A quantum walk framework for multialternative decision making

Recent findings of Markov violations challenge Markov random walk processes for decision making. On the other hand, quantum walk processes explain these Markov violations in a natural way, but they have only been applied to binary alternative decision making. In this work, we propose a general framework for extending quantum walk processes to multi-alternative decision making. The multi-alternative quantum walk model operates in a direct sum space of the alternatives, with Hamiltonian built for each pair of alternatives to model context effects. Order effects come naturally from the matrix non-commutativity of the Hamiltonians. Future works built on this framework can connect parameters of the models with the expected utilities.