[extropy-chat] what is probability?
gts_2000 at yahoo.com
Mon Jan 15 00:56:25 UTC 2007
> Methinks the problem is that there is no such thing as "two identically
> rational agents"
That is almost certainly true for now and may remain true into the
indefinite future, but here we are discussing theories and principles. In
the argument I presented, the two rational agents are in principle
absolutely identical with respect to their rationality and background
knowledge/inputs, including in this important respect: they each have an
identical ability to make totally arbitrary decisions between equally
In machine terms this would mean they each have the ability to output a
random number (real or pseudo-random, it makes no difference here) to
facilitate their arbitrary decisions.
Is it rational for the agents to make arbitrary decisions between rational
alternatives? I think so. The alternative leads to paradox.
But a consequence is that rational agents with the same background
knowledge may be permitted to have different judgemental probabilities on
the same outcome, as in the subjective theory of probability.
(The only way to escape this conclusion short of abandoning the principle
of indifference even as a heuristic tool, would be, at least that I can
see, to prove somehow that one of the three alternative physical
parameters are preferable to the other two for setting a prior probability
on the dimensions of the unseen cube.)
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