MATHEMATICAL STRUCTURE OF QUANTUM DECISION THEORY

Mathematical Structure of Quantum Decision Theory

Following the ideas of Bohr, Von Neumann, and Benioff, we formulate quantum decision theory (QDT) as the quantum-mechanical theory of measurement for probability operators. QDT captures the effect of superposition of composite prospects, including many incorporated intentions. It is based on the hypothesis that the thought processes of real human beings involved in the definition and analysis o...

Quantum Theory. A Mathematical Approach

Mathematical Structure of Evolutionary Theory

Here we postulate three laws which form a mathematical framework for the evolutionary dynamics in biology. The second law is most quantitative and is explicitly expressed in a unique form of stochastic differential equation. Salient features of Darwinian evolutionary dynamics are captured by this law: the probabilistic nature of evolution, ascendancy, and the adaptive landscape. Four dynamical ...

Quantum Decision Theory

We argue that, contrary to conventional wisdom, decision theory is not invariant to the physical environment in which a decision is made. Specifically, we show that a decision maker (DM) with access to quantum information resources may be able to do strictly better than a DM with access only to classical information resources. In this respect, our findings are somewhat akin to those in computer...

Quantum Decision Theory

We present a “quantum decision theory” (QDT) of decision making based on the mathematical theory of separable Hilbert spaces on the continuous field of complex numbers. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reporte...