Daniel Ellsberg (1961) demonstrated that human decision makers tend to avoid unknown probabilities by using a pair of gamble comparisons. The ambiguity aversion has been studied by psychologists, economists, and more recently neuroscientists. For example, non-additive probability can be considered as a descriptive model to explain the ambiguity aversion. However, it lacks a cognitive processing model. In this paper, a computational approach to modeling cognitive process of choice under ambiguous probability by using cellular automata is proposed. By designing cellular automaton in a torus consisting of "local matches" with the state transition rule by stochastic local q-majority vote, which is considered as a model of the working memory of decision maker, this paradox can be simulated. In addition, a similar but differently used version of this model can simulate the event-splitting effect which is known to induce, or eliminate, violation of first order stochastic dominance.