"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.
