Harry Potter and the Methods of Rationality (63 page)

“Let Chaos reign,” chorused his four Lieutenants.

“My hovercraft is full of eels,” said Harry.

“I will not buy this record, it is scratched,” chorused his four Lieutenants.

“All mimsy were the borogroves.”

“And the mome raths outgrabe!”

That concluded the formalities.

“How goes the confusion?” Harry said in a dry whisper like Emperor Palpatine.

“It goes well, General Chaos,” said Neville in the tone he always used for military matters, a tone so deep that the boy often had to stop and cough. The Chaotic Lieutenant was neatly dressed in his black school robes, trimmed in the yellow of Hufflepuff House, and his hair was parted and combed in the usual look for an earnest young boy. Harry had liked the incongruity better than any of the cloaks they’d tried. “Our Legionnaires have begun five new plots since yesterday evening.”

Harry smiled evilly. “Do any of them have a chance of working?”

“I don’t think so,” said Neville of Chaos. “Here’s the report.”

“Excellent,” said Harry, and laughed chillingly as he took the parchment from Neville’s hand, trying his best to make it sound like he was choking on dust. That brought the total to sixty.

Let Draco
try
to handle that. Let him
try
.

And as for Blaise Zabini…

Harry laughed again, and this time it didn’t even take an effort to sound evil. He really needed to borrow someone’s pet Kneazle for his staff meetings, so he’d have a cat to stroke while he did this.

“Can the Legion stop making plots now?” said Finnigan of Chaos. “I mean, don’t we have enough already -”

“No,” Harry said flatly. “We can
never
have enough plots.”

Professor Quirrell had put it perfectly. They were pushing the boundaries further, perhaps, than they had ever been pushed; and Harry wouldn’t have been able to live with himself if he’d turned back now.

There came a knock at the door.

“That will be the Dragon General,” Harry said, smiling with evil prescience. “He arrives precisely as I expected. Do show him in, and yourselves out.”

And the four Lieutenants of Chaos shuffled out, casting dark looks at Draco as the enemy general entered into Harry’s secret lair.

If he wasn’t allowed to do this when he was older, Harry was just going to stay eleven forever.

The sun was dripping through the red curtains, sending rays of blood dancing across the floor from behind Harry Potter’s grownup-sized cushioned chair, which he had covered in gold and silver glitter and insisted on referring to as his throne.

(Draco was beginning to feel a lot more confident that he’d done the right thing in deciding to overthrow Harry Potter before he could take over the world. Draco couldn’t even
imagine
what it would be like to live under his rule.)

“Good evening, Dragon General,” said Harry Potter in a chill whisper. “You have arrived just as I expected.”

This was not surprising, considering that Draco and Harry had agreed on the meeting time in advance.

And it also wasn’t evening, but by now Draco knew better than to say anything.

“General Potter,” Draco said with as much dignity as he could manage, “you know that our two armies have to work together for
either
of us to win Professor Quirrell’s wish, right?”

“Yesss,” hissed Harry, like the boy thought he was a Parselmouth. “We must cooperate to destroy Sunshine, and only then fight it out between us. But if one of us betrays the other earlier on, that one could gain an advantage in the later fight. And the Sunshine General, who knows all this, will try to trick each of us into thinking the other has betrayed them. And you and I, who know that, will be tempted to betray the other and pretend that it is Granger’s trickery. And Granger knows
that
, as well.”

Draco nodded. That much was obvious. “And… both of us
only
want to win, and there’s no one else who’ll punish either of us if we defect…”

“Precisely,” said Harry Potter, his face now turning serious. “We are faced with a
true
Prisoner’s Dilemma.”

