From: Stuart Armstrong (dragondreaming@googlemail.com)
Date: Wed May 20 2009 - 05:29:52 MDT
> But even if it were, a satisfying solution may not be possible. Benji's solution distinguishes between agents that are certain of their mortality and agents that are certain of their immortality. The latter will optimize utility over an infinite time window, but so would an agent that was uncertain of its immortality. Both would chose option A ($1 per day forever) over the option of a single, finite payout of the agent's choosing. Since their behaviors are identical, we can conclude that there is no difference between certain and uncertain belief in immortality, unless there is another test to distinguish them.
Replace Benji's set-up with a system with finite pay-off:
Option A gives you (1/2)^n each day forever, where n is the day.
Option B gives you the option of claiming, on any day n, the payoff of
option A from say 0 up to day 2n, say. (this gives a pay off of 2 -
2^(2n+1))
Then use Dutch book type approaches to determine what relative price
the agent would put on option A and option B.
Stuart
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