Classical probability can’t explain this. If the first player knew for sure that the second was cooperating, it would make most sense to defect. If the first knew for sure that the second was defecting, it would also make most sense to defect. Since no matter what the other player is doing, it’s best to defect, then the first player should logically defect no matter what.
A quantum explanation for why player one might cooperate anyway would be that when one player is uncertain about what the other is doing, it’s like a Schrödinger’s cat situation. The other player has the potential to be cooperating and the potential to be defecting, at the same time, in the first player’s mind. Each of these possibilities is like a thought wave, Wang says. And as waves of all kinds (light, sound, water) are wont to do, they can interfere with each other. Depending on how they line up, the can cancel each other out to make a smaller wave, or build on each other to make a bigger one. If “the other guy’s going to cooperate” thought wave gets strengthened in a player’s mind, he might choose to cooperate too.
The making of a decision collapses a thought wave into a particle, according to Jerome Busemeyer and Peter Bruza’s book Quantum Models of Cognition and Decision. “We argue that the wave nature of an indefinite state captures the psychological experience of conflict, ambiguity, confusion, and uncertainty; the particle nature of a definite state captures the psychological experience of conflict resolution, decision, and certainty,” they write.
The act of answering a question can move people from wave to particle, from uncertainty to certainty. In quantum physics, the “observer effect” refers to how measuring the state of a particle can change the very state you’re trying to measure. In a similar way, asking someone a question about the state of her mind could very well change it. For example, if I’m telling a friend about a performance review I have coming up, and I’m not sure how I feel about it, if she asks me “Are you nervous?” that might get me thinking about all the reasons I should be nervous. I might not have been nervous before she asked me, but after the question, my answer might become, “Well, I am now!”
This doesn’t necessarily happen every time someone asks you a question—some answers you just know, you don’t have to make them up on the spot, which means there might not be an observation effect. “For many questions you do have a stored answer that is simply retrieved on demand (e.g. Have you ever read a certain book?),” Busemeyer and Bruza write. “But other questions are new and more complex and you have to construct an answer from your current state and context (e.g. Did you like the moral theme of that book?).”
Another key concept in quantum cognition is the idea of “complementarity.” Two ideas are complementary if they are incompatible, if you can’t think about them both at the same time. This is similar to the uncertainty principle in quantum physics, which states that if you are certain of a particle’s position in space, you must necessarily be uncertain of its speed, and vice versa. Translated to decision-making, this means that if you are certain about what you think about one thing, you can’t simultaneously be certain what you think about another thing.