Perhaps I should have said 90% that my plan is the plan or superior to whatever Harry comes up with.

I'm 95% sure you will find your plan superior to whatever Harry comes up with.
I'm 99% sure I won't. And that neither will Eliezer.

Well, looks like I was completely wrong. I think my solution is still superior to everyone still thinking Hermoine is a murderer, and Harry losing all of his money and going into debt.

"It's all right, Gregory," Draco said, as gently as he could. "All you've got to do is worry about protecting me. Nobody's going to blame you for following my orders, not my father, not yours."

Hmm I wonder how much trouble they are in, they were supposed to keep Draco from harm and he almost got killed.

I am now convinced (>51%) that Harry is going to sell out Quirrell to buy Hermione's freedom. I originally came to this hypothesis because it is a solid plan; Harry frames Professor Quirrell using his knowledge of Azkaban to free Hermione. He can do this by framing Quirrell as Voldemort, but each conjunction makes a probability less likely so I'll stick with just the above (even though I personally believe this will be the case). With the Watsonian parts hammered down, I'm awestruck by the elegance of the Doylist reasons.

Instead of looking at fiction as a series of words, we can instead look at it as a way to maximize tension, humor, and dramatic irony while keeping believability as strong as possible. Believability is important. Many other stories have their characters act stupid or out of character to create dramatic moments. At the eleventh hour a (badfanfic!)Harry decides to run off instead of get his friends, or randomly (badfanfic!)Hermione decides to side with Lucius for no goddamn reason. In HPMoR's case, we will have everyone working in their own rational self interest, intelligently, and coming out with a result that flows seamlessly to create maximal drama.

Harry falsely (accidentally truthfully) rats out Quirrell to save Hermione. From Harry's point of view he'll be forced to attack a (guilty but he thinks) innocent man who's done nothing but help him. Harry knows that Quirrell offered to fake a Voldemort fight for him (partially easing Harry's guilt), but now he's doing it without his consent. +1 irony for using Quirrell's own plan against him.

From Lucius' point of view he'll have (Harry!)Voldemort lying about the existence of Voldemort to his face. Lucius will inadvertently help Harry by preventing legillimency being done on Harry because Lucius thinks Harry is Voldemort and Voldemort is an occlumens. Even while we and Harry know he's not Voldemort, Lucius will not. And Harry will think that Lucius will be helping Harry because he wants to back out of taking revenge while saving face in front of the Wizengamot. Meanwhile Lucius will merely want to prevent the higher standard of evidence from being admitted and realize he's been outmaneuvered by (who he thinks is) the Dark Lord.

From Quirrell's point of view he'll have enacted a perfect plan to break Harry's 'side of goodness' while having Lucius destroy Dumbledore for him... only to be foiled by that fool boy messing up the plan again. Just like in Azkaban he'll underestimate Harry's need to save others, but in this case it'll take the form of betraying Quirrell. Since Harry is the only person Quirrell has ever liked (or possibly even loved), he can take this opportunity to turn even more evil and declare Harry his mortal enemy etc. It's possible he's even already laid the groundwork to break Hermione out (ex imperius the auror transferring her), but did not think for Harry to fail two of his lessons at once (be willing to lose / avada kedavra lesson in azkaban).

The story will get to use the investments from TSPE, Occlumency training, and Lucius' belief in Harrymort. I'm actually kind of in awe of this. Each one of those flowed naturally to create a believable world and fascinating reading in themselves. But that they can be recycled with such efficiency is amazing. Hopefully it's not just hindsight bias, but I'm seeing threads all the way back 50 chapters woven together. It makes me view Eliezer with a kind of formidableness in storytelling, like the ET Jaynes of fanfiction.

From a narrative point of view, the Voldemort reveal to the world has to occur soon. Voldemort needs to become an adversary to Harry before the final act, and it would require an entire build-up cycle again to make that happen. The Voldemort reveal (to harry) has to occur eventually as well and this preserves it until the very end for maximal drama.

So, in universe it makes sense. Out of universe it creates a beautiful story. I suspect it's too clever a resolution for Eliezer not to write. If I am correct in my guess, remember that Eliezer is a writer maximizing good storytelling and drama, not a writing trying to trick his audience. Plus, no one reading the chapters as a completed book would have ever figured it out, even as the parts flowed seamlessly together.

And if I'm incorrect in my guess.... well I guess I get a great lesson in humility and calibrating confidence.

So you're 90% certain that if you are incapable of imagining something, Eliezer can't either?

Wow.

