Prisoners, Games, and Kant
Saturday August 5, 2006 by Patrick N. R. Julius
Mathematics is, at its core, an extension of rational thought. It takes the basic principles of logic, and through definition and deduction alone, expands it into a complete system of reasoning in its own right.
But today I’d like to go back to the roots of mathematics, the question of what makes our choices rational.
The prisoner’s dilemma leaps to mind; it’s always an interesting puzzle to consider, and it forces us to question what rationality really is.
What’s this dilemma? It has many versions, but here’s mine—-it places the stakes a little higher than most. You have been captured by the Russian Mafia. You also learn that another person, Steve, whom you have never met, is likewise captured.
The Russians believe you and Steve are working together in a plan to blackmail one of their agents. You have no such plans, but they don’t believe you when you say so.
You are placed into an interrogation room, and asked to confess to collusion with Steve.
If you confess and Steve refuses, you will be released, but Steve will be executed. If you do not confess, and Steve does, you will be executed, and Steve will be released. If you both confess, you’ll both be tortured for the rest of your lives. But if you both refuse, you’ll both be detained for one year.
In other words, this is a bad situation, in which you have two bad options—-a dilemma.
Now, if we stick to mathematics as it is commonly understood, we go to game theory. In game theory, it’s every (hu)man for himself, and you’re out for your own best interest.
Well, consider the options Steve has:
If he confesses, you’ll be tortured one way, and executed the other way. So obviously the first way is better.
If he doesn’t confess, you’ll be set free one way, and detained the other way. Again, the first way is better.
Game theory’s answer is clear, for the Nash Equilibrium is obvious: you both confess. And hence you are both tortured. Nicely done.
Where does this go wrong? Wasn’t it rational to confess either way?
No, it wasn’t! It was totally irrational! You should keep your mouth shut!
Why? Because rationally runs deeper than mathematics. Life isn’t game theory—-and it’s not always about you.
Immanuel Kant understood this, and in formulating his theory of rational ethics, disregarded any notions of “self-interest” or “individual pleasure,” for he recognized something subtle but important: seeking your self-interest is not in your self-interest.
Sounds really weird, but think about it; if everyone in the world analyzed life with game theory, any time we got in a prisoner’s dilemma sort of situation, we’d all end up screwed.
As Kant realized, we can only truly achieve our best interest if everyone agrees to the rules. Society only works if the rules can be generalized, or as he said, “universalized.” You don’t act for your own self-interest in each and every decision; you act for your own self-interest in the formulation of general rules.
Hence, the general rule here would be, “do what’s best for both prisoners.” And so neither of you confess, and once the year is up, you’ll be let go, to go on with your life.
Now, what if Steve doesn’t feel this way? What if he decides to betray you, and confesses anyway? Ultimately, that’s out of your control. If Steve isn’t as Kantian as you, you might end up dead by his malfeasance. But at least you’ll have done the right thing.
And the only way society can work is by people doing the right thing, not the thing whis is “rational”—-which is only apparently so.
Besides, Steve’s conscience will catch up with him eventually.
I don’t think this is true. At least, not in this particular situation. This is a one-time thing. And if you screw it up, you’re dead. And the only way to guarantee that you don’t end up dead is to betray Steve.
It is not necessarily the most moral thing to do, and it does not help society as a whole, but it is the most rational thing to do in terms of self-interest.
The thing is, the situations in which seeking your own self-interest isn’t in your self-interest are the repeated ones. If you’re planning to play several games of prisoner’s dilemma, the best thing to do is not to betray your partner until your partner betrays you. This has been shown mathematically, and if everyone playing follows this rule, not only does each individual playing get the least amount of jail time possible, but the group as a whole does as well.
But in life or death situations, morality and rationality generally show completely different courses of action.
— Hallie Aug 7, 01:21 PM #