- Ron wrote:
Let's consider a legal analogy. If witness A denigrates the character of
witness B, do you believe witness A? No fair-minded person would do so
without trying to find other evidence bearing on the case. And if there
no other evidence, the fair-minded person would surely be forced to
judgment, in other words, treat witness A's testimony as unreliable,
is, the testimony cannot be relied upon to be true.
My approach would be to mentally adjust downward the probability that A
was telling the truth and also adjust downward the probability that B
was telling the truth. If witness A and B conflict, it lowers the
probability of truth for both. I suppose one might argue about whether
this is "fair", but from a strict information processing point of view,
I believe it is correct.
Digression on probability -
Recently I've gained a little more insight into common perceptions of
probability, so I'd like to elaborate on what I mean by "probability".
In recent decades there have been two "camps" in statistics, a Bayesian
camp, and a frequentist or traditional camp. My current approach
incorporates elements of both. In a way it is analogous to the 3SH. I
get the best of both competing camps, by introducing a change in
assumptions. I find traditional statistics to be correct, but
incomplete. I also disagree with the largest segment of the Bayesian
camp, in that I don't think probability=personal belief. Rather I see it
as an extension of logic from the deductive realm into the inductive
''Degrees of belief are relative to a person and a time but not to
evidence...Inductive probabilities are the opposite of this; they are
relative to evidence but not to a person or a time.' Maher ()
Maher, P. : 'A Conception of Inductive Logic', Philosophy of
Science, 73, pp. 513-23.
But, moving away from my specific approach, one thing I've discovered is
that for many probability=frequency. Dice or coins come to mind, where
we know the limiting frequency. Thus when I say P=1/6th, I am making a
statement of fact. It's an odd sort of fact, but still a fact. We are
uncertain about the next outcome, but certain about the frequency.
However, the more interesting questions, I believe, are when we are
uncertain about the frequency as well. Here the probability is our best
estimate of that frequency, (both Bayesians and frequentists can make
this move). For Bayesians we are then dealing with "meta-probabilities"
or probabilities of probabilities. I think not making this jump is what
leads some outside the field to favor frequentist statistics, and not
the Bayesian sort, whereas in reality this move is not something that
can distinguish them. The camps will treat this move in different ways,
but they can both make this move.
That is a long way of getting at the point that if I say there is a 50%
chance witness A is telling the truth, that is not mean that I think we
know that 50% of the time the witness is truthful. Rather, given our
ignorance of the frequency, this is the estimate of that frequency which
minimizes our mean-square error.
Probably too technical, and way off topic I suppose. But if anyone would
like a copy of my paper (currently under review), I think I can share at
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