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Several apparent violations of transitivity have been reported in the literature on decision making. However, these effects have been shown to be compatible with random preference models, in which preferences are transitive at each point in time but vary at random over time. Such models imply that choice proportions will conform to a set of conditions called the triangle inequalities, and no clear triangle inequality violations have been empirically demonstrated to date. This article examines a broader class of choice models—“context-sensitive preference models”—in which the current and prior history of choice contexts can systematically influence decision makers’ stochastic preferences. These models generate violations of the triangle inequalities even when preferences are always transitive. Furthermore, the article develops an analysis of decision making under incomplete information, in which rational decision makers draw inferences from the present choice context, but have limited memory for past contexts. It is shown that such decision makers can exhibit intransitive choice cycles of arbitrary magnitude as a result of context-dependent switching between transitive preference orders. Two experiments test the model’s predictions, and clear violations of the triangle inequalities are observed.