Paradox

As a single game theory scenario, the prisoner's dilemma is a thought experiment revealing the shortcomings of selfishness. But when treated as an iterative game, it gains a strategic dimension and becomes a powerful working model for understanding human cooperation.

When is our own self-interest best served by going against what reason tells us is our own self-interest?

The prisoner's dilemma is a game theory scenario designed to answer that exact question. The scenario usually looks something like this.

Imagine you are in a casino designed by a depraved psychologist. There are no slot machines, no card games. The only tokens are your own dollar bills. There are only two games.

The first, Game A, is simple: You pay the casino $1, and you always lose. It's sort of like playing the lottery.

The second, Game B, at least gives you a chance to win, but is more expensive and is still stacked in the house's favor. You count your money. If the total is an even amount, you win $3, Otherwise you pay $5.

Suppose you are invited to play a game. You are shown two boxes. The first box is open and contains a thousand dollars. The second box is closed. You are told that it contains either a million dollars or nothing. You can choose to take home either the contents of the closed box, or the contents of both boxes. You cannot open the box until you make your choice.

A paradox

The judge was known for his creative sentences. For this particular prisoner, who had made a habit of ambushing his victims, the judge's death penalty came with an ironic twist. The prisoner would be executed by hanging one morning within the next week, but the actual day of the execution would be a complete surprise. The prisoner would not know which morning it was to be, until the hangman showed up at the cell door.

Simpson's paradox is named after statistician Edward Simpson, who first described the effect in a 1951 paper titled The Interpretation of Interaction in Contingency Tables. Simpson described a scenario where the results of a scientific study appear to support one conclusion, but when the results are split to account for a particular variable, the results show a different conclusion.

“It ain’t what you don’t know that gets you into trouble,” Mark Twain once said. “It’s what you know for sure that just ain’t so.”