4.1.1. Data Analysis General Results

The first set of results displayed in Table 1's first column establishes that distraction i.e., the question related to the non-determinant perspective - has a statistically significant impact on the final choice (*p* = 0.005). This result stands across different specifications see Table A1 in the Appendix A). In particular, it appears that everything else being constant, the predicted probability of choosing ECF is 11.1% lower for an individual in the incompatible condition than for an individual in the control condition. By contrast, there is no statistically significant impact of the compatible question on the final decision (*p* = 0.173). This result is also persistent over alternative specifications. Note however that the effect of the compatible question on the final choice is nonzero. We come back to this later on.

Not surprisingly, there is a statistically significant impact (*p* = 0.046) on the final choice of the declared determinant—i.e., Honesty versus Urgency, which captures an element of preferences. Here again, the influence is robust to alternative specifications (see Table A1 in the Appendix A). More precisely, the predicted probability of choosing ECF is 6.33% higher for an individual claiming that Honesty is determinant than for someone who reported Urgency as determinant to her choice. By contrast there is no statistically significant impact (*p* = 0.7) of the order of presentation of the project descriptions on the final decision.

The correlation between covariates were not bigger than −0.13 (between Age and Male)—hence putting aside potential issues of multicollinearity. In particular, regressing on revealed preferences (i.e., choice between Honesty and Urgency) shows no relationship with the order of presentation of the descriptions (ECF-TF and TF-ECF). Interestingly, none of the variables significantly affected the revealed preferences.



*Note:* <sup>∗</sup> *p* < 0.1; ∗∗ *p* < 0.05; ∗∗∗ *p* < 0.01. Coefficients are transformed as : *exp*(*β*) − 1.

#### Advanced Results

As shown by Table 1, we find that the distraction effect is not homogeneous across subgroups. First, we find that the distraction effect was stronger in the Urgency subgroup than in Honesty subgroup: for Urgency-individuals, the predicted probability of choosing ECF in the incompatible condition is 14.93% lower compared to the control condition (*p* = 0.051); for Honesty-individuals, it is 10.05% lower (*p* = 0.031). Next, it appears that the impact of distraction is most pronounced for those who were presented the Tiger Forever project first and Elephant Crisis Fund last (TE subgroup; see Table 1). Distraction statistically significantly affected the final choice in that group (corresponding to 50% of the respondents). In fact, TE-participants in the incompatible condition had a predicted probability of choosing ECF that was 16.3% lower than TE-participants in the control condition (*p* = 0.006; see Table 2).

**Table 2.** Predicted Probability Difference between Incompatible and Control condition.


When combining the TE presentation order with the Honesty subgroup: the difference in predicted probability to choose ECF between the incompatible condition and the control condition is 17.9% (*p* = 0.01). For ET-Urgency a 17.4% change in probability can be seen (cf. Figure 3, Tables 2 and 1), even though the effect fails to reach statistical significance at the 5% level (*p* = 0.097). Note however that group only constitutes around 15% of the sample, while the TE-Honesty subgroup represents around 34% of the data. For the other two subgroups, distraction had no statistical significant impact (*p* = 0.555), but a switch of 12.5% may still be noticed for TE-Urg.

#### 4.1.2. Interpretation

First, we note that the significance of preferences (i.e., the answer to "what is determinant to your choice") for the final choice combined with the fact that a majority of participants who chose Honesty also chose ECF regardless of their condition, suggests that the initial texts were generally well-understood. As explained earlier, the description of the Elephant project was designed to suggest more trust to the NGO managing the project and the description of the Tiger project to suggest a higher level of urgency.

The general results show with no ambiguity that the question triggered by the incompatible information (distraction) had a significant impact on the final choice. It induced some extent of switch as compared to both the control group and the compatible information group. Interestingly, the switch does not reflect the thematic content of the screens. This is consistent with the fact that the information in the screens did not favor any one of the projects. The quantum model provides an explanation for why Urgency individuals made aware of corruption problems reduced their support for ECF (presumably managed by the more reliable WWF). Distraction can induce such change. This is the case for example when the two perspectives (Urgency and Honesty) are uncorrelated (45◦ rotation as in the example) for a class of project-states and preferences. And it does seem reasonable to expect no or minimal correlation between Urgency of the cause and the Honesty of the NGO (in people's mind). The fact that the compatible information had no statistically significant impact supports the thesis that being simply exposed to a general information screen does not affect the choice. Instead it is only when the appending question induces a change in perspective that something happens.

