- •Preface
- •Contents
- •Contributors
- •Modeling Meaning Associated with Documental Entities: Introducing the Brussels Quantum Approach
- •1 Introduction
- •2 The Double-Slit Experiment
- •3 Interrogative Processes
- •4 Modeling the QWeb
- •5 Adding Context
- •6 Conclusion
- •Appendix 1: Interference Plus Context Effects
- •Appendix 2: Meaning Bond
- •References
- •1 Introduction
- •2 Bell Test in the Problem of Cognitive Semantic Information Retrieval
- •2.1 Bell Inequality and Its Interpretation
- •2.2 Bell Test in Semantic Retrieving
- •3 Results
- •References
- •1 Introduction
- •2 Basics of Quantum Probability Theory
- •3 Steps to Build an HSM Model
- •3.1 How to Determine the Compatibility Relations
- •3.2 How to Determine the Dimension
- •3.5 Compute the Choice Probabilities
- •3.6 Estimate Model Parameters, Compare and Test Models
- •4 Computer Programs
- •5 Concluding Comments
- •References
- •Basics of Quantum Theory for Quantum-Like Modeling Information Retrieval
- •1 Introduction
- •3 Quantum Mathematics
- •3.1 Hermitian Operators in Hilbert Space
- •3.2 Pure and Mixed States: Normalized Vectors and Density Operators
- •4 Quantum Mechanics: Postulates
- •5 Compatible and Incompatible Observables
- •5.1 Post-Measurement State From the Projection Postulate
- •6 Interpretations of Quantum Mechanics
- •6.1 Ensemble and Individual Interpretations
- •6.2 Information Interpretations
- •7 Quantum Conditional (Transition) Probability
- •9 Formula of Total Probability with the Interference Term
- •9.1 Växjö (Realist Ensemble Contextual) Interpretation of Quantum Mechanics
- •10 Quantum Logic
- •11 Space of Square Integrable Functions as a State Space
- •12 Operation of Tensor Product
- •14 Qubit
- •15 Entanglement
- •References
- •1 Introduction
- •2 Background
- •2.1 Distributional Hypothesis
- •2.2 A Brief History of Word Embedding
- •3 Applications of Word Embedding
- •3.1 Word-Level Applications
- •3.2 Sentence-Level Application
- •3.3 Sentence-Pair Level Application
- •3.4 Seq2seq Application
- •3.5 Evaluation
- •4 Reconsidering Word Embedding
- •4.1 Limitations
- •4.2 Trends
- •4.4 Towards Dynamic Word Embedding
- •5 Conclusion
- •References
- •1 Introduction
- •2 Motivating Example: Car Dealership
- •3 Modelling Elementary Data Types
- •3.1 Orthogonal Data Types
- •3.2 Non-orthogonal Data Types
- •4 Data Type Construction
- •5 Quantum-Based Data Type Constructors
- •5.1 Tuple Data Type Constructor
- •5.2 Set Data Type Constructor
- •6 Conclusion
- •References
- •Incorporating Weights into a Quantum-Logic-Based Query Language
- •1 Introduction
- •2 A Motivating Example
- •5 Logic-Based Weighting
- •6 Related Work
- •7 Conclusion
- •References
- •Searching for Information with Meet and Join Operators
- •1 Introduction
- •2 Background
- •2.1 Vector Spaces
- •2.2 Sets Versus Vector Spaces
- •2.3 The Boolean Model for IR
- •2.5 The Probabilistic Models
- •3 Meet and Join
- •4 Structures of a Query-by-Theme Language
- •4.1 Features and Terms
- •4.2 Themes
- •4.3 Document Ranking
- •4.4 Meet and Join Operators
- •5 Implementation of a Query-by-Theme Language
- •6 Related Work
- •7 Discussion and Future Work
- •References
- •Index
- •Preface
- •Organization
- •Contents
- •Fundamentals
- •Why Should We Use Quantum Theory?
- •1 Introduction
- •2 On the Human Science/Natural Science Issue
- •3 The Human Roots of Quantum Science
- •4 Qualitative Parallels Between Quantum Theory and the Human Sciences
- •5 Early Quantitative Applications of Quantum Theory to the Human Sciences
- •6 Epilogue
- •References
- •Quantum Cognition
- •1 Introduction
- •2 The Quantum Persuasion Approach
- •3 Experimental Design
- •3.1 Testing for Perspective Incompatibility
- •3.2 Quantum Persuasion
- •3.3 Predictions
- •4 Results
- •4.1 Descriptive Statistics
- •4.2 Data Analysis
- •4.3 Interpretation
- •5 Discussion and Concluding Remarks
- •References
- •1 Introduction
- •2 A Probabilistic Fusion Model of Trust
- •3 Contextuality
- •4 Experiment
- •4.1 Subjects
- •4.2 Design and Materials
- •4.3 Procedure
- •4.4 Results
- •4.5 Discussion
- •5 Summary and Conclusions
- •References
- •Probabilistic Programs for Investigating Contextuality in Human Information Processing
- •1 Introduction
- •2 A Framework for Determining Contextuality in Human Information Processing
- •3 Using Probabilistic Programs to Simulate Bell Scenario Experiments
- •References
- •1 Familiarity and Recollection, Verbatim and Gist
- •2 True Memory, False Memory, over Distributed Memory
- •3 The Hamiltonian Based QEM Model
- •4 Data and Prediction
- •5 Discussion
- •References
- •Decision-Making
- •1 Introduction
- •1.2 Two Stage Gambling Game
- •2 Quantum Probabilities and Waves
- •2.1 Intensity Waves
- •2.2 The Law of Balance and Probability Waves
- •2.3 Probability Waves
- •3 Law of Maximal Uncertainty
- •3.1 Principle of Entropy
- •3.2 Mirror Principle
- •4 Conclusion
- •References
- •1 Introduction
- •4 Quantum-Like Bayesian Networks
- •7.1 Results and Discussion
- •8 Conclusion
- •References
- •Cybernetics and AI
- •1 Introduction
- •2 Modeling of the Vehicle
- •2.1 Introduction to Braitenberg Vehicles
- •2.2 Quantum Approach for BV Decision Making
- •3 Topics in Eigenlogic
- •3.1 The Eigenlogic Operators
- •3.2 Incorporation of Fuzzy Logic
- •4 BV Quantum Robot Simulation Results
- •4.1 Simulation Environment
- •5 Quantum Wheel of Emotions
- •6 Discussion and Conclusion
- •7 Credits and Acknowledgements
- •References
- •1 Introduction
- •2.1 What Is Intelligence?
- •2.2 Human Intelligence and Quantum Cognition
- •2.3 In Search of the General Principles of Intelligence
- •3 Towards a Moral Test
- •4 Compositional Quantum Cognition
- •4.1 Categorical Compositional Model of Meaning
- •4.2 Proof of Concept: Compositional Quantum Cognition
- •5 Implementation of a Moral Test
- •5.2 Step II: A Toy Example, Moral Dilemmas and Context Effects
- •5.4 Step IV. Application for AI
- •6 Discussion and Conclusion
- •Appendix A: Example of a Moral Dilemma
- •References
- •Probability and Beyond
- •1 Introduction
- •2 The Theory of Density Hypercubes
- •2.1 Construction of the Theory
- •2.2 Component Symmetries
- •2.3 Normalisation and Causality
- •3 Decoherence and Hyper-decoherence
- •3.1 Decoherence to Classical Theory
- •4 Higher Order Interference
- •5 Conclusions
- •A Proofs
- •References
- •Information Retrieval
- •1 Introduction
- •2 Related Work
- •3 Quantum Entanglement and Bell Inequality
- •5 Experiment Settings
- •5.1 Dataset
- •5.3 Experimental Procedure
- •6 Results and Discussion
- •7 Conclusion
- •A Appendix
- •References
- •Investigating Bell Inequalities for Multidimensional Relevance Judgments in Information Retrieval
- •1 Introduction
- •2 Quantifying Relevance Dimensions
- •3 Deriving a Bell Inequality for Documents
- •3.1 CHSH Inequality
- •3.2 CHSH Inequality for Documents Using the Trace Method
- •4 Experiment and Results
- •5 Conclusion and Future Work
- •A Appendix
- •References
- •Short Paper
- •An Update on Updating
- •References
- •Author Index
- •The Sure Thing principle, the Disjunction Effect and the Law of Total Probability
- •Material and methods
- •Experimental results.
- •Experiment 1
- •Experiment 2
- •More versus less risk averse participants
- •Theoretical analysis
- •Shared features of the theoretical models
- •The Markov model
- •The quantum-like model
- •Logistic model
- •Theoretical model performance
- •Model comparison for risk attitude partitioning.
- •Discussion
- •Authors contributions
- •Ethical clearance
- •Funding
- •Acknowledgements
- •References
- •Markov versus quantum dynamic models of belief change during evidence monitoring
- •Results
- •Model comparisons.
- •Discussion
- •Methods
- •Participants.
- •Task.
- •Procedure.
- •Mathematical Models.
- •Acknowledgements
- •New Developments for Value-based Decisions
- •Context Effects in Preferential Choice
- •Comparison of Model Mechanisms
- •Qualitative Empirical Comparisons
- •Quantitative Empirical Comparisons
- •Neural Mechanisms of Value Accumulation
- •Neuroimaging Studies of Context Effects and Attribute-Wise Decision Processes
- •Concluding Remarks
- •Acknowledgments
- •References
- •Comparison of Markov versus quantum dynamical models of human decision making
- •CONFLICT OF INTEREST
- •Endnotes
- •FURTHER READING
- •REFERENCES
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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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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: