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HonoreDB comments on Harry Potter and the Methods of Rationality discussion thread, part 10 - Less Wrong
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If Harry does not manage to find the real culprit, then how does he save Hermione from having her wand broken?
Breakout/Direct Attack on the Wizengamot / Malfoy Manor
Transfigure a one-atom line of antimatter through the earth's crust all the way to the Wizengamot or Malfoy Manor, and then a small bubble there. His wand is then touching the item to be transformed, and it will work.
Go to Azkaban and round up a few hundred dementors.
Stealth
Bringing Hermione under the aegis of a noble house
Bribery, Trade, or Begging
Harry could offer to pay Lucius Malfoy something in restitution. It couldn't just be money or an incredible favor. As the original 'Taboo Tradeoffs' paper mentions, people only get more angry when you try to do that. Harry would need an accurate model of Lucius suspecting him as Harrymort and be able to trade him something that Harrymort would consider sacred.
Trade his invisibility cloak to Lucius for Hermione's freedom. Make sure to play up that it is 1/3rd of the Deathly Hallows and thus something Harrymort considers sacred/invaluable.
Trade Lucius a blood debt from the House of Potter.
Make an unbreakable vow to protect Draco or otherwise help Lucius (or some other ritual).
(Assuming Roger Bacon's diary is indeed the diary Horcrux and Harry manages to discover that) Trade Lucius a piece of Voldemort's soul as apology.
None of the trades seem particularly smart or likely, but Harry might consider a few of them if he got really desperate. They seem to be of sufficient value to Lucius (or rather, to Harry's model of Lucius' model of Harrymort) to prove that Harry is genuinely sorry and be worth Hermione's life/magic/future.