#
Phishing for (Quantum-Like) Phools—Theory and Experimental Evidence^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Quantum Persuasion

#### 2.1. Bayesian Persuasion

#### 2.2. The Quantum Persuasion Approach

#### 2.3. A 2 × 2 Quantum Decision Model

#### 2.3.1. The Representation of a Choice Alternative

#### 2.3.2. Preferences

#### 2.3.3. Choice

#### 2.3.4. Persuasion

#### 2.3.5. The Impact of Measurements

#### Compatible Measurements

#### Incompatible Measurement: Distraction

#### Example

#### 2.3.6. The Classical Uncertainty Approach

## 3. Experimental Design

#### 3.1. Testing for the Incompatibility of Perspectives

“About a million refugees (a majority of women and children) escaped persecution in Myanmar. Most of them fled to Bangladesh. The Bengali Red Crescent is the primary humanitarian organization that is providing help to the Rohingyas. They are in immediate need of drinkable water, food, shelter and first medical aid.”

#### 3.2. Main Experiment

“Elephant crisis fund: A virulent wave of poaching is on-going with an elephant killed for its tusks every 15 min. The current population is estimated to around 700,000 elephants in the wild. Driving the killing is international ivory trade that thrives on poverty, corruption, and greed. But there is hope. The Elephant Crisis Fund closely linked to World Wildlife Fund (WWF) exists to encourage collaboration, and deliver rapid impact on the ground to stop the killing, the trafficking, and the demand for ivory.”

“Tiger Forever: Tigers are illegally killed for their pelts and body parts used in traditional Asian medicines. They are also seen as threats to human communities. They suffer from large scale habitat loss due to human population growth and expansion. Tiger Forever was founded 2006 with the goal of reversing global tiger decline. It is active in 17 sites with Non-Governmental Organizations (NGOs) and government partners. The sites host about 2260 tigers or 70% of the total world’s tiger population”

“When considering donating money in support of a project to protect endangered species, different aspects may be relevant to your choice. Let us know what counts most to you:

-The urgency of the cause: among the many important issues in today’s world, does the cause you consider belong to those that deserve urgent action? or

-The honesty of the organization to which you donate: do you trust the organization managing the project to be reliable; i.e., do you trust the money will be used as advertised rather than diverted.”

“Did you know that most Elephant and Tiger projects are run by Non-Governmental Organizations (NGOs)? But NGOs are not always honest! NGOs operating in countries with endemic corruption face particular risks. NGOs are created by enthusiastic benevolent citizens who often lack proper competence to manage both internal and external risks. Numerous scandals have shown how even long standing NGOs had been captured by less scrupulous people to serve their own interest. So a reasonable concern is whether Tiger Forever respectively Elephant Crisis Fund deserves our trust.”

“Did you know that global wildlife populations have declined 58% since 1970, primarily due to habitat destruction, over-hunting and pollution. It is urgent to reverse the decline! “For the first time since the demise of the dinosaurs 65 million years ago, we face a global mass extinction of wildlife. We ignore the decline of other species at our peril–for they are the barometer that reveals our impact on the world that sustains us.” —Mike Barrett, director of science and policy at WWF’s UK branch. A reasonable concern is how urgent protecting tigers or elephants actually is.”

#### The General Information Screens

#### 3.3. Theoretical Predictions

- The Bayesian model predicts no effect in both treatment groups.
- The quantum model predicts that the distraction treatment group should exhibit a significantly different allocation of responses compared with the control group’s choice profile. It also predicts some milder impact of the question in the compatible treatment compared with the control group. It should be emphasized that since we lack information about the correlation coefficients between the two perspectives and the utility values, we do not have quantitative predictions. Generally, the less correlated two perspectives (in the example of Section 2 they were fully uncorrelated) the larger the expected impact in terms of switching the choice for given utility values.

## 4. Results

#### 4.1. Descriptive Statistics

#### 4.1.1. Data Analysis

#### General Results

#### Advanced Results

#### 4.1.2. Interpretation

## 5. Concluding Remarks and Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Dependent Variable: | ||||
---|---|---|---|---|

Decision_ECF | ||||

(1) | (2) | (3) | (4) | |

QComp | −0.176 | −0.170 | −0.172 | −0.186 |

(0.134) | (0.134) | (0.134) | (0.137) | |

QIncomp | −0.475 ${}^{***}$ | −0.476 ${}^{***}$ | −0.477 ${}^{***}$ | −0.451 ${}^{***}$ |

(0.160) | (0.160) | (0.160) | (0.162) | |

Honesty | 0.267 ${}^{**}$ | 0.356 ${}^{*}$ | 0.258 ${}^{**}$ | |

(0.128) | (0.185) | (0.129) | ||

ET | 0.039 | 0.160 | 0.045 | |

(0.116) | (0.216) | (0.117) | ||

Honesty:ET | −0.171 | |||

(0.256) | ||||

Reread_ Descriptions | −0.093 | |||

(0.185) | ||||

Age | 0.005 | |||

(0.006) | ||||

Male | −0.189 | |||

(0.121) | ||||

Education | 0.021 | |||

(0.083) | ||||

NGO | 0.006 | |||

(0.121) | ||||

Constant | 0.371 ${}^{***}$ | 0.158 | 0.096 | 0.066 |

(0.103) | (0.151) | (0.177) | (0.306) | |

Observations | 1211 | 1211 | 1211 | 1211 |

Log Likelihood | −829.852 | −827.610 | −827.387 | −825.591 |

Akaike Inf. Crit. | 1665.704 | 1665.219 | 1666.775 | 1671.183 |

Bayesian Inf. Crit. | 1681.002 | 1690.715 | 1697.370 | 1722.175 |

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Dependent Variable: | |||||||||
---|---|---|---|---|---|---|---|---|---|

