Harry Potter and the Way of Reason

I just said it silently to myself over and over until I could choose to go to sleep: it all adds up to J.K. Rowling. [1]

The decision theory used in this chapter is not the mainstream academic version.It is based on the still-in-development "Timeless Decision Theory" [2] by Gary Drescher, Wei Dai, Vladimir Ness, and, uh... (cough cough) me.

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The frightening thing is the speed at which the whole situation spiraled out of control.

"Albus," Minerva said, not even bothering to hide the worry in her voice.The two walked into the auditorium together, "Some measures must be taken."

Hogwarts is always bright and cheerful leading up to the Christmas season.The Great Hall was decked out in red and green in honor of a Slytherin and a Gryffindor whose Christmas wedding became a symbol of friendship that transcended houses and factions, and left a legacy almost as old as Hogwarts The tradition has even spread to the Muggle countries.

But now, some of the students who were eating were looking behind them nervously, some were staring in the direction of other tables maliciously, and some were arguing fiercely at certain tables.The atmosphere might be described as tense, but the words that emerged in Minerva's mind were alert level five.

Divide a school into four colleges...

Now in each grade, three more armies are at war.

The power of Dragon, Sunshine, and Chaos has spread beyond the first grade; they have become the ranks of those who did not join the army.Students wear armbands with images of flames, smiling faces or raised hands and cast spells on each other in the hallways.All three first-year generals had told them to stop doing it - even Draco Malfoy had nodded gravely when she had finished - but the so-called followers hadn't listened at all.

Dumbledore looked at the long tables, his eyes wandering into the distance. "In every city," the old wizard said softly, "the people have been divided from the very beginning into blue and green... They fight against their opponents, not knowing that they will end up harming themselves... As a result, there is a wave against them. The gratuitous hostility of companions grows and never dies, and it leaves no place for marriage unions, love, and friendship, even among brothers or relatives, if their allegiances are to different factions. I, it seems to me, can only Call it a disease of the soul..."[3]

"Sorry," Minerva said, "I don't—"

"Procopius," said Dumbledore, "in the Roman Empire they take chariot racing very seriously. Yes, Minerva, I agree that something must be done."

"As soon as possible," said Minerva, even more quietly, "Albus, I think something must be done by Saturday."

On Sunday, most students leave Hogwarts to spend the holidays with their families; so Saturday is the day when the three first-year armies will battle to determine Professor Quirrell's thrice-cursed Christmas To whom the wish will be rewarded.

Dumbledore looked at her seriously, and said thoughtfully: "You are afraid that when the conflict breaks out, someone will be injured."

Minerva nodded.

"And will be blamed on Professor Quirrell."

Minerva nodded, expression tense.She was already familiar with the various possible reasons why the Defense Professor would be dismissed. "Albus," said Minerva, "we can't lose Professor Quirrell now, we can't! As long as he stays until the end of January, our fifth graders will pass their Ordinary Wizarding Levels, and if he stays By the end of March, our seventh graders will have passed their ultimate wizarding exams, he's made up for years of omissions in a few months, and a whole generation will have grown up enough to protect themselves, even in the face of the black The devil's curse—you must stop this battle, Albus! Disband the army at once!"

"I'm not sure the Defense Professor would be happy with that," said Dumbledore, looking at Quirrell at the guest table, his saliva dripping into the soup. "He does seem to like his armies very much, although when I promised him, I thought there would be four teams in each grade." The old wizard sighed, "A wise man may have good intentions; but Maybe it's not smart enough, I'm afraid. Disbanding the military may also lead to conflict."

"But if so, Albus, what would you do?"

The old wizard smiled kindly at her. "Well, of course some conspiracy. This is the new fashion at Hogwarts."

By this time they were so close to the table of honor that Minerva had no chance to say anything else.

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The frightening thing is the speed at which the whole situation spiraled out of control.

The first fight in December was... a mess, or so Draco had heard.

The second battle was madness.

And the next one will be worse, unless the three of them together make a last-ditch effort to stop it from happening.

