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.