Are quantum-like Bayesian networks more powerful than classical Bayesian networks?

Recent works in the literature have proposed quantum-like Bayesian networks as an alternative decision model to make predictions in scenarios with high levels of uncertainty. Despite its promising capabilities, there is still some resistance in the literature concerning the advantages of these quantum-like models towards classical ones. In this work, we developed a Classical Latent Bayesian network model and we compared it against its quantum counterpart: the quantum-like Bayesian network. The comparison was done using a well known Prisoner’s Dilemma game experiment from Shafir and Tversky (1992), in which the classical axioms of probability theory are violated during a decision, and consequently the game cannot be simulated by pure classical models. In the end, we concluded that it is possible to simulate these violations using the Classical Latent Variable model, but with an exponential increase in its complexity. Moreover, this classical model cannot predict both observed and unobserved conditions from Shafir and Tversky (1992) experiments. The quantum-like model, on the other hand, is shown to be able to accommodate both situations for observed and unobserved events in a single model, making it more suitable and more general for these types of decision problems.