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Gabriel comments on The Singularity Institute's Arrogance Problem - Less Wrong
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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.
It seems to me that the "perceived arrogance quotient" used by most people is the following: (status asserted by speaker as perceived by listener)/(status assigned to speaker by listener)
However, I think this is wrong and unfair, and it should instead be: (status asserted by speaker as perceived by speaker)/(status assigned to speaker by listener)
That is, before you call someone arrogant, you should have to put in a little work to determine their intention, and what the world looks like from their point of view.