I'm pretty sure you flipped the fraction upside-down here. Shouldn't it be perceived difficulty of the task divided by perceived competence? Gifted high-school student who boldly declares that he will develop a Theory of Everything over the course of summer vacation is arrogant (low competence, high difficulty). Top-notch theoretical physicist who boldly declares that he will solve a problem from a high-school math contest is not. So SIAI is actually infinitely arrogant, according to your assumptions.
I'm pretty sure I did too. But the whole explanation seems much less intuitive to me now, so I'll retract rather than correct it.
I intended Leveling Up in Rationality to communicate this:
But some people seem to have read it and heard this instead:
This failure (on my part) fits into a larger pattern of the Singularity Institute seeming too arrogant and (perhaps) being too arrogant. As one friend recently told me:
So, I have a few questions: