Dynamic Decision Making under Uncertainty: existing approach and quantum ideas

Contemporary solutions to dynamic decision making (DM) tasks under uncertainty use classical (Kolmogov’s) probability to describe/model the uncertainty present.

These solutions are in a significant conflict with the experimental data observed in cognitive and descriptive research, which yields different paradoxes and inconsistencies [3], [4]. Although it has been demonstrated that a quantum-like approach to DM resolves these inconsistencies [2], the underlying reasons for this success remain unknown.

This talk (based on the speaker's master thesis [1]) presents a new framework that:

• uses a more general formalisation of DM task
• shows that under realistic assumptions a solution is found without prior definition of probability
• demonstrate the quantum nature of uncertainty which partially explains the phenomena above.

The talk will also mention the related open questions.

References:

[1] A. Gaj. Quantum Model of Uncertainty for Dynamic Decision Making, MSc thesis, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague, 2024.

[2] Jerome R. Busemeyer and Peter D. Bruza. Quantum Models of Cognition and Decision. Cambridge University Press, 2012.

[3] Daniel Ellsberg. Risk, Ambiguity, and the Savage axioms. The Quarterly Journal of Economics, 75(4):643–669, 1961.

[4] Maurice Allais. Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l'école américaine. Econometrica, 21(4):503–546, 1953.

[5] A. Gaj, M. Kárný. Quantum-like modelling of uncertainty in dynamic decision making. In Quantum Information and Probability: from Foundations to Engineering (QIP24), Växjö, Sweden, 2024.