Step one: Stand up and loudly explain how a patronus works, and what a dementor actually is, under the guise of arguing for a diffrent punisment - This will make the entire wizengamot, including the aurors controling the dementor present incapable of casting expecto patronum. Destroy the dementor before it eats anyone. Now the wizengamot has to shut down azkaban (Because the secret would get out). This would not exactly endear him to anyone at all, but they cannot seriously retaliate, because they need him to kill off the dementors before they run out of aurors who havent heard the truth yet. This doesnt actually free Hermonie, just stops them from sending her (or anyone) to azkaban.
Side bonus Harry cannot predict: This would probably also convince Lucius that he isnt Pottermort.
This is the answer that I thought of when I read the chapter (specifically with the ‘blunt force’ amendment below). Unfortunately, it doesn't fit in with the narrative clues that we've been given: there's no taboo trade-off, and it doesn't treat the Wizengamot as individuals. Nevertheless, it would be awesome.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: