Expect Truth To Correlate With Your Judgement Of It
Cross-posted from my short-form on LessWrong. You'll be surprised what kinds of things get debated there.
If you understand the core claims being made, then unless you believe that whether or not something is "communicated well" has no relationship whatsoever with the underlying truth-values of the core claims, if it was communicated well, it should have updated you towards belief in the core claims by some non-zero amount.
Certainly don’t expect it to anti-correlate or be completely uncorrelated.
All of the vice-versas are straightforwardly true as well.
You need no more than the following equations and Bayes’ Theorem.
Let A = the statement "A" and p(A) be the probability that A is true. Then ¬A can refer to the statement “¬A” and p(¬A) the probability that ¬A is true.
Let B = A is "communicated well" and p(B) the probability that A is communicated well. Then ¬B means A is “communicated badly” and p(¬B) the probability that A is “communicated badly.”
Interestingly, “communicated badly” means that I understand the claim(s) you are making and what they mean, but you’ve somehow convinced me that they are not true, or some other thing is true (whatever the opposite may mean).
p(A | B) is the probability that A is true given that it has been "communicated well" (whatever that means to us).
We can assume, though, that we have "A" and therefore know what A means and what it means for it to be either true or false.
What it means exactly for A to be "communicated well" is somewhat nebulous, and entirely up to us to decide. But note that all we really need to know is that ~B means A was communicated badly, and we're only dealing with a set of 2-by-2 binary conditionals here. So it's safe for now to say that B = ¬¬B = "A was not communicated badly." We don't need to know exactly what "well" means, as long as we think it ought to relate to A in some way.
p(A | B) = claim A is true given it is communicated well
p(A | ¬B) = claim A is true given it is not communicated well. If (approximately) = p(A), then p(A) = p(A|B) = p(A|¬B) (see below).
p(B | A) = claim A is communicated well given it is true
p(B | ¬A) claim A is communicated well given it is not true
etc..
If p(A) = p(A|¬B):
If being communicated badly has no bearing on whether A is true, then being communicated well has no bearing on it either.
Likewise being true would have no bearing on whether it would be communicated well or vice-versa.
To conclude, although it is "up to you" whether B or ¬B or how much it was in either direction, this does imply that how something sounds to you should have an immediate effect on your belief in what is being claimed, as long as you agree that this correlation in general is non-zero.
In my opinion, no relationship is kind of difficult to justify, an inverse relationship is even harder to justify, but a positive relationship is possible to justify (though to what degree requires more analysis).
Also, this means that statements of the form "I thought X was argued for poorly, but I'm not disagreeing with X nor do I think X is necessarily false" is somewhat a priori unlikely. If you thought X was argued for poorly, it should have moved you at least a tiny bit away from X.
If you deceptively argue against A on purpose, then if A is true, your argument may still come out "bad." If A isn't true, your argument may still come out “good”, even if you didn't believe in A (perhaps the case of someone marketing a product using the persuasion skills they’ve learned to use regardless of how well the product they’re trying to sell works).
If you state "A" and then intentionally write gibberish afterwards as an "argument", that's still in the deceptive case. Thus "communicated well" takes into account whether or not this deception is given away.
If A is true, then sloppy and half-assed arguments for A are still technically valid and thus will support A. At worst this can only bring you down to "no relationship" but not in the inverse direction.
The important thing to remember is that you determine how “well” something is argued. And therefore, an “argument” for some claim might at first be deemed sufficient but then later be deemed to be insufficient.
For example, suppose I had some reason to doubt your claim that you purchased a lottery ticket. Then, I could simply ask you for proof that you indeed purchased it, and wait for you to deliver said proof. The delivery of said proof would amount to a “good” argument and non-delivery would amount to a “bad” argument.
All this requires you to judge your own judgement.