An evidential Markov decision making model
This addresses a specific cognitive modeling problem for researchers in decision theory, but it is incremental as it builds on existing evidence theory and Markov models.
The paper tackled the disjunction fallacy in decision-making by proposing an Evidential Markov model that incorporates uncertainty and Deng entropy, successfully predicting the disjunction effect with fewer parameters than existing models.
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 laws. In this paper, an Evidential Markov (EM) decision making model based on Dempster-Shafer (D-S) evidence theory and Markov modelling is proposed to address this issue and model the real human decision-making process. In an evidential framework, the states are extended by introducing an uncertain state which represents the hesitance of a decision maker. The classical Markov model can not produce the disjunction effect, which assumes that a decision has to be certain at one time. However, the state is allowed to be uncertain in the EM model before the final decision is made. An extra uncertainty degree parameter is defined by a belief entropy, named Deng entropy, to assignment the basic probability assignment of the uncertain state, which is the key to predict the disjunction effect. A classical categorization decision-making experiment is used to illustrate the effectiveness and validity of EM model. The disjunction effect can be well predicted and the free parameters are less compared with the existing models.