Harry Potter and the Methods of Rationality

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.

War in water. You couldn't defend a perimeter, attackers could come at you from any direction, and even with the potion you couldn't see very far in the darkness of the lake.

And if you swam too far away from the action, you would start to glow after a while, and be easy to hunt down - ordinarily if an army scattered and ran instead of fighting, Professor Quirrell would just declare them defeated; but today they were working on a points system. Of course you still had some time before you started to glow, if you wanted to play assassin.

Dragon Army had been set low in the water at the start of the game; above and far away, the distant underwater moon shone. The murky water was mostly lit by Lumos Charms, though his soldiers would extinguish the lights as soon as they began maneuvers. There was no point in letting the enemy see you before you saw them.