# A quantum dynamic belief decision making model

## TL;DR

This paper introduces a quantum dynamic belief decision making model that incorporates quantum mathematics and Dempster-Shafer theory to better capture human decision-making, especially in cases violating classical probability laws.

## Contribution

It presents a novel quantum dynamic model combining Dempster-Shafer evidence theory with fewer free parameters to accurately model human decision processes and interference effects.

## Key findings

- The model effectively captures the disjunction fallacy in human decisions.
- It demonstrates reduced free parameters compared to existing models.
- Experimental results validate the model's ability to reflect real decision-making behavior.

## Abstract

The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical probability laws. In this paper, a new quantum dynamic belief decision making model based on quantum dynamic modelling and Dempster-Shafer (D-S) evidence theory is proposed to address this issue and model the real human decision-making process. Some mathematical techniques are borrowed from quantum mathematics. Generally, belief and action are two parts in a decision making process. The uncertainty in belief part is represented by a superposition of certain states. The uncertainty in actions is represented as an extra uncertainty state. The interference effect is produced due to the entanglement between beliefs and actions. Basic probability assignment (BPA) of decisions is generated by quantum dynamic modelling. Then BPA of the extra uncertain state and an entanglement degree defined by an entropy function named Deng entropy are used to measure the interference effect. Compared the existing model, the number of free parameters is less in our model. Finally, a classical categorization decision-making experiment is illustrated to show the effectiveness of our model.