I think you have a point. However, I strongly disagree with the framing of your post, for several reasons.
One is advertising your hedge fund here, that made me doubt of the entire post.
Second, is that the link does not go to a mathematical paper, rather to the whitepapers section of your startup. Nevertheless, I believe the first PDF there appears to be the math behind your post.
Third, calling that PDF a mathematical proof is a stretch (at least, from my pov as a math researcher). Expressions like "it is plausible that" never belong in a mathematical proof.
And most importantly, the substance of the argument:
In your model, you assume that effort by allies depends on the actor's confidence signal (sigma), and that allies' contribution is monotonic (larger if the actor is more confident). I find this assumption questionable, since, from an ally/investor perspective, unwarranted high confidence can undermine trust.
Then, you conflate the fact that the optimal signal is higher (when optimizing for outcomes) than the optimal forecast (when optimizing for accuracy) as an indication against calibration. I would take it as an indication for calibration, but including possible actions (such as signaling) as variables to optimize for success.
In my view, your model is a nice toy model to explain why, in certain situations, signaling more confidence than what would be accurate can be instrumental.
Ironically, your post and your whitepaper do what they recommend, using expressions like "demonstrate" and "proof" without properly acknowledging that most of the load of the argument rests on the modelling assumptions.
I think allowing this debate to happen would be a fantastic opportunity to put our money where our mouth is regarding not ignoring systemic issues:
https://80000hours.org/2020/08/misconceptions-effective-altruism/#misconception-3-effective-altruism-ignores-systemic-change
On the other hand, deciding that democratic backsliding is off limits, and not even trying to have a conversation about it, could (rightfully, in my view) be treated as evidence of EA being in an ivory tower and disconnected from the real world.