Psychological findings show that under uncertainty, there are many situations where humans make irrational decisions (Tversky & Kahneman, 1974). By irrational, we mean decisions that violate the laws of classical probability theory and logic. These decisions have a deep impact in current decision support systems, since they cannot be predicted: if decision systems are based on classical probabilistic models and on the notions of set theory, then the system cannot capture human irrationalities that violate these theories.
Under a psychological point of view, these violations are explained by models that primarily assume a preference for fast, heuristic-based processing and strong computational assumptions about the human mind. In order to overcome these assumptions, a new field has emerged that generalizes the notions of classical probability theory by using the mathematical formalisms and concepts from quantum mechanics.
Although quantum cognitive models have been able to predict and accommodate human paradoxical decisions reported over the literature, an important question still remains: are these quantum models successful uniquely because of the properties of quantum mechanics or can other non-classical models, such as fuzzy theory or Dempster-Shafer theory also be successfully applied under these paradoxical decision scenarios? What are the advantages and limitations of each these non-classical frameworks in decisions under uncertainty?
In this project, we want to investigate and compare different non-classical probabilistic models with current quantum-like models of the literature in paradoxical human decisions and understand what are the main fundamental principles that a non-classical theory must have in order to be able to accommodate and predict paradoxical human decisions under uncertainty.
Some of the activities involved in this project are the following:
- Investigation of non-classical mathematical theories for probabilistic inferences
- Investigation of the main properties of quantum-like probabilistic models
- Compare models in terms of their properties and assumptions
- Test if the investigated models can predict and accommodate human decisions under uncertainty.
We expect the results of this topic to include:
- An understanding of the main properties that are relevant for accommodating and predicting human decisions
- Identification of the main advantages and limitations of each framework
- Publication of results in scientific journals
Skills and experience
We expect you to have the following skills:
- Probabilistic Models: Bayesian models, Fuzzy theory, Dempster-Shafer theory, etc.
- Linear algebra
- Calculus with complex numbers
- Programming skills: Matlab (preferred), Mathematica (preferred), Python.
- Quantum cognitive models
- Fuzzy theory
- Dempster Shafer theory
- Non-Kolmogorovian models
- Mathematical modelling
- Bayesian statistics
Contact the supervisor for more information.