# Comparing Markov and quantum random walk models of categorization decisions

Quantum probability theory has successfully provided accurate descriptions of behavior in the areas of judgment and decision making, and here we apply the same principles to two category learning tasks, one task using overlapping, information-integration (II) categories the other using overlapping, rule-based (RB) categories. Since II categories lack verbalizable descriptions, unlike RB categories, we assert that an II categorization decision is constructed out of an indefinite state and characterized by quantum probability theory, whereas an RB categorization decision is read out from a definite state and governed by classical probability theory. In our experiment, participants learn to categorize simple, visual stimuli as members of either category S or category K during an acquisition phase, and then rate the likelihood on a scale of 0 to 5 that a stimulus belongs to one category and subsequently perform the same likelihood rating for the other category during a transfer phase. Following the principle of complementarity in quantum theory, we expect the category likelihood ratings to exhibit order effects in the task that employs II categories, but not in the one that uses RB categories. In the task with II categories, we found that the quantum random walk model notably outperforms an analogous Markov random walk model and there are definitive order effects in the likelihood ratings. But in the task with RB categories, we found that the performance gap between the Markov and quantum models is reduced and the order effects in the likelihood ratings are not significant.

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