The Prisoner’s Dilemma, according to Harry’s teachings, ran thus: Two prisoners had been locked in separate cells. There was evidence against each prisoner, but only minor evidence, enough for a prison sentence of two years apiece. Each prisoner could opt to
defect,
betray the other, testify against them in court; and this would take one year off their own prison sentence, but add two years to the other’s. Or a prisoner could
cooperate,
staying silent. So if both prisoners defected, each testifying against the other, they would serve three years apiece; if both cooperated, or stayed silent, they would serve two years each; but if one defected and the other cooperated, the defector would serve a single year, and the cooperator would serve four.

And both prisoners had to make their decision without knowing the other one’s choice, and neither would be given a chance to change their decision afterward.

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

Harry had nodded and said that was
one
way to resolve the Prisoner’s Dilemma - and in fact both Death Eaters would
want
there to be a Dark Lord for exactly that reason.

(Draco had asked Harry to stop and let him to think about this for a while before they continued. It had explained a
lot
about why Father and his friends had agreed to serve under a Dark Lord who often wasn’t nice to them…)

In fact, Harry had said, this was pretty much the reason why people had governments -
you
might be better off if you stole from someone else, just like each prisoner would be individually better off if they defected in the Prisoner’s Dilemma. But if
everyone
thought like that, the country would fall into chaos and everyone would be worse off, like what would happen if both prisoners defected. So people let themselves be ruled by governments, just like the Death Eaters had let themselves be ruled by the Dark Lord.

(Draco had asked Harry to stop again. Draco had always taken for granted that ambitious wizards put themselves in power because they wanted to rule, and people let themselves be ruled because they were scared little Hufflepuffs. And this, on reflection, still seemed true; but Harry’s perspective was fascinating even if it was wrong.)

But, Harry had continued afterward, the fear of a third party punishing you was not the
only
possible reason to cooperate in the Prisoner’s Dilemma.

Suppose, Harry had said, you were playing the game against a magically produced identical copy of yourself.

Draco had said that if there were two Dracos, of course neither Draco would want anything bad to happen to the other one, not to mention that no Malfoy would let himself become known as a traitor.

Harry had nodded again, and said that this was yet
another
solution to the Prisoner’s Dilemma - people might cooperate because they cared about each other, or because they had senses of honor, or because they wanted to preserve their reputation. Indeed, Harry had said, it was rather difficult to construct a
true
Prisoner’s Dilemma - in real life, people usually cared about the other person, or their honor or their reputation or a Dark Lord’s punishment or
something
besides the prison sentences. But suppose the copy had been of someone
completely
selfish -

(Pansy Parkinson had been the example they’d used)

- so each Pansy only cared what happened to
her
and not to the other Pansy.

Given
that this was all Pansy cared about… and that there was no Dark Lord… and Pansy wasn’t worried about her reputation… and Pansy either had no sense of honor or didn’t consider herself obligated to the other prisoner…
then
would the rational thing be for Pansy to cooperate, or defect?

Some people, Harry said, claimed that the rational thing to do was for Pansy to defect against her copy, but Harry, plus someone named Douglas Hofstadter, thought these people were wrong. Because, Harry had said, if Pansy defected - not at random, but for what seemed to her like
rational reasons
- then the other Pansy would think exactly the same way. Two identical copies wouldn’t decide different things. So Pansy had to choose between a world in which both Pansies cooperated, or a world in which both Pansies defected, and she was better off if both copies cooperated. And if Harry had thought ‘rational’ people
did
defect in the Prisoner’s Dilemma, then he wouldn’t have done anything to spread that kind of ‘rationality’, because a country or a conspiracy full of ‘rational’ people would dissolve into chaos. You would tell your
enemies
about ‘rationality’.

Which had all
sounded
reasonable at the time, but
now
the thought was occurring to Draco that…

“
You
said,” Draco said, “that the rational solution to the Prisoner’s Dilemma is to cooperate. But of course
you
would want me to believe that, wouldn’t you?” And if Draco was fooled into cooperating, Harry would just say,
Ha ha, betrayed you again!
and laugh at him about it afterward.

“I wouldn’t fake your lessons,” Harry said seriously. “But I have to remind you, Draco, that I didn’t say you should just automatically cooperate. Not on a
true
Prisoner’s Dilemma like this one. What I said was that when you choose, you shouldn’t think like you’re choosing for just yourself,
or
like you’re choosing for everyone. You should think like you’re choosing for all the people who are
similar enough
to you that they’ll probably do the same thing you do for the same reasons. And also choosing the predictions made by anyone who knows you well enough to predict you accurately, so that you never have to regret being rational because of the correct predictions that other people make about you - remind me to explain about Newcomb’s Problem at some point. So the question you and I have to ask, Draco, is this: are we similar enough that we’ll probably do the
same thing
whatever it is, making our decisions in mostly the same way? Or do we know each other well enough to predict each other, so that
I
can predict whether you’ll cooperate or defect, and
you
can predict that I’ve decided to do the same thing I predict you’ll do, because
I
know that you can predict me deciding that?”

…and Draco could not help but think that since he had to strain just to understand
half
of that, the answer was obviously ‘No’.

“Yes,” said Draco.

There was a pause.

“I see,” said Harry, sounding disappointed. “Oh, well. I guess we’ll have to think of some other way, then.”

Draco hadn’t thought that was going to work.

Draco and Harry talked about it back and forth. They had both agreed much earlier that what they did on the battlefield would
not
count as broken promises in real life - though Draco was a little angry about what Harry had done in Professor Quirrell’s office, and said so.

But if the two of them couldn’t rely on honor or friendship, that
did
leave the question of how to get their armies to work together on beating Sunshine, despite everything Granger might try to break them up. Professor Quirrell’s rules didn’t make it tempting to let Sunshine kill the other army’s soldiers - that just increased the bar you had to pass yourself - but it did tempt each side to steal kills instead of acting like a single army would, or to shoot some of the other side’s soldiers during the confusion of battle…

Hermione was walking back to Ravenclaw not really looking where she was going, her mind preoccupied with war and treachery and other age-inappropriate concepts, and she turned a corner and bumped straight into a grownup.

“Sorry,” she said automatically, and then, entirely without thinking, “
Eeeeek!
”

“Don’t worry, Miss Granger,” said the cheerful smile, set beneath the twinkling eyes, and above the silver beard, of the HEADMASTER OF HOGWARTS. “You are quite forgiven.”

Her gaze was helplessly locked on the kindly face of the most powerful wizard in the world, who was also the Chief Warlock, who was also the Supreme Mugwump, who had gone insane years ago from the stress of fighting the Dark Lord, and numerous other facts that were popping up into her mind one after the other while her throat went on making little embarrassing squeaks.

“In fact, Miss Granger,” said Albus Percival Wulfric Brian Dumbledore, “it is quite lucky that we bumped into each other. Why, I was just now wondering curiously what the three of you were thinking of asking for your wishes…”

Saturday dawned bright and clear and with the students speaking in hushed voices, as though the first to shout might set off the explosion.

Draco had hoped that they would be fighting in the upper levels of Hogwarts again. Professor Quirrell had said that real fights were more likely to take place in cities than forests, and fighting inside schoolrooms and corridors was supposed to simulate that, with ribbons to mark the allowed areas. Dragon Army had done well in those fights.

Instead, just as Draco had feared, Professor Quirrell had come up with something
special
for this battle.

The battleground was the Hogwarts Lake.

And not in boats, either.

They were fighting
underwater
.

The Giant Squid had been temporarily paralyzed; spells had been set in place to keep away the grindylows; Professor Quirrell had gone and talked to the merfolk; and all the soldiers had been issued
potions of underwater action
that allowed them to breathe, see clearly, talk to each other, and swim not quite as fast as a fast walk by kicking their legs.

A huge silver sphere hung in the center of the battleground, shining like a small underwater moon. It would help to provide a sense of direction - at first. The moon would slowly go into eclipse as the battle went on, and when it had gone entirely dark, the battle would end if it hadn’t already.