"Professor Quirrell, this is crazy," Draco said bluntly, "it's not even Slytherin, but..." Draco was at a loss for words, he waved his hand helplessly, and said: "There's so much mess going on, you can't have any real strategy. Last battle, one of my soldiers faked suicide. Even the Hufflepuffs try to plot, they think they can, but they're wrong Now anything can happen, it doesn't matter who's the smartest, or which team plays the best, so..." He couldn't even describe the scene.

"I agree with Mr. Malfoy," Granger said in a tone that he couldn't even believe he could say that. "Allowing traitors isn't going to work, Professor Quirrell."

Draco had tried banning plotting by everyone in his army but himself, but it had only allowed those plots to go underground, no one wanted to be left behind when the soldiers of the other ranks could be plotting.After tragically losing the last battle, he finally capitulated and withdrew his orders; but by then his soldiers had begun to put their own plans into practice, without any central dispatch.

After learning of all the tricks - or what the soldiers called them - Draco tried to come up with a plan that would win the final battle.It took far more than three different things to go well, and then Draco put a blaze on the paper, and cleaned up the ashes with a waste cleaner.Because if father sees this, he will disown him.

Professor Quirrell half-closed his eyes, resting his head on his hands on the desk. "What about you, Mr. Potter?" said the Defense Professor. "Do you agree?"

"We were only one step away from shooting Franz Ferdinand [4] to start World War I," said Harry. "It was a total mess. I'm absolutely for it."

"Harry!" Draco said in shock.

It wasn't until a second later that he realized he was saying it at the same time, with the same indignation as Granger.

Granger gave him a surprised look, and Draco was careful to maintain a calm expression.ah oh.

"That's it!" said Harry. "I betrayed you! You two! Again! Haha!"

Professor Quirrell smiled slightly, although his eyes were still half-closed. "Then why did you do it, Mr Potter?"

"Because I think I can deal with chaos better than Miss Granger and Mr Malfoy," said the traitor, "Our war is a zero-sum game[5], and overall it doesn't matter whether it's easy or hard, it's just who does it." better or worse."

Harry Potter learns a little too quickly.

Professor Quirrell looked down at Draco, then Granger. "Honestly, Mr. Malfoy, Miss Granger, I can't forgive myself for stopping the catastrophe before it reaches its peak. One of your soldiers is even a quadruple agent."

"Fourfold?" Granger said, "But only three parties participate in the war!"

"Yeah," said Professor Quirrell, "you'd think that, wouldn't you. I'm not sure if there's ever been a quadruple agent in history, or an army with such a high percentage of true and false traitors. We're exploring New territory, Miss Granger, we cannot turn back now."

Draco gritted his teeth and walked out of the Defense Professor's office, Granger beside him looked even angrier than him.

"I can't believe you're doing this, Harry!" Granger said.

"Sorry," Harry said, but it didn't sound like he was sorry at all, and the corners of his mouth curled up in a pleasant smirk. "Remember, Hermione, this is just a game, so why only generals like us can make suggestions? And, what are you two going to do about this matter? Join forces to deal with me?"

Draco and Granger exchanged a few glances, knowing his expression was as tense as hers.Harry's dependence on Draco's refusal to join forces with a Mudblood girl was becoming more and more obvious and triumphant; and Draco was starting to get tired of having this used against him.If it went on like this, he was really ready to ally with Granger just to beat Harry Potter, and see how much the mudblood liked that.

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The frightening thing is the speed at which the whole situation spiraled out of control.

Hermione stared at the parchment Zabini handed her, feeling utterly helpless.

There are names on it, and the names are connected by lines, some of the lines are of different colors, and...

"Tell me," said General Granger, "is there anyone in my army who isn't a spy?"

The two of them were not in the office, but in another deserted classroom, just the two of them; for, Colonel Zabini said, it was now almost certain that at least one of the captains was a traitor.It might have been Captain Goldstein, but Zabini wasn't sure.

