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

is

no other evidence, the fair-minded person would surely be forced to

suspend

judgment, in other words, treat witness A's testimony as unreliable,

that

is, the testimony cannot be relied upon to be true.

Dave:

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

realm.

''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 ([2006])

Maher, P. [2006]: '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

this point.

Dave Gentile

Riverside, IL

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