We found significant variations between subgroups. First, we could exhibit a distinction in the reaction to distraction depending on preferences alone. On average, Urgencyindividuals have been more sensitive to distraction than Honesty-individuals. This could be explained by a the fact that Urgency people tend to be more passionate about the situation. A passionate individual may feature a more pronounced quantum-like working of

the mind because she is expected to be less constrained by the rational mind (see below for further arguments).

More intriguing is the fact that when combining preference and the order of presentation, we find that individuals whose preferences are congruent with the last presented project (TE-Hon and ET-Urg) tend to be more sensitive to distraction. The order of presentation of the projects is an element of the "preparation procedure '( in QM, the state of a quantum system is determined by a suitable preparation procedure). One possible explanation is that "congruent respondents" are more manipulable because both beliefs and preferences are indeterminate. Although this paper focuses on the indeterminacy of beliefs, both beliefs and preferences are mental objects that we expect can exhibit quantumlike properties. Indeed a number of works in quantum cognition address preference indeterminacy (see for instance [55]). As we discuss in the next section the rational mind tends to constrain the quantum-like working of the mind. We can thus conjecture that "congruent respondents" include respondents for whom the rational mind was less constraining. Their preferences were partly determined by the information received just before they had to respond to "what is most important for you?". This line of interpretation goes outside of our quantum model which focuses on beliefs indeterminacy however. It suggests that future research in quantum cognition should address both determinants of decision-making simultaneously.

Even when looking more closely at the results, we find no statistically significant impact of the compatible question. This is consistent with the Bayesian model because no information relevant to the choice between the two projects is provided. Note however that, despite the lack of statistical significance, the effect in the compatible condition is nonzero. We note that in the ET-Honesty subgroup is close to the effect of the incompatible condition. We recall that the theoretical model predicts some mild impact on the belief state. An U-individual who chooses TF on the basis of mixed beliefs will choose ECF with some probability if she is forced to decide for herself whether the cause is urgent YES or NO, prior to decision (see Section 2.3.4). The same holds for those who choose ECF while holding mixed beliefs. We conjecture that, at the sample level these effects also counter-balance each other so the overall impact is not statistically significant.

The time for responding to the whole questionnaire was between 1 and 3 min which is rather short. We interpret this feature as an evidence that the quantum working of the mind could be part of what Nobel prize Kahneman calls System 1—the fast, non-rational reasoning [12]: no new information of relevance for the choice was provided yet decision-making was affected. The respondent did not take time to reflect, they reacted spontaneously to the distraction. Recall that we do not elicit their preferences for the projects but only for what is determinant in a class of situations. That choice in our experiment was made to minimize interference from the rational mind. Nevertheless, we found that those determinants were highly correlated with the final choice both in the control and compatible information groups. The significance of the impact of distraction distraction results suggest that as we had conjectured respondents were not aware of the correlation (and the logic behind it). Therefore, they were not confronted with a (conscious) cognitive dissonance when the distraction changed their focus and eventually affected their decision. In the same line of thoughts the respondents overwhelmingly passed the chance to reassess their understanding of the project before making their choice. Only 12% used the opportunity re-read before making their choice.

An interesting finding is that the results are fully independent of population variables which supports the hypothesis that the quantum-like structure is a general regularity of the human mind.

#### **5. Concluding Remarks and Discussion**

In this paper, we have proposed an explanation of the manipulability of people's decision-making based on the intrinsic indeterminacy of the individual's subjective representation of the world. We first developed a simple quantum model of choice between

two uncertain alternatives. Compared with the classical approach, the main distinction is in the modelisation of uncertainty. Where the classical approach relies on a single integrated representation on the world, the quantum-like modelling of uncertainty allows for a multiplicity of equally valid but subjectively incompatible perspectives on the world which is the expression of the intrinsic indeterminacy of mental objects. We show how an indeterminate representation of the world can be exploited to manipulate a decision-maker by a Sender who simply asks questions. Our focus has been on introspective questions, that is question about beliefs that bring no new information from the outside world. This allows establishing a clear distinction between the classical model's predictions and the quantum one. In particular, we show with an example that the quantum model predicts that distractive questions have strong persuasion power when the classical model predicts no impact of such questions at all.

We provided a first empirical test of that prediction in an experiment where individuals choose between supporting either one of two projects to save elephants respectively tigers. In the experiment that we performed, the change of focus or of narratives brought about by the distractive question was shown to statistically significantly affect revealed preferences for the projects. This central result is in accordance with the predictions of the quantum model when dealing with two incompatible perspectives here Urgency and Honesty. Looking closer, we find some significant differences in reaction between subgroups, with some reacting very strongly and others much less so. While this calls for further investigation, we find that this first experimental test was successful in providing some support for the hypothesis that the manipulability of people may have its roots in the indeterminacy of their subjective representation of the world.

In the real world however, a cause can simultaneously be urgent and the NGO supporting the project dishonest. There is thus a discrepancy between the properties of the true classical objects (the projects) and the properties of their representation, the mental objects (project-states). When Receiver processes information about a classical object as if it was a quantum system, she is mistaken. But as amply evidenced in Kahneman's best selling book "Thinking Fast and Slow", information processing is not always disciplined by (Bayesian) rational thinking when the brain operates quickly. The two-system approach does also open the way for manipulation because when the individual thinks fast she makes mistakes which could be exploited. Our view is that the quantum approach rather than being an alternative to most behavioral explanations, provides a rigorous foundations to a number of them. The interpretation that arises from its structure can however be different. Quantum cognition proposes that all forms of thinking are contextual due to the intrinsic indeterminacy of mental objects including beliefs and preferences. Conscious thinking may however interfere and constrain contextuality. Galberti [44] relies on a similar argument to explain Receiver's resistance to change worldview. The reason is that individuals have a resistance to changing their mind without a "good reason" due to drive toward consistency. This drive needs not be related to true rationality however but instead to an entrenched attachment to a stable identity or ego. The existence of a stable identity has been questioned by numerous experimental results (see e.g., self-perception theory and [56]). Those studies are consistent with a contextual and thus unstable identity [56]. As in the two-system approach the extent of conscious thinking matters. This is because the drive toward maintaining a coherent ego is more effectual when the individual is conscious about her instability. As argued in [55] cognitive dissonance and its resolution is an expression of that drive in face of instability (arising from intrinsic indeterminacy). We close this short discussion by suggesting that the quantum-like nature of mental objects needs not reflect a cognitive failure but would be the expression of the intrinsic indeterminacy (contextuality) of *human reality*. The question of rationality in such a context deserves further investigation.

Finally, we recognize that quantum cognition experiments cannot have the same degree of precision of physical experiments which prevents making and testing quantitative predictions. To a large part, this is because it is (today) impossible to fully characterize the state of a cognitive system which is incommensurably more complex that of an atomic particle. Nevertheless, our experimental exercise shows that it may be useful to test some theoretical predictions in contrast with standard classical (Bayesian) ones.

**Author Contributions:** Theory: A.L.-M.; Methodology: A.L.-M., A.C.; Data analysis: A.C.; Writing: A.L.-M., A.C. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Paris School of Economics' small grants.

**Institutional Review Board Statement:** Not requested by funding agency.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** We would like to thank seminar participants at Paris School of Economics and at the QI2028 symposium for their enriching comments as well as Jerome Busemeyer for a very valuable suggestions on the design of the experiment.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

**Table A1.** Alternative Specifications.


Note: ∗ *p* < 0.1; ∗∗ *p* < 0.05; ∗∗∗ *p* < 0.01

## **References**