Her question brought a sarcastic smile to the young Slytherin's face.Blaise Zabini seemed to have always looked down on her a bit, but he didn't seem to dislike her; not like he always taunted Draco Malfoy, nor did he develop a grudge against Harry Potter.At first she was worried that Zabini would betray her, but the boy seemed to be doing his best to show that the other two generals were no better than him; Hermione felt that Zabini might be happy to betray her to anyone else, but he would never Let Malfoy and Harry win.

"Most of your soldiers are still loyal to you, I'm sure," Zabini said, "it's just that everyone doesn't want to miss out on the fun." Slytherin had a contemptuous look on his face, presumably thinking of something not serious Treat people with intrigue. "So they thought they could be double agents, pretending to betray us while secretly working for us."

"The same goes for people in other armies who say they want to be our spies," Hermione said cautiously.

The young Slytherin shrugged. "I think I can tell pretty well who really wants to sell out to Malfoy, but I don't think anyone's going to really sell out to you on Potter. But Nott definitely betrayed Potter to Malfoy because I made Ann Twhistle pretending to have approached him on Malfoy's behalf, and Antwhistle actually reporting to us, is at least reliable—"

Hermione closed her eyes for a moment and said, "We're losing, aren't we?"

"Look," Zabini said patiently, "you're leading in Quirrell points now. As long as we don't lose all in the final battle, you'll have enough Quirrell points to win your Christmas wish."

Professor Quirrell announces that he has been asked to use the official scoring system in the final battle to avoid arguing afterwards.Every time you knock someone down, the general of your army gets two Quirrell points and strikes a gong that spreads across the battlefield (they don't know where they'll be fighting yet, but Hermione hopes it's still in the forest, The Suns did well there), the pitch will indicate which team got the point.If someone pretends to be hit, the gong will also sound, and then after an indeterminate time, the gong will sound twice to announce the cancellation of the score.If you shout a certain team's name, like "For Sunshine!" or "For Chaos!" or "For Dragons!", your team allegiance will change...

Even Hermione saw the flaws in this set of rules, but Professor Quirrell went on to announce that if you were assigned to Team Sunshine in the first place, no one could kill you in the name of Sunshine—or, yes, but The Sunshine team will lose a point of Chilo points, marked by three gongs, to prevent shooting their own soldiers in order to score, and to prevent you from committing suicide before being caught by the enemy, but you can still shoot spies if necessary .

Now, Hermione has 244 Quirrell points, Malfoy has 219 points, Harry has 221 points, and each team has 24 soldiers.

"So we have to fight carefully," said Hermione, "just try not to lose too badly."

"No," Zabini said, the young Slytherin's expression serious. "The problem is, both Malfoy and Potter know the only way they can win is to beat us together, and then fight each other. So I think we should do it—"

Hermione felt a little dizzy as she left the classroom.Zabini's strategy is not straightforward, but weird, complex, and deep.She could have expected Harry to figure this out, but not Zabini.It felt wrong for her to understand the ruse.Little girls shouldn't be able to understand such tricks.If the Sorting Hat had foreseen that she would understand such a ploy, it would have put her in Slytherin...

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Best of all was the speed at which the chaos expanded after he had deliberately done it.

Harry sat in his office; he had the right to order furniture from house-elves, so he ordered a throne, and black and crimson patterned curtains.Scarlet light, like blood, mixed with shadows, poured on the floor.

Somewhere in Harry's mind he felt that he was finally home.

Before him stood four lieutenants of Chaos, his most trusted favourites, one of whom was a traitor.

this.This is how life should be.

"We're assembled here," said Harry.

"Let Chaos fall," said the four lieutenants in unison.

"My hovercraft is full of eels," said Harry.

"I don't buy this record, it's scratched.[6]" the four lieutenants said in unison.

"The pineapple bird is scruffy and pathetic."

"The green hairy pig got lost and made a fuss![7]"

Li Bi.

"How's the chaos going?" Harry whispered dryly, like Emperor Palpatine.

"Everything is going well, General Chaos," Neville said in his usual tone of military answers, so low that he often had to stop to cough twice.The Chaos lieutenant was neatly dressed in black school robes with Hufflepuff yellow, and his hair was parted in the usual way of a serious young boy.Harry liked the incongruity, better than any of the robes they had tried on. "From last night to now, our fighters have started five new projects."

