Wednesday, 16 October 2013

Prisoner's Dilemma

Tonight’s lesson was the Prisoner’s Dilemma. I gave her the basic problem in a school setting; you can pick A or B as your grade, and a partner can also pick their grade. If you each give yourself a B, though, you both get Bs.

“I’d pick my best friend as my partner,” The Girl said. “I know I can count on her.”

You don’t get to choose, I said. You might not even meet your partner, or know who they are.

 “That doesn’t sound very fair,” she said. It’s not about being fair, I said – it’s a hypothetical situation to demonstrate the lesson.

I continued: If you pick B and the other guy picks A, you get a C. Her jaw dropped in indignation.

But if you give yourself an A and they pick B, you keep the A and they get a C.

“What happens if we both give ourselves As?” She asked. That’s the penalty, I said. You can only get an A by giving the other person a C. If you both try to give yourself an A, you both get Fs.

“What if you don’t think you really deserve an A?” she said.

You’re fantastic, I said. Too few people ever ask themselves that. But for the purposes of this situation, let’s assume that you want to get the best you can. We went over the details of this a few times to make sure we had it straight, and I took a piece of paper and drew a cross through the middle of the page.

This is called a Punnett Square, I said, a cross to represent the four possibilities …
  1. You and the other person both give yourself a B, and you both keep your Bs.
  2. You can give yourself an A and they can give themselves a B – you keep the A and they get a C.
  3. The same thing in reverse – you give yourself a B. they give themselves an A, and you get a C.
  4. You both try to give yourselves As, and you both get Fs. 
She thought about it. “I would give myself a B,” she said.

Why? I asked. “Because that’s what everybody ought to do,” she said.

I smiled. Why is that what people ought to do? I asked. “Because then everyone would have enough,” she said, “without hurting anyone else.”

I’m really proud of you, I said – people should use that reason more often.

“What do they usually say?” she asked. Well, I said, often people try to get the best they can for themselves, even if it hurts other people. If you’re just trying to do that, picking A is better. But being selfish only works for you if a lot of other people are being selfless.

This is called the Prisoner’s Dilemma, I said, because people used to show it with a story about two people who’d been caught by police, accused of robbing a store and killing someone. They were both guilty of robbery, which is a small crime, but the police couldn’t convict them of murder. So they talked to each prisoner separately and told them they’d be convicted of the small crime, but if they accused the other guy of the murder, they’d be set free. Does that sound familiar? I asked.

“It’s the same thing,” The Girl said.

Right, I said – they could co-operate and both have only a small penalty, or be greedy and go free. If they’re both greedy, though, they both go to prison for a long time.

“If they both just picked B, they’d be okay,” The Girl said.

Yes, I said – but they’re criminals, so you don’t want them to be okay. And they’re not as likely to be honourable to each other because … well, criminals.

“Is it bad people who pick A, and good people who pick B?” she asked.

Generally that’s true, I said – but nothing’s ever that simple, and no one’s a bad person in their own mind. If you have roommates someday, you’ll all need to take turns cleaning, and if you’re tired some night it will be easy to let somebody else do it. We all do that sometimes – you might do it even if you’re not a terrible person. But if everyone does that all the time, the place gets filthy fast.

“So most grownups pick B – or something like it – most of the time?” she asked. 

It’s part of what it means to be a grownup, I said. And when we assume our brakes work, or that the faucet water is clean, or that our rubbish is picked up, we’re relying on a thousand strangers being grown-ups. But what happens if we get everyone picking B?

“Everyone would be okay for everyone else,” The Girl said, Yes, I said, but it wouldn’t be excellent for anyone. And the more Bs there are, the more tempting A gets. So what happens if you get a class full of Bs, and then someone picks A?

“Everyone might go back to A,” The Girl said. “All of the sudden.”

Exactly, I said – trust takes years to build and a moment to break.

“Does that happen a lot?” she asked.

All the time, I said. But then you think at all the time things do work or run on time, and you realise that people are usually doing the right thing, even though everyone thinks everyone else won’t. We’re better than we realise.

As I kissed The Girl good night, I thought of the Jewish legend of the Tzaddikim – righteous people who, as I understand it, prevent God from destroying the world. They look like everyone else, unnoticed, but they are keeping the rest of us alive.

1 comment:

Andy Brown said...

What a good lesson to teach. Did you see that researchers recently ran the experiment with actual prisoners. They did considerably better than the contrasting group of students.

http://www.businessinsider.com/prisoners-dilemma-in-real-life-2013-7