# 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 a category learning task using overlapping, information-integration (II) categories. Since II categories lack verbalizable descriptions, unlike rule-based (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 this experiment. Although we have just begun to collect data, so far a quantum random walk model has more successfully captured the responses from participants compared to an analogous Markov random walk model with the same number of parameters.

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