On 2/5/07, gts <[EMAIL PROTECTED]> wrote:
I wonder how a logically-omniscient player might be defined. Will you please explain your meaning?
An entity capable of proving or disproving the truth of any statement which has a logical proof or disproof. (Requires infinite computing power.) I don't see that agents need to be logically omniscient to avoid being
bilked by omniscient bookies. They need only be careful to be coherent in the De Finetti sense. This is not an especially problematic constraint.
What's the probability that the 2535431st digit of pi is 7? 10%, you say? But it's really either 0 or 1, we just don't know off the top of our heads which is the case. In some contexts it would be still reasonable to say that your _subjective_ probability estimate is 10%. However, the definition of subjective probability involved a situation where you are _forced_ to bet on the result. If I can force you to bet, I can precalculate digits of pi and choose one where I know the answer. In that scenario, you can't do better than always bet 50%. (I remark on this because the "who gets to choose" question is a hole in a great many arguments based on concepts like subjective probability, not just this one.) ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
