The Platonist’s Dilemma
“You two miscreants are going away for a long time. Here’s the deal: We have enough on you to put you behind bars for five years. If you talk, you can go home right now. No bid, no record. If you don’t, and your friend does, you’ll be in here for a dime. If you both get conversational, you’ll be guaranteed less than ten years.”
Phillip looked at the guy sitting next to him. Friend? Certainly not. Maybe his partner in crime, but he was never good at long-term relationships to begin with. He’d just met the dude—what was his name? Michael? Max?—a few hours ago, there was no reason to give him preferential treatment. Of course, that also meant M— should not receive unwarranted betrayal.
Phillip thought back to his childhood, playing Blockus with his friends. They’d quickly discovered the ideal strategy was to pair up, work together to block off half the board. Betrayal gave you a slight edge if the other person remained loyal, but not a significant one. Plus, it ended up hurting you both far more than you would benefit from the defalcated space. The utilitarian argument said Phillip should keep his silence.
Matthew looked over at Phillip, watching his mind turn like a 50MHz laptop. Doesn’t the idiot realize the detective can read every facial expression he makes, like the micro frown when the word “friend” was mentioned? Phillip was certainly not a friend; in fact he probably couldn’t even remember Matthew’s name. Regardless, Matthew needed to leave the room with the best possible outcome. Phillip clearly had an IQ at the top of the bell curve, so how could Matthew use that to his advantage?
Matthew enjoyed these kinds of problems. As a kid, his favorite game was Risk. Calculating the odds, buying loyalty and selling integrity, all to gain an upper hand. He always played with the gray pieces, and loved to see the board fill up with a miniature storm of soldiers. He’d gotten very good at the game. Somehow, the more he played, the more innocent he appeared to his competitors. Occasionally Matthew worried he had become a pathological liar, but then he remembered that he didn’t actually believe his lies. Maybe he was a good liar, but that was different; that was good.
Phillip and Matthew looked at each other. Stared into each other’s eyes, judged their decisions. “I’m not talking—you can trust me,” each said with the same unwavering voice. Each believed the other. After all, Phillip was a philosophizing fool and Matthew was a meritable genius.
The detective smiles. Perfect, everything going right on plan. He calls one of his juniors over, tells him all he has to do is sit in the interrogation room with the charge. Wait for them to do the talking.
Matthew goes off with this new detective, to a room not any different than the one he just left. They sit there a few minutes—Matthew doesn’t want to appear too eager to rat out his friend. Then a few minutes more, making his mathematical argument concrete. Game theory says he should always talk: If Phillip betrays him, then he’ll still get a lighter sentence, and if he doesn’t, Matthew would get off scot-free! “Mr. Detective, I’m ready to talk.”
When the door shuts behind Matthew, the first detective begins work on Phillip.
“Phillip, I know you’re not the mastermind here, so I’ll give you a special deal. If you talk, I’ll guarantee you at most three years. If he talks too, he’ll get seven years, but I’m hoping I can nail him for more than a day and a night. Do you want to help me out?”
Phillip reconsiders his options. The utilitarian argument doesn’t apply anymore. No matter what he does, the same number of prison years will be meted out. Plus, utilitarianism doesn’t work in real life. Communism never worked out, and the animal kingdom has no concept of sharing. Evolutionarily, Phillip should work entirely in his best interests. The answer is simple: “Mr. Detective, I’m ready to talk.”
Wait a second. That’s not working in my best interests here. I’m not being brutal enough. The leader of a pride slaughters his opponents children to ensure his genes pass on. Phillip may not be a lion king, but he should certainly act more like The Prince! When he looks back on this interrogation, he wants to be proud of how he accomplished it. He wants to do it right. “Sir, actually, could I confer with my fellow prisoner first?”
Matthew opens his mouth to speak, but then something stops him. Phillip is a sophist. What if his soft brain-matter reasons him into talking? Matthew needs to talk to Phillip first to help him through the math. If both agents are equally intelligent, they should choose the same probability for whether or not to defect. That may be 0 or 1, but it should be the same. Calculating it out… the minimum occurs when both choose not to defect. Matthew will conveniently forget to mention this math assumes they will repeat the experiment several times—after all, Phillip is no Eisenstein, he wouldn’t figure that out on his own. Matthew opens his mouth to speak again. “Sir, actually, could I confer with my fellow prisoner first?”
The detective brings them back together. They’re squirming. Phillip hobbles in. Takes a furtive glance at Matthew. Matthew rolls in with a little more machismo.
“Phillip, I’ve done the math. We both win if we stay silent—here let me show you.”
It’s comical to see Matthew proving carthusianism when he knows it’s all air. He won’t mourn that son’s fate longer than it takes to say, “send me home! He did it!” Phillip listens patiently, nodding along. Then it’s his turn to reply:
“Mufasa, I completely agree. To show how much I agree, I’ve called our mutual friend and instructed him to give you a very friendly talk if you decide that’s a favorite pastime.”
The detective’s smile widens. “Alright, time’s up! You boys are going to separate rooms for some small talk—the weather, if you’re both honest lads, or maybe something with a little more thunder.”
This time Phillip leaves with Detective Junior.
“It’s just you and me now, Matthew. You ready to talk?”
“Absolutely, let me figure out how to begin.”
Matthew is a little rattled from his conversation with Phillip. An outside enforcer! How did he know that changes the game? If I snitch, and he’s not bluffing, I’ll get stitches and end up in a ditch. Matthew reevaluates his analysis of Phillip. The average man may not be nearly as smart as him, but then again, their line of work calls for more deviant specimens. Maybe Matthew had his priors all wrong. Phillip could be far more foxy than he first appeared.
What about the detective? Had he misjudged him too? The whole time Matthew had been trying to maximize his success in this game the detective created, but who’s to say the detective was telling the truth? If Phillip could be so foxy, the detective could be equally devious. The game might just be an illusion, only working as long as Matthew accepts it as an axiom. In fact, that makes the most sense. A court would never trust the word of a convicted criminal—the detective has no reason to lighten Matthew’s sentence if he talks, but he could accidentally implicate himself.
Phillip walks into the neighboring room with a smile. Regardless of his motives, Mormon wouldn’t dream of snitching now. He was a clever chap—trying so hard to convince Phillip to stay quiet, probably because he planned to do the exact opposite. Well regardless, he now had firm motivation to stay silent.
What about the police officer? What could his motivations be? Well, he probably wants to get criminals off the streets. He probably doesn’t care too much how he does it, what with the mind games and all. He probably doesn’t care to be honest as long as he gets that Moroni guy locked up, that’s why he gave different rules to him. Wait, what else could he be lying about? We have enough on you to put you away for five years. If he really does, then why is he playing this game, and why would he allow one criminal to walk out onto the streets just by selling out the other? That goes against his civic duties. The detective must not have any evidence at all!
He leaned across the table, looked at the badge, cleared his throat, and finally began talking.
“I ain’t a snitch, and I ain’t helping you.”