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PK comments on Zut Allais! - Less Wrong

23 Post author: Eliezer_Yudkowsky 20 January 2008 03:18AM

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Comment author: PK 20 January 2008 08:31:03PM 1 point [-]

There is a certain U(certainty) in a game, although there might be better ways to express it mathematically. How do you know the person hosting the game isn't lying to you an really operating under the algorithm: 1A. Give him $24,000 because I have no choice. 1B. Tell him he had a chance to win but lost and give nothing.

In the second situation(2A 2B) both options are probabilities and so the player has no choice but to trust the game host.

Also, I am still fuzzy on the whole "money pump" concept. "The naive preference pattern on the Allais Paradox is 1A > 1B and 2B > 2A. Then you will pay me to throw a switch from A to B because you'd rather have a 33% chance of winning $27,000 than a 34% chance of winning $24,000."

Ok, I pay you one penny. You might be tricking me out of one penny(in case you already decided to give me nothing) but I'm willing to take that risk.

"Then a die roll eliminates a chunk of the probability mass. In both cases you had at least a 66% chance of winning nothing. This die roll eliminates that 66%. So now option B is a 33/34 chance of winning $27,000, but option A is a certainty of winning $24,000. Oh, glorious certainty! So you pay me to throw the switch back from B to A."

Yes yes yes, I pay you 1 penny. You now owe me $24,000. What? You want to somehow go back to a 2A 2B situation again? No thanx. I would like to get my money now. Once you promised me money with certainty you cannot inject uncertainty back into the game without breaking the rules.

I'm afraid there might still be some inferential distance to cover Eliezer.