Thoth Hermes's Shortform

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. 

All of the vice-versas are straightforwardly true as well. 

$p\left(A\right)=p\left(A|B\right)p\left(B\right)+p\left(A|\neg B\right)p\left(\neg B\right)$
$p\left(B\right)=p\left(B|A\right)p\left(A\right)+p\left(B|\neg A\right)p\left(\neg A\right)$
$p\left(\neg A\right)=p\left(\neg A|B\right)p\left(B\right)+p\left(\neg A|\neg B\right)p\left(\neg B\right)$
$p\left(\neg B\right)=p\left(\neg B|A\right)p\left(A\right)+p\left(\neg B|\neg A\right)p\left(\neg A\right)$

let A = the statement "A" and p(A) be the probability that A is true.

let B = A is "communicated well" and p(B) the probability that A is communicated well.

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., etc.. 

if p(A) = p(A|~B):
p(A) = p(A|B)p(B) + p(A)p(~B)
p(A)(1 - p(~B)) = p(A|B)p(B)
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.

P(B | A) = p(A | B)P(B) / p(A | B)p(B) + p(A | ~B)p(~B) = p(A)p(B) / p(A)p(B) + p(A)p(~B) = p(A)p(B) / p(A) = p(B).

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.  

Addendum: 

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, it may still come out good, even if you didn't believe in A. 

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. 

A short, simple thought experiment from "Thou Shalt Not Speak of Art":^[1]

From my perspective: I chose the top one over the bottom one, because I consider it better. You, apparently, chose the one I consider worse.

$Me◯⟶◯Good$

$You◯⟶◯Worse$

From your perspective: Identical, but our positions are flipped. You becomes Me, and Me becomes You.

$You◯⟶◯Worse$

$Me◯⟶◯Good$

However, after we Ogdoad:

$Me◯⟶◯Good$

$You◯⟶◯Good$

It becomes clear that the situation is much more promising than we originally thought. We both, apparently, get what we wanted.

Our Ogdoad merely resulted in us both being capable of seeing the situation from the other’s perspective. I see that you got to have your Good, you see that I get to have my Good. Boring and simple, right?

It should be. Let’s make sure that any other way can only mess things up. Our intuitions say that we ought to simply allow ourselves to enjoy our choices and not to interfere with each other. Are our intuitions correct?

$Me◯⟶◯Good$

$\searrow$

$You◯⟶◯Better$

This is the perspective if I choose to see your perspective as superior than mine. If I consider yours authoritative, then I have made your choice out to be “better” than mine. Likewise, if you choose to do the same for me, you’ll see mine as better. The only situations that could result from this are:

1. We fight over your choice.
2. We share your choice, and I drop mine.
3. We swap choices, such that you have mine and I have yours.

All three easily seem much worse than if we simply decided to stay with our original choices. Number 1 and 2 result in one of us having an inferior choice, and number 3 results in both of us having our inferior choice.

Apparently, neither of us have anything to gain from trying to see one another’s preferences as “superior.”

1. ^{^}

   "Speaking of art" is a phrase which refers not just to discussing one's preferences openly, but specifically doing so while assuming an air of superiority and judgementality. I.e., to be condescending to others about what they want or do not want.