Dr Emmanuel Pothos at Swansea University and Dr. Jerry Busemeyer at Indiana University  developed the model after proving that violations of the 'sure thing' principle demonstrated  by participants in prisoner dilemma games cannot be explained by standard classical probability.

Dr Pothos explains: "The sure thing principle, from standard probability theory, states that if you are going to do action A under state of the world X and you are also going to do action A under the complementary state of the world not-X, then it should not matter whether you have X or not-X in deciding whether to do action A or not. So, in lay terms, if you think 'I will take my coat with me if it is raining' AND you also think 'I will take my coat with me if it is not raining' then it should not make any difference whether it is raining or not, in your decision to take your coat."

"The prisoner dilemma (PD) task shows a violation of this fundamental law of probability theory.  This two player game involves a different payoff depending on whether each person defects or cooperates.  If defecting results in the biggest payoff, then it makes sense that each player defects.  Suppose the payoffs are set so that defection is the best strategy. Then, if you and I were playing the PD game, for example, and I am told you cooperate, I should clearly defect.  If I am told you defect then I should clearly defect as well.  So, according to the sure thing principle, it should not matter whether I am told you cooperate or defect, since I always choose to defect regardless. 

"However, when participants are NOT told what the other person is doing, they often reverse their judgment and decide to cooperate. This is an empirical demonstration of violations of the sure thing principle. Such violations cannot be explained by the standard classical probability theory approaches to modelling cognition.  Quantum mechanics however, offers an alternative probabilistic framework which subsumes classic probability, but allows for violations of the sure thing principle."

"In order to specify a particular quantum probability model for cognition, we need to specify a state vector, which in the example given corresponds to the possibilities of defecting or cooperating. We then need to specify a particular time evolution for the state vector; this time evolution corresponds to the thought process and is computationally implemented by a Hermitian matrix, H.

"Specifying this matrix H is the hardest part of the problem. We have derived a matrix on the basis of two considerations: first, higher payoffs for cooperating/defecting should increase the probability for cooperating/defecting. Secondly, we assume that when we decide to cooperate we are thinking that the other player is probably cooperating as well and vice versa. Psychologically, this is a process of cognitive dissonance (we make our beliefs match our actions). Computationally, this process is the one that can lead to violations of the sure thing principle. Given the above, the resulting model produces good fits to performance."

For further information about the School of Human Sciences at Swansea, visit: http://www.swan.ac.uk/human_sciences/