Adding details to a story makes it seem more probable to humans (it fits together making a better story), when in fact every additional detail reduces the probability. malthrin linked this earlier, you should read: http://lesswrong.com/lw/jk/burdensome_details/

I think your scenario is a conjunction of unlikely events. I think the chance Harry will use a time turner in the solution is quite low, less than 10%, because the set up is such that he won't have access to it until more than 6 hours have passed. I'll give only a 50% chance that Harry will frame anyone at all, and if he does frame someone, I have no reason to believe that it will be Jugson-- I'd say 50% of the time he'll frame Dumbledore (just because it's easy), with decreasing chances for Quirell, Snape, other professors, and finally Jugson occupies such a small bit of my probability mass here that it wouldn't even occur to me.

Just these three items (time turner, frame, Jugson) reduce your scenario's probability to something very small; I put 2% on predictionbook, but my true probability is probably much lower.

(ETA: I realized on a re-read that my usage of "frame" above is non-standard; I was thinking broadly of turning the blame onto someone, not just of retroactively planting evidence, to which I give a much lower probability.)

Has it occurred to you that if you're really that confident you could be making money on bets?

Edit: No, I'm sorry, that was unethical of me. I think you're being ludicrously overconfident and would lose any money you put up. Please don't actually make bets.

For an optimal solution Harry teaches his enemies that poking him with a stick is very dangerous, and manages to turn this to his advantage by harming an enemy.

I'd just like to note that even then, Harry comes out the loser from this whole chain of events. Most importantly, he loses Draco as an ally, and suffers from knowing he hurt Draco's relationship with this father. Less importantly, Hermione has been psychologically hurt (I'd say traumatized), and won't get any personal redress. Finally, if Harry sets someone else up, he will lose the ability to expose the true culprit in the future, if he learns who that was, and so loses a powerful avenue of action against that culprit. The true culprit (or someone else) may even find proof of Harry framing Jugson, and then blackmail Harry with that proof.

The only way Harry could come out genuinely ahead is if he found and exposed the culprit, rather than frame a random enemy. Including scenarios where he could delay Hermione's punishment, or cancel it using blood debts, so that he'd gain time to search out the real culprit.

I believe a major psychological reason for people proposing so many theories for Harry's solution, some of them very impractical, is that they have an "intent to kill"; they don't want to propose a solution that settles for second best, like yours. They want Harry to win.

It does, doesn't it?

With a plan this complex there are many variables, so I just filled in my favorite guesses such as the person being framed, the order, etc.

Harry realizes the plan in that moment of desperation then gets the vote stopped to admit new evidence. He then presents to the court the testimony of George and Fred Weasley who say that during the night of the attempted murder they were out of their bed pulling a prank, when they saw Lord Jugson entering the Trophy room. They thought it was strange but since they were out of bed pulling a prank they didn’t want to tell anyone, until they realized that morning it could be connected. They then went straight to a Professor who brought them to the Wizengamot, and they repeat their testimony under veritaserum.

Lord Jugson claims they were false memory charmed, but Harry responds to this by saying that if you are so confident of it why not let us examine the last spells cast on your wand, and that of Hermoine’s and Draco’s? After all you have nothing to hide. Lord Jugson agrees and hands over his wand, and then priori incantum reveals to his shock that his wand has been used recently to do the imperius, obliviate and the false memory charm. Hermoine's wand has been faked to use the Blood Chilling charm but Draco's has no evidence of a duel past the army fight on it at all.

Harry explains that Lord Jugson in a fit of rage at Draco for losing to a mudblood and Hermoine for beating him made a plot to punish them both after the army fight. He disappeared after the fight, and remained in Hogwarts to imperius Draco to challenge Hermoine to a duel at midnight. Then he either simply stayed in Hogwarts until midnight, used a secret passage or apparated outside the wards and flew in a broomstick, or used the floo network to enter Hogwarts right before midnight. He made his way to the trophy room, stunned Draco and Hermoine as they entered, disillusioned them all, and took them outside of the wards of Hogwarts to do the obliviation and false memory charms returning them after the deed was done. Lord Jugson won’t have an alibi for the hours of 11:30 to 12:30 as everyone in his household would be asleep at the time.

He used Hermoine's wand to cast spells simulating a duel followed by the blood chilling charm figuring that when Draco died he could prompt an investigation into her which would reveal the evidence on her wand combined with veritaserum to convict her. He obliviated Draco and false memory charmed him as well just in case Draco was discovered, but he didn't bother to tamper with Draco's wand figuring no one would have a reason to investigate it, and the wands show this.

Harry further explains that Lord Jugson decided that Draco had become too friendly to mudbloods and was no longer fit to be a leader of the blood purists. By killing him after his public showdown with Hermoine he could get rid of Draco, Hermoine AND set his own son up to assume leadership of the blood purists now that the Malfoy’s had no heir. After the plot ended he obliviated himself (if he isn't an occlumens) to safely hide the plot forever. Lord Jugson is sentenced to Azkhaban, by Harry invoking Lord Malfoy's blood debt to Harry to decide the sentencing, Hermoine is freed and the blood purists lose face politically for wanting to kill an innocent girl.

In my next post I will explain how Harry did it.