QUANTUM INTERACTION 2013, LEICESTER, UK A Quantum Framework for ‘Sour grapes’ in Cognitive dissonance. Polina Khrennikova, School of Management, University of Leicester

COGNITIVE DISSONANCE BIAS The bias of cognitive dissonance firstly discovered by Leon Festinger in 1950 th Is often referred to as an action- opinion theory, where actions can influence a person’s opinions, beliefs, identity, see also Self- Perception theory by Bem. The term refers to various situations ( contexts) were the individual is faced with conflicting cognitions ( e.g a smoker, a person engaging in an unpleasant activity to reach a goal) An tension in the person’s mental state occurs influenced by his/ her beliefs, emotions, attitudes, identity, and other dissonant elements The choices, opinions and actions are influenced by the personal endeavor to balance the conflicting cognitions and restore the mental harmony ‘The agents that are comfortable with dissonance will likely be able to maintain attitudes that do not conform to their actions while those who prefer a consistent cognitive state will experience a significant swing in attitude as a result of actions that they choose to take ’ ( Kitto, Boschetti, Bruza, 2012, p.8)

COGNITIVE DISSONANCE AND VIOLATION OF BAYESIAN UPDATING Cognitive dissonance type of behavior is biased and inconsistent with the postulates of rational homo economicus. Incorrect updating of new information and the violation of classical probabilistic framework takes place. Individuals are processing information incompletely ignoring some factors not to cause uneasiness and cognitive discomfort -making excuses and lowering the significance of the dissonant element -or exaggerating the importance of some factors Disjunction and Conjunction errors take place e.g the information about unhealthiness of smoking, liking of an ‘ unpleasant boring’ task or job.

OUTLINE OF THE PAPER To show how this type of behavior works in practice we present : a) a ‘gedanken experiment’ in a simplified context b) illustrative experiment ‘the forbidden toy paradigm’ by Aronson and Carlsmith (1963 ) with real data. After presenting the experimental data we will strive for a solution of the cognitive dissonance problem with the help of the quantum framework We use the quantum probabilistic framework to find the interference effect and to test if Born’s rule can be applied for decision probabilities

BAYES RULE AND THE LAW OF TOTAL PROBABILITY

THEORETICAL GEDANKEN EXPERIMENT

“GEDANKEN EXPERIMENT” – OUTCOMES

EXPERIMENT FORBIDDEN TOY PARADIGM

METHOD 22 preschool children ( 11 boys and 11 girls ranging in age from 3.8 to 4.6 years) all children took part in both experimental conditions (Mild and Severe) with a time interval of 45 days Part A: a ranking of the toys two by two, until a choice between 10 pairs of toys is established. The experimenter takes second ranked toy places it on a low board and leaves the room. The child is observed for 10 min through a one way mirror. Part B: the experimenter comes back and gives each child a chance to play with the toys again. After the second ranking list is established. an increase of attractiveness of the toy after the threat in the Severe condition and a decrease in the Mild condition is observed. the authors make an additional experiment on 11 children to establish a baseline for the effect of ´increased desirability’ in S context

ANALYSIS OF EXPERIMNTAL DATA P(L+|M)0.636 P(L-|M)0.364 P(L+|S)1 P(L-|S)0

MOTIVATION FOR USAGE OF QUANTUM FRAMEWORK

QUANTUM PROBABILISTIC REPRESENTATION OF DATA

SUMMARIZING REMARKS we observed non – classicality of children's behavior, were Kolmogorov’s probabilistic framework was violated an illustration of a direct violation of the Bayes formula ( in the gedanken experiment part) was shown We applied to our problem the quantum probabilistic framework and found a positive interference of transition probability amplitudes We checked whether Born’s rule can be applied for this context to obtain the final probabilities As a next step we propose to use dynamical quantum equation for modeling the state transition and finding final choice probabilities we remark that there is no claim about universality of Quantum framework possibly alternative classical probabilistic frameworks could be suggested We primarily strive to accurate and more general mathematical framework

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