We study random choice to capture violations of the weak axiom of revealed preference. Using comparisons of choice probabilities, we introduce the notion of a stochastic preference. We show that the Luce model is the unique rule that has a context-independent stochastic preference. To address well-known difficulties of the Luce model in situations where choice objects have overlapping attributes, we introduce a new random choice model, the weighted attributes rule. We show that it is identified by a context-independent stochastic preference over attributes
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