Harry smiled wickedly. "Is there any chance they'll work?"

"I don't think so," said Neville of Chaos. "Here's the report."

"Very well," said Harry, taking the parchment from Neville's hand, and sneered a few times, trying to make it sound as though he'd choked on a mouthful of ashes.This brings the total number of plans to sixty.

Let Draco try to deal with this.Let him try it.

As for Blaise Zabini...

Harry laughed again, this time with a sinister tone without even trying to.He really needs to borrow someone's pet cat, Lizi, for a staff meeting, so that he can pet the cat and smile evilly[9].

"Can the Legion stop making plans now?" said Finnigan of Chaos. "I mean, isn't that enough—"

"No," said Harry flatly, "we can never have too many plans."

Professor Quirrell set it up perfectly.They'd pushed the boundaries further, perhaps further than ever; and Harry couldn't bear to let himself stop now.

There was a knock on the door.

"It's Dragon General," said Harry, smiling with evil foreboding. "I expect him to come by now. Tell him to come in, you guys to get out."

The four lieutenants of the Chaos Legion retreated, gloomily watching the enemy general Draco enter Harry's secret lair.

If he wasn't allowed to do this when he grew up, Harry really wanted to stay at the age of 11 forever.

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The sun shone through the red curtains, and streaks of blood danced on the floor behind Harry Potter's adult-sized armchair, which he had sprinkled with gold and silver glitter, and insisted on calling it his throne .

(Draco was even more convinced that his decision to stop Harry Potter before he could rule the world was right. Draco couldn't even imagine what it would be like to live under his rule.)

"Good evening, Dragon General," Harry Potter whispered icily. "As I expected, you are here."

This wasn't surprising, since Draco and Harry had already scheduled their meeting in advance.

And it wasn't night yet, but Draco knew it was best not to say anything.

"General Potter," Draco said with as much dignity as possible, "you know our two armies have to work together for either of us to have a chance of winning Professor Quirrell's award, don't you?"

"It's hiss—" Harry hissed, as though the boy thought he was a Parseltongue. "We have to work together to destroy the Army of the Sun, and then we'll face each other. But if either of us betrays the other before then, he'll have the upper hand in the rest of the battle. General Sunshine knows this and will try to deceive us , let us believe that the other party has betrayed us. And you and I, knowing this, will be tempted to betray each other, and then pretend that this is Granger's conspiracy. Granger knows this too."

Draco nodded.These are all obvious. "However... both of us just want to win, and if we defect, no one else can punish either of us..."

"Exactly," said Harry Potter, looking serious now. "What we are facing is a real prisoner's dilemma [10]."

The prisoner's dilemma, according to Harry's teaching, is carried out like this: two prisoners are locked in two cells respectively, and there is evidence of two crimes, but neither is important evidence, and each can only be sentenced to two years in prison.Each prisoner has the option to betray, to betray the other, to testify against him in court; this would remove one year from his own sentence, but add two years to the other.Or the prisoner may choose to cooperate and remain silent.If two people betray, they will each serve three years in prison; if both choose to cooperate, then they will each serve two years in prison; Year.

Both prisoners must make a decision without knowing the other's choice, and neither can change their choice afterwards.

Draco commented that if the two prisoners had been Death Eaters during the Wizarding Wars, the Dark Lord would have killed any traitors.

Harry nodded, saying that was one of the solutions to the Prisoner's Dilemma - in fact the Death Eaters would want the Dark Lord around for exactly that reason.

(Draco asked Harry to pause for a second, to think before they continued. This effectively explained why Father and his friends agreed to serve a Dark Lord who was often treating them badly...)

In fact, Harry said, that's basically why people need government—you'd probably be better off if you stole from other people, as if each prisoner himself was more willing to mutiny in the Prisoner's Dilemma.But if everyone thinks that way, the country will be in chaos, and everyone will be worse off, as if two prisoners had mutinied.So people let the government rule them, just like the Death Eaters let the Dark Lord rule them.

