Inferable dynamic Markov model to predict interference effects

Abstract

Common decision-making models assume that the system would change over time. But when system is in a particular moment, decision-maker has to make a specific judgment which would put the system in a determined state not an uncertain state. Most decision-making models emphasize the determined state of the system after the judgment and ignore the uncertain state prior to the judgment. So, it would be biased in simulating real-life decision experiments if these uncertain information were lost. Besides, some cognitive decision-making experiments have demonstrated that the law of total probability would not be applicable in practice. What is the reason for this phenomenon? Some researchers thought that interference effects in decision-making process is the main reason, which has been verified from the mathematical proof. Moreover, the interference effects is produced due existing of uncertain information. Quantum theory uses probability amplitude to model uncertainty information of system that would exist simultaneously in multiple states. It is able to better model uncertain states before making a judgement, where judgement can be understood as measurement in quantum theory. Hence, the paper proposed an inferable dynamic Markov decision-making model to quantitatively predict and determine the value of interference effects in the decision-making process. The new model used probability amplitude to represent uncertain information in the decision process, and combined it with Markov decision-making model to study the evolution between different moments in the decision process. Additionally, based on quantum theory principles, it is possible to estimate and infer the related parameters reasonably.