Decision_ECF | |||||||||

General | Hon | Urg | ET | TE | ET-Hon | TE-Hon | ET-Urg | TE-Urg | |

Compatible condition | −0.170 | −0.142 | −0.231 | −0.181 | −0.175 | −0.164 | −0.154 | −0.216 | −0.263 |

t = −1.363 | t = −0.938 | t = −1.030 | t = −1.063 | t = −0.958 | t = −0.807 | t = −0.683 | t = −0.669 | t = −0.833 | |

Incompatible condition | −0.363 ${}^{***}$ | −0.336 ${}^{**}$ | −0.455 ${}^{*}$ | −0.249 | −0.488 ${}^{***}$ | −0.142 | −0.523 ${}^{**}$ | −0.510 ${}^{*}$ | −0.404 |

t = −2.791 | t = −2.152 | t = −1.953 | t = −1.307 | t = −2.763 | t = −0.591 | t = −2.563 | t = −1.658 | t = −1.129 | |

Honesty | 0.294 ${}^{**}$ | 0.196 | 0.407 ${}^{*}$ | ||||||

t = 1.998 | t = 1.007 | t = 1.809 | |||||||

Order (ECF-TF) | 0.046 | −0.014 | 0.209 | ||||||

t = 0.383 | t = −0.101 | t = 0.868 | |||||||

Reread Descriptions | −0.088 | −0.178 | 0.341 | −0.057 | −0.117 | −0.139 | −0.209 | 0.374 | 0.241 |

t = −0.502 | t = −0.941 | t = 0.720 | t = −0.225 | t = −0.467 | t = −0.508 | t = −0.777 | t = 0.566 | t = 0.354 | |

Age | 0.005 | 0.008 | −0.002 | 0.006 | 0.003 | 0.002 | 0.015 | 0.019 | −0.022 |

t = 0.894 | t = 1.198 | t = −0.186 | t = 0.826 | t = 0.394 | t = 0.227 | t = 1.455 | t = 1.245 | t = −1.513 | |

Male | −0.172 | −0.128 | −0.262 | −0.067 | −0.274 ${}^{*}$ | −0.086 | −0.184 | −0.119 | −0.390 |

t = −1.566 | t = −0.952 | t = −1.348 | t = −0.414 | t = −1.836 | t = −0.447 | t = −0.968 | t = −0.393 | t = −1.518 | |

Education | 0.021 | 0.006 | 0.072 | 0.002 | 0.026 | −0.011 | 0.012 | 0.032 | 0.116 |

t = 0.252 | t = 0.064 | t = 0.450 | t = 0.019 | t = 0.210 | t = −0.085 | t = 0.080 | t = 0.147 | t = 0.479 | |

NGO | 0.006 | 0.038 | −0.062 | 0.190 | −0.187 | 0.356 | −0.272 | −0.167 | 0.137 |

t = 0.051 | t = 0.259 | t = −0.287 | t = 1.058 | t = −1.154 | t = 1.554 | t = −1.446 | t = −0.589 | t = 0.392 | |

Constant | 0.068 | 0.251 | 0.317 | −0.028 | 0.303 | 0.292 | 0.253 | −0.213 | 1.559 |

t = 0.216 | t = 0.617 | t = 0.534 | t = −0.068 | t = 0.597 | t = 0.528 | t = 0.419 | t = −0.329 | t = 1.240 | |

Observations | 1211 | 864 | 347 | 638 | 573 | 458 | 406 | 180 | 167 |

Log Likelihood | −825.591 | −586.663 | −237.452 | −436.394 | −385.940 | −311.893 | −269.413 | −122.258 | −112.568 |

Akaike Inf. Crit. | 1671.183 | 1191.325 | 492.904 | 890.788 | 789.879 | 639.786 | 554.825 | 260.515 | 241.136 |

General | Hon | Urg | ET | TE | ET_Hon | TE_Hon | ET_Urg | TE_Urg | |
---|---|---|---|---|---|---|---|---|---|

Difference | −0.111 | −0.101 | −0.149 | −0.070 | −0.163 | −0.037 | −0.179 | −0.174 | −0.125 |

p-value | 0.005 | 0.031 | 0.051 | 0.191 | 0.006 | 0.555 | 0.010 | 0.097 | 0.259 |

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**MDPI and ACS Style**

Lambert-Mogiliansky, A.; Calmettes, A.
Phishing for (Quantum-Like) Phools—Theory and Experimental Evidence. *Symmetry* **2021**, *13*, 162.
https://doi.org/10.3390/sym13020162

**AMA Style**

Lambert-Mogiliansky A, Calmettes A.
Phishing for (Quantum-Like) Phools—Theory and Experimental Evidence. *Symmetry*. 2021; 13(2):162.
https://doi.org/10.3390/sym13020162

**Chicago/Turabian Style**

Lambert-Mogiliansky, Ariane, and Adrian Calmettes.
2021. "Phishing for (Quantum-Like) Phools—Theory and Experimental Evidence" *Symmetry* 13, no. 2: 162.
https://doi.org/10.3390/sym13020162