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quantum machine learning

34 A. Lambert-Mogiliansky et al.

about the exact correlation coe cients between the two perspectives, we do not have precise quantitative predictions.

4 Results

Data were processed, cleaned and analyzed with Stata. Mainly due to missing values, but also to solve a technical misstep8 and in order to equally balance the number of participants in each condition, 471 participants had been removed from the data. Probit regression models were conducted to analyze the impact of the variables of interest.

4.1Descriptive Statistics

As shown in Table 2, overall, 72,7% of the participants valued the Honesty of the NGO more than the Urgency of the cause, 87,2% made their final decision without reading the descriptions a second time, and 54,6% voted for Elephants Crisis Fund (ECF). Furthermore, after further distinctions, we observe that while most of participants preferred elephants to tigers in the control condition and in the compatible one (59% and 56% respectively), the tendency reverses for the incompatible condition (51% chose tigers). Regarding the revealed preferences, overall, the majority of participants who preferred Urgency chose Tigers (52%), whereas the majority of those who preferred Honesty chose Elephants (57%).

Table 2. Descriptive statistics

Variable

Mean

Std. Dev.

 

 

 

ChoiceHU

0.727

0.446

 

 

 

DecisionRead

0.872

0.334

 

 

 

FinalChoice

0.546

0.498

 

 

 

Age

35.368

10.522

 

 

 

Gender

0.606

0.489

 

 

 

Education

1.98

0.706

 

 

 

NGO

0.424

0.495

 

 

 

Notes. ChoiceHU-choice between Urgency (=0) and Honesty (=1); DecisionRead-decision to read the descriptions again (=0) or not (=1); FinalChoice-final choice between Tigers (=0) and Elephants (=1); Gender-females (=0) and males (=1); Education-highest level of formal education between secondary school (=0), high school (=1), undergraduate (=2), graduate and over (=3); NGO-donation of either nothing (=0) or something (=1) in the last 3 years.

8Some participants were likely to have taken the questionnaire twice and so were deleted.

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quantum machine learning

The Power of Distraction: An Experimental Test of Quantum Persuasion

35

4.2Data Analysis

As Table 3 shows, the first set of results establishes that incompatible information has a statistically significant impact on the final choice (p-value = .011), whereas the compatible information did not significantly lead to di erent results compared to the baseline (p-value = .314). The e ect of the incompatible condition on the final decision thus seems to be as expected i.e. it significantly reverses the direction of the choice observed in the control condition. More precisely,

everything else being constant, the predicted probability of choosing Elephants is 10.52% (marginal e ect ) lower for an individual in the incompatible condition.

Table 3. Regression matrix for Final Choice

 

(1)

(2)

(3)

(4)

(5)

 

FinalChoice

FinalChoice

FinalChoice

FinalChoice

FinalChoice

 

 

 

 

 

 

FinalChoice

 

 

 

 

 

 

 

 

 

 

 

Info

0.0936

0.100

 

 

0.105

 

(0.364)

(0.335)

 

 

(0.314)

InfoIncomp

0.270

0.259

 

 

0.265

 

(0.009)

(0.013)

 

 

(0.011)

Age

 

0.00198

 

0.00261

0.00171

 

 

(0.630)

 

(0.523)

(0.679)

 

 

 

 

 

 

Gender

 

0.0768

 

0.0820

0.0695

 

 

(0.381)

 

(0.347)

(0.429)

Education

 

0.00852

 

0.0212

0.0177

 

 

(0.888)

 

(0.726)

(0.771)

NGO

 

0.000512

 

0.00357

0.00885

 

 

(0.995)

 

(0.967)

(0.919)

Order

 

0.00660

 

0.00882

0.00982

 

 

(0.938)

 

(0.917)

(0.908)

 

 

 

 

 

 

ChoiceHU

 

 

0.214

0.210

0.213

 

 

 

(0.023)

(0.026)

(0.024)

 

 

 

 

 

 

DecisionRead

 

 

 

 

0.0428

 

 

 

 

 

(0.739)

cons

0.236

0.225

0.0408

0.0444

0.138

 

(0.001)

(0.313)

(0.610)

(0.841)

(0.597)

p-values in parentheses

= p ≤ 0.05, = p ≤ 0.01, = p ≤ 0.001

Not surprisingly there is also a significant impact on the final decision of the choice of determinant (p-value = 0.024) i.e., honesty versus urgency which captures the preferences. In other words, those who claimed to prefer Honesty

chose Elephants significantly more than those who preferred Urgency regardless of the condition in which they have been assigned(p-value = .025). Everything

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quantum machine learning

36 A. Lambert-Mogiliansky et al.

else being constant, the predicted probability of choosing Elephants is 8.44% (marginal e ect ) higher for an individual who preferred Honesty. All of these

e ects remained significant when the other variables were included or removed from the regression. None of the control variables (order of the descriptions included) seemed to significantly influence the final decision, which means that the di erence in decision-making were essentially not due to the sample heterogeneity. Similarly, the decision to reread descriptions did not significantly impact

the final choice (p-value = .740). Both the compatible and incompatible condition significantly lead to a tendency to read the descriptions again (p-value =

.001 and p-value = .006, respectively). In other words, the more information, the more one reads previous information again. We are currently working on further investigation of the data in a companion paper.

4.3Interpretation

In line with our hypotheses, our results show with no ambiguity that incompatible information - that is “distraction” - has a significant impact on the final choice by inducing some extent of switch as compared to both the control group and the compatible information group.

These results are fully consistent with the predictions of the quantum persuasion model and contradict the predictions of the Bayesian model with respect to the impact of incompatible information. Moreover the fact that general compatible information had no impact also supports the view that it is not merely “information” that a ects the choice because the person is slightly “upset”. Instead it is when information induces a change in perspective that something happens even though nothing of relevance is learned.

In addition, the participants’ age, gender, level of education or experience with NGOs had no e ect on the decision to vote for ECF or TF. The final choice seemed to depend only on the descriptions, the conditions and participants’ own beliefs and preferences. We can therefore conclude that our distraction e ect – or change of focus – is quite stable among individuals. This supports the hypothesis that the quantum-like structure is a general regularity of the human mind.

The importance of elicited preferences i.e., the answer to “what is determinant to your choice” to the final choice underlines that the initial texts were well-understood. The description of the Elephant project was designed to suggest more trust to the NGO, while the Tiger project aimed at suggesting higher level of urgency. That explains why respondents who declared Honesty (resp. Urgency) to be determinant were significantly more likely to support the Elephant Crisis Fund (resp. Tiger Forever).

The average time to respond to the questionnaire was between 1 and 2 min, which is rather quick. In addition only a tiny proportion of participants (15%) actually used that opportunity to reassess their understanding of the project by rereading the projects descriptions. These two facts support the idea of an absence of conscious reasoning, that is, the respondents did not take time to reflect and reacted spontaneously to the distraction. This is particularly interesting for us since the quantum working of the mind is not rational reasoning: