buybuydandavis comments on Harry Potter and the Methods of Rationality discussion thread, part 18, chapter 87 - Less Wrong Discussion
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It would also reflect terribly on Hermione. She'd be an utter fool to attempt that kind of thing without using Harry's brilliance and resourcefulness. Her influence over Harry is one of her most useful powers and killing stuff ingeniously (and surviving) is pretty much Harry's specialty. It isn't hers.
It's one thing to insist on having your own team in a school battle-games. It's quite another to waste the opportunity to accept aid (and in this case even leadership) from an ally in a situation that means the life and death of yourself and others. It'd be disgustingly immature, take 'silliness' to a whole new level and be completely irrational. Unless Hermione's goal in attacking Azkaban really is more about her ego and signalling and not about the need for Azkaban to be attacked for some direct reason... and she had some reason to be completely confident that it wouldn't kill her.
No respect points for ego when it is at the expense of shut up and multiply.
I go into more detail in the post below, but I only picture Hermione attacking the dementors under some kind of time pressure with Harry unavailable.
http://lesswrong.com/lw/g1q/harry_potter_and_the_methods_of_rationality/8441
But I'd disagree that it would reflect terribly on Hermione. It wouldn't be optimal, but few people behave optimally. Lily's futile attempt to save Harry was suboptimal, but I don't think it reflected terribly on her.
Unfortunately, Hermoine's particularly suboptimality is exactly this - trying to prove that she is as effective and powerful as Harry, and so not wanting Harry's help. She should know better. And she does, in a sense, and better than Harry or Draco. She was the general who got her army to help do the planning for the battle. She could accept their help, and sought it out. But her Prodigy Superiority Complex is threatened by help from Harry.
This whole scenario is taking a grim turn in my mind. Hermione may sacrifice herself to destroy the dementors, only to have Harry see that the sacrifice was unnecessary, and could have been avoided if he updated the note he gave to her on dementors.