Quantum Theory May Explain Wishful Thinking

http://www.neuroquantology.com/repository/...y&Itemid=71
Written by Lisa Zyga

Saturday, 18 April 2009 08:20

Humans donâ€™t always make the most rational decisions. As studies have

shown, even when logic and reasoning point in one direction, sometimes

we chose the opposite route, motivated by personal bias or simply

"wishful thinking." This paradoxical human behavior has resisted

explanation by classical decision theory for over a decade. But now,

scientists have shown that a quantum probability model can provide a

simple explanation for human decision-making - and may eventually help

explain the success of human cognition overall.

If you were asked to gamble in a game in which you had a 50/50 chance

to win $200 or lose $100, would you play? In one study, participants

were told that they had just played this game, and then were asked to

choose whether to try the same gamble again. One-third of the

participants were told that they had won the first game, one-third

were told they had lost the first game, and the remaining one-third

did not know the outcome of their first game. Most of the participants

in the first two scenarios chose to play again (69% and 59%,

respectively) , while most of the participants in the third scenario

chose not to (only 36% played again). These results violate the â€œsure

thing principle,â€ which says that if you prefer choice A in two

complementary known states (e.g., known winning and known losing),

then you should also prefer choice A when the state is unknown. So why

do people choose differently when confronted with an unknown state?

In a recent study, psychologists Emmanuel M. Pothos of Swansea

University in the UK and Jerome R. Busemeyer of Indiana University in

the US have presented an alternative framework for modeling

decision-making of this kind, based on quantum probability. As they

note, the original motivation for developing quantum mechanics in

physics was to explain findings that seemed paradoxical from a

classical point of view. Possibly, quantum theory can better explain

paradoxical findings in psychology, as well. In recent years, a

growing number of researchers have investigated using quantum

formalism in cognitive situations, such as in modeling human judgment

and perception. Pothos and Busemeyerâ€™s results are published in a

recent issue of Proceedings of the Royal Society B.

â€œA few decades ago, Tversky and Kahneman (1974) challenged ubiquitous

assumptions regarding what is the most suitable framework for modeling

human cognition,â€ Busemeyer told PhysOrg.com. â€œUntil then, most

psychologists sought to understand cognition using classic probability

theory. In our paper we raise the question, which mathematical

framework is most appropriate for cognitive modeling? In this article,

for the first time, we present a fundamentally different, and more

powerful, approach to probabilistic models of cognition, based on

quantum principles. Employing minimal assumptions, we derive a

Hamiltonian directly from the parameters of the problem (e.g., the

payoffs associated with different actions) and known general

principles of cognition (e.g., a well known phenomenon of cognitive

dissonance); every step in our model is psychologically interpreted

and rigorously justified.â€

Defecting Dilemma

In their study, the scientists compared two models, one based on

Markovian classical probability theory and the other based on quantum

probability theory. They modeled a game based on the Prisonerâ€™s

Dilemma, which is similar to the gambling game. Here, participants

were asked if they wanted to cooperate with or defect from an

imaginary partner. Overall, each partner would receive larger pay-outs

if they defected, making defecting the rational choice. However, if

both partners cooperated, they would each receive a higher pay-out

than if both defected. Similar to the results from the gambling games,

studies have shown that participants who were told that their partner

had defected or cooperated on the first round usually chose to defect

on the second round (84% and 66%, respectively) . But participants who

did not know their partnerâ€™s previous decision were more likely to

cooperate than the others (only 55% defected). It seems as if these

individuals were trying to give their partners the benefit of the

doubt, at the expense of making the rational choice.

As the scientists showed, both classical and quantum probability

models accurately predict an individualâ€™s decisions when the

opponentâ€™s choice is known. However, when the opponentâ€™s action is

unknown, both models predict that the probability of defection is the

average of the two known cases, which fails to explain empirical human

behavior. The problem is that the models are purely rational, meaning

they try to maximize utility.

To address this problem, the scientists added another component to

both models, which they call cognitive dissonance, and can also be

thought of as wishful thinking. The idea is that people tend to

believe that their opponent will make the same choice that they do; if

an individual chooses to cooperate, they tend to think that their

opponent will cooperate, as well. If both partners cooperate, both

will receive a higher pay-out than if both defected. (And if an

individual thought that his opponent would cooperate and so decided to

defect to maximize his own pay-out, he would then be compelled to

assume that the opponent would also defect, according to cognitive

dissonance.) In other words, an individual views his opponent as a

mirror of himself.

The difference between the classical and quantum models lies in how

the rational component and the cognitive dissonance component are

combined. Even after adding the second component, the classical model

predicts that the probability in the unknown scenario must equal the

average of the probability for the two known cases. As such, the

classical model continues to obey the law of total probability, and

fails to explain the violations of the sure thing principle.

In the quantum model, on the other hand, the addition of the cognitive

dissonance component produces interference effects that cause the

unknown probability to deviate from the average of the known

probabilities. While in the classical model an individual is committed

to exactly one preference at any given time, in the quantum model an

individual experiences a superposition of these preferences.

Mathematically, the probability (or amplitude) of defecting in the

unknown scenario is obtained from the superposition of probabilities

(amplitudes) for the two known cases. These interference effects

enable the probability of unknown events to be lower than the

probability of either event individually, which is observed in the

empirical studies.

â€œCognitive dissonance can arise in other decision making situations

and is not limited to games with an intelligent opponent,â€ Busemeyer

said. â€œIn the gambling game, you play against nature. In this case,

however, your belief that you will win the game becomes coordinated

with your intentions to play the game. Cognitive dissonance effects

are not even limited to adult humans but have also been found with

young children and even with nonhuman primates.â€ (See Egan, L. C.,

Santos, L. R. & Bloom, P. (2007). The origins of cognitive dissonance:

evidence from children and monkeys. Psychological Science, 18, 978-

983.)

Quantum Cognition

While classical probability theory is too restrictive to fully

describe human decision-making, this study shows that quantum theory

provides a promising framework for modeling human cognition. In

addition to making accurate predictions of the gambling game and

Prisonerâ€™s Dilemma, the quantum model also agrees with the empirical

evidence that people make the same decision in back-to-back identical

scenarios. In classical models, on the other hand, back-to-back

choices remain probabilistic, which fails to explain human behavior.

â€œClassic probability theory, including Markov processes, must obey the

law of total probability,â€ said Busemeyer. â€œHowever, human judgments

often exhibit interference effects which violate the law of total

probability. Quantum probability was originally developed specifically

for the purpose of explaining interference effects found in physics.

This same mathematical formalism provides an explanation for

interference of thoughts in human judgments.â€

Pothos and Busemeyer hope that further research on quantum probability

models of human cognition could help answer fundamental questions

about the nature of how we think. For example, what does it mean to be

rational? Another example is Schrodingerâ€™s equation, which predicts a

periodic oscillation between choices after a minimum length of time.

This oscillation matches with electroencephalogra phy signals and may

explain why the longer you debate on a decision, the more you

fluctuate. Overall, if our brains use quantum principles, and quantum

computation is known to be fundamentally faster than classical

computation in computers, then perhaps quantum principles can even

help explain the success of human cognition.

More information: Pothos, Emmanuel M. and Busemeyer, Jerome R. â€œA

quantum probability explanation for violations of â€˜rationalâ€™ decision

theory.â€ Proc. R. Soc. B. doi:10.1098/ rspb.2009. 0121.

Last Updated on Saturday, 18 April 2009 08:25