Magical Thinking

Don't blame Al Gore for the idea that "If we lead, China will follow." This view is extremely widespread. Googling  the phrases "China will follow" and "climate change" results in 189,000 pages. It probably came from many sources.

The Naïve Approach. Such games have been studied intensively for 50 years, both in the real world and in experiments. And much has been learned what can make people cooperate when they will cheat. But nowhere in this vast literature will you find a confirmation of Al Gore's claimed solution: "If the United States leads, China will follow."

In fact, if the U.S. leads it will make action by others less urgent but no less costly. This is "solving" the free-rider problem by guaranteeing a free ride. But it is wrong to blame Al Gore. This view is extremely widespread. Googling  the phrases "China will follow" and "climate change" results in 189,000 pages.

Magical Thinking. Although Gore seems oblivious to game theory, Shafir and Tversky, two Princeton game theorists have studied the nature of Gore's strategy with fascinating results. Students played a prisoner's dilemma game with on difference. Some times instead of both moving without seeing the others move, one would move first and the other would be told if the first mover had "cooperated" or not.

When informed of a cooperative first move, 16 percent cooperated in return. But only 3 percent cooperated if told the first mover defected. This does not seem too puzzling. There are 3 percent die-hard cooperators in the world, and a few more who will cooperate if you're nice to them and 84% are natural-born defectors. Now you would think (or at least, I would) that not telling them the first move would not turn any defectors into cooperators. If they won't cooperate with either first move, why cooperate if they don't know which it was?

But here's the mystery. One quarter of the 84 percent defectors (21 percent) turned into cooperators when they did know how the other player moved! That raised the total number of cooperators from 16 to 37 percent. But why?

The only explanation that makes sense is that players think that their action will lead others to act the same. If they lead, then other player will follow. This thought process controls up to 37 percent of the students. That is why, when you tell them that the other player already cooperated, they realized that there is no need and possibility of controlling what has already happened, so they say to them selves, "since they've already cooperated, I don't need to lead them to cooperation by example, so I will defect (cheat) and get a bigger payoff."

Shafir and Tversky call this "quasi-magical" thinking, because there is no way short of magic that one players can influence the other's in a game where both move at once and there is know communication.

Now, the leader follower belief could come from either of two sources. (1) It could be a recognition that when people learn you are cooperative, the chance they will cooperate with you goes up from 3 to 16 percent. (2) It could come from the belief that other's will naturally follow our thinking. View #1 is more sophisticated, but that very sophistication would cause one to realize it was not a sure fire approach. View #2 seems more likely because it's quite common to believe that undetectable thinking has magical power, so it must be much more common to believe that when thinking is made visible by action it will surely carry the day.

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