Abstract
This paper elaborates on a well-known and widespread bias -‘cognitive dissonance’. The bias occurs when a person has conflicting cognitions framed by his/her values, beliefs etc. In such complex situations the individual choices and actions become emotionally tinted and thus inconsistent with the postulates of rational homo economicus. We evidence that classical probabilistic updating of information does not work correctly: hidden factors and motivations come into play to balance the conflicting cognitions and restore mental harmony. To support this inference we present a scheme of a ‘gedanken experiment’ in combination with known statistical data from a real experiment, the forbidden toy paradigm. Our findings show that the phenomenon of cognitive dissonance is a source of probabilistic non-classicality directly violating Bayes formula for conditional probability and so the law of total probability. Furthermore, we aim to show with the help of the quantum framework that the quantum probability formula and Hilbert space state representation of observables can well account for the ‘incorrect behavior’ among participants.
Sour grapes: Is a metaphorical illustration of the cognitive dissonance bias, from the fable “The fox and the grapes” by Aesop [17]. The fox cannot reach the grapes on the tree and convinces himself that he doesn’t want them after all because they are sour.
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- 1.
Self-perception theory is an alternative explanation for the biased behavior, based on the idea that we mainly act to observe our actions, hereby forming our identity. The term was first introduced by Bem, see [5].
- 2.
We do not elaborate on the ethical side of the experiment where the word ‘punishment’ could possibly cause anxiety and stress of small children. The data is chosen purely for illustrative purpose.
- 3.
We make an important note that in the real forbidden toy experiment P(G+|S) = 0 and P(G+|M) = 0. This is a disadvantage for our theoretical study, since “nobody playing’’ result implies zero/one probabilities, which are not very convenient for quantum-like analysis. For that reason the probabilities in this part are ‘theoretical’ to illustrate the principle of Bayesian updating scheme. In further works we consider to perform analogous studies for statistical data with nonzero probabilities.
- 4.
The same data can be collected by taking the record of children’s distribution between experimental contexts. By employing the direct question scheme we bring a closer analogy with the measurement in quantum physics. In our “gedanken experiment’’ in part B the experimenter searches to find out the contextual structure of the part A. To make our experiment more real, we could proceed with two different experimenters: one person that is setting up part A of the experiment and the second experimenter that comes into the room in part B (after the children were allowed to play) and gets to know about the contextual structure of part A from the children’s behavior.
- 5.
We remark that the observers choose for their purposes not the absolute favorite but the second ranked toy (N2). The authors explain their choice by giving the children space to increase the desirability of the toy. The obtained frequencies could be very different if the children had to abstain from playing with the most favorite toy e.g. they would still play with it despite the threat condition.
- 6.
Detailed depiction of the experimental conditions and experimenter’s phrases can be found in the original text [2].
- 7.
Other possible factors behind the increased desirability highlighted in the paper: the children paid more attention to the N2 toy, because the experimenter enhanced its value by the impossibility to play with it. Also the participants were likely to become bored playing with other toys thus favoring the key toy more.
- 8.
The ½ frequency is a common type of group division within experiments e.g., Hawaii experiment, Gambling experiment by Tversky and Shafir [22]. The participants are either equally divided in two groups or the same number of participants is firstly placed in one group and after a time period in the second group. It enables to compare face to face the change of preferences. In the toy experiment we directly see that liking for the toy decreases with ca. 36 % for those kids who are in the M group. Another group division would give a similar result.
- 9.
Contains those participants, who ranked the toy higher or the same after the threat context. Since the increased desirability of the toy is not a consequence of a particular condition, we treat it similarly as the ‘not-decreasing desirability’.
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Acknowledgments
I would like to thank the participants of Quantum Interaction 2013 Conference and Prof. Ehtibar Dzhafarov for fruitful discussion and useful comments that contributed to the accomplishment of this paper.
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Khrennikova, P. (2014). A Quantum Framework for ‘Sour Grapes’ in Cognitive Dissonance. In: Atmanspacher, H., Haven, E., Kitto, K., Raine, D. (eds) Quantum Interaction. QI 2013. Lecture Notes in Computer Science(), vol 8369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54943-4_24
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