is 1e, which is just under 37%. With twenty superrational players all throwing icosahedral dice, the chance that you will come up the big winner is very close to 120e, which is a little below 2%. That’s not at all bad! Certainly it’s a lot better than 0%.

The objection many people raise is: “What if my roll comes up bad? Then why shouldn’t I send in my name anyway? After all, if I fail to, I’ll have no chance whatsoever of winning. I’m no better off than if I had never rolled my die and had just voluntarily withdrawn!” This objection seems overwhelming at first, but actually it is fallacious, being based on a misrepresentation of the meaning of “making a decision”. A genuine decision to abide by the throw of a die means that you really must abide by the throw of the die; if under certain circumstances you ignore the die and do something else, then you never made the decision you claimed to have made. Your decision is revealed by your actions, not by your words before acting!"

If you came up with this solution and would genuinely do it in this situation you are to some degree a superrational thinker.

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