(Draco asks Harry to pause again. Draco always thought that aspiring wizards seek power because they want to rule others, and that people allow themselves to be ruled by others because they are scared little Hufflepuffs. And This, on reflection, seems to be true; but Harry's point of view is interesting, even if it is wrong.)

But, Harry continued later, the fear of a third party punishing you is not the only reason for cooperation in the Prisoner's Dilemma.

Suppose, Harry said, that you were playing the game against a magically created replica of yourself.

Draco said that if there were two Dracos, of course neither Draco would want the other to suffer, let alone a Malfoy who would not be known as a traitor.

Harry nodded again, saying it was another solution to the Prisoner's Dilemma - people would choose to cooperate because they cared about each other, or they had a sense of honor, or they wanted to keep their reputations.In fact, Harry says, it's hard to frame a true Prisoner's Dilemma—in real life, people often care about other people, or about their own honor, reputation, the Dark Lord's punishment, or anything other than a prison sentence. anything else.But let's say it's a replica of someone who's downright selfish—

(They used Pansy Parkinson as an example.)

—then each Pansy cared only what would happen to him, and not the other Pansy.

Assuming that's all Pansy cares about...and there's no Dark Lord...and that Pansy doesn't worry about his own reputation...and that Pansy has no sense of honor, or any obligation to another prisoner...then , for Pansy, the reasonable choice is cooperation or betrayal?

Some people, Harry said, insisted that the logical choice for Pansy was to betray her duplicate, but Harry, and someone called Douglas Hofstadt, thought they were wrong.Because, Harry said, if Pansy had chosen to betray—not by accident, but by a seemingly rational choice—then the other Pansy would have thought the same.Two identical replicas don't choose different things.So Pansy has to choose between worlds where both Pansys cooperate, or both Pansys betray.She would be better off if both of them choose to cooperate.And if Harry's "rational people" really chose to defect in the Prisoner's Dilemma, then he wouldn't do anything to promote this "rationality", because a country or gang full of such "rational people" will dissipate into chaos.You will teach your enemies this "rationality".

It all sounded reasonable back then, but now the thought reminds Draco...

"You said," Draco said, "that the logical solution to the Prisoner's Dilemma is cooperation. But of course you'd want me to believe that, wouldn't you?" And if Draco was really tricked into cooperating, ha Li can only say, haha, I betrayed you again!Then laugh at him after the fact.

"I'm not going to cheat on your lessons," said Harry gravely, "but I have to remind you, Draco, that I didn't say you should automatically choose to cooperate. It can't be done in this true Prisoner's Dilemma. I mean, when you make a choice, you shouldn't feel like you're making a choice for yourself, and you shouldn't feel like you're making a choice for everyone. You should think of it this way, that you're choosing for everyone who is similar enough to you to probably Make choices by people who make the same choices for the same reasons you do, and anticipate choices made by people who know you well enough to predict your actions in advance, so that you never have to because of what those people do to you Predicting correctly and regretting making a reasonable choice - reminds me to go back and explain Newcomb's Dilemma [12]. So Draco, the question you and I have to ask is: are we similar enough that we might do anything in the same , make decisions in nearly the same way? Or do we know enough about each other to predict each other's actions so that I can predict that you will choose to cooperate or defect, and you can predict that I will decide to do what I predict , you would have made the same decision because I know you could have predicted that I would have decided?"

...and Draco couldn't help thinking that since he'd only understood half of it with all his might, the obvious answer was "no."

"Yes." Draco said.

A moment of silence.

"I see," said Harry, sounding a little disappointed. "Oh, good. Guess we'll have to think of something else."

Draco didn't think it would work either.

Draco and Harry discussed it back and forth.They'd agreed long ago that what was done on the battlefield wasn't a real-life breach of trust - although Draco was still a little pissed at what Harry had done in Professor Quirrell's office, and said so.

