[extropy-chat] what is probability?

[Rafal Smigrodzki]

On 1/13/07, gts <gts_2000 at yahoo.com> wrote:

>
> If the Bertrand paradox is fundamentally unsolvable then it seems to me
> the principle of indifference is toast as a logical principle, and if so
> then it seems two rational agents would be free in certain cases to use
> different bayesian priors.

### I would see it this way: The meaning of "random" is "obeying the
principle of indifference, where the sample space is unambiguously
described". If the sample space is exactly two outcomes, then each one
must occur 50% of the time, or else the coin is weighted, and the
tosses are not quite random anymore.

But regarding the second issue, I would somewhat agree with you. As a
general rule, fully rational agents must agree on questions of fact
(as Robin Hanson says) but then there seem to be exceptions.
Disagreement is at times unavoidable, principally where the agents are
not aware of each other's calibration, or may be perhaps unable to
communicate the magnitude of differences in their calibration (a small
child and an adult, or a human and an SAI). If agents cannot
quantitatively assess each other's calibration, at least one of them
may be unable to properly adjust its priors, and disagreement will
remain, even in the absence of self-deception.

Rafal