But since neither of them can depend on honor or friendship, it does leave the question of how to bring their Legions together and defeat the Army of the Sun, no matter what Granger might do to sabotage them.Under Professor Quirrell's rules, it's not tempting to let Sun's army kill another army's soldiers - it only makes the score between you and Sunshine even further - but it does tempt both sides to take credit for each other, Instead of behaving like the same army and tempted to shoot another team's soldiers in the melee...

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Hermione walked back to Ravenclaw, not really paying attention to where she was going, her mind was so full of war, treachery, and other ideas that were inappropriate for her age, she turned a corner and ran directly into on an adult.

"I'm sorry," she said automatically, and then, without thinking, "Ouch!"

"Don't worry, Miss Granger," said the cheerful smile, with the sparkling eyes and silver beard underneath, that of the Hogwarts headmaster. "I don't blame you at all."

She stared helplessly at the benign face of the world's most powerful wizard, who was also the first wizard, and the president of the International Federation of Wizards, who had gone mad years ago from the pressure of fighting the Dark Lord, and the many facts one by one. Popping out of her head, a few more little embarrassing screams escaped her throat.

"Actually, Miss Granger," said Albus Percival Wulfric Bryan Dumbledore, "we were lucky to bump into each other. Well, I was wondering about the three of you What is your wish..."

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Saturday dawn was bright and clear, and the voices of the students were quiet, as if the first person to shout would cause an explosion.

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Draco had hoped that they would fight in the upper floors of Hogwarts again.Professor Quirrell said that real battles are more likely to take place in cities than in forests, and fighting in classrooms and corridors should be more similar to this, with ribbons marking available areas.The Dragons performed well in those few battles.

However, as Draco feared, Professor Quirrell had a special surprise in store for this battle.

The battlefield is Hogwarts Lake.

And not on a boat.

They are going to fight underwater.

The giant squid has been temporarily paralyzed; the spell to banish Grindylow has been cast; Professor Quirrell has gone to talk to the merfolk; the underwater activity potion has been given to all soldiers to allow them to breathe, see clearly, talk to each other, and kick You can swim at a slower speed than brisk walking.

A large silver sphere hangs in the center of the battlefield, shining like an underwater moon, to create a sense of direction—at first.As the battle progresses, this moon will gradually become waning, and when it goes completely dark the battle ends - if not before then.

water battle.You can't defend yourself for a week, attackers will come at you from any angle, even with the help of potions, you can't see very far in the dark lake.

If you swim too far from the battlefield, it will start to glow after a while, and it is easy to catch - usually if an army is routed and flees instead of fighting, Professor Quirrell will directly declare them defeated; but today They used a scoring system.Of course there is still some time before you start to shine if you want to be an assassin.

The starting position of the dragon team is arranged in the deep water; the underwater moon shines far above.The dark water was mostly lit by Lumos, but his soldiers would turn off the lights as soon as they started maneuvering.There's no reason to let the enemy see you before you see them.

Draco stepped on the water a few times to float himself higher up, overlooking his soldiers suspended in the water.

The conversation fell silent under Draco's icy stare, and his soldiers looked up at him with satisfying fear and concern,

"Listen to me," General Malfoy said.His voice was deep, and he was a little slurred with the air bubbles. He only frowned, but his voice came out clearly. "There's only one way for us to win. First we'll team up with Chaos, march to the sun, defeat the sun, and then we'll take on Potter and win. It has to be, see? No matter what else happens, these It has to be done—"

Draco then explained Harry and the plan he had conceived.

The soldiers exchanged shocked glances.

"—if any of your tricks thwarts this plan," Draco said finally, "I'll burn you alive as soon as we're out of the water."

There was a nervous "yes sir" voice.

"And everyone who has a secret mission, make sure you get every word," Draco said.

Half of his soldiers nodded visibly, and Draco remembered them as dead when he took power.

Of course all the secret missions are fake, like telling one dragon warrior to pass on a fake traitor mission to another dragon warrior, and then quietly telling the latter to report everything the first guy said.Draco told every dragon warrior that the whole war was about this, and he wanted them to understand that it was far more important than any other plans they had made themselves.With any luck this will keep all the idiots in a good mood, and if reports and pointers