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Dual Random Utility Maximisation (dRUM) is Random Utility Maximisation when utility depends on only two states. dRUM has many relevant behavioural interpretations and practical applications. We show that it is (generically) the only stochastic choice rule that satisfies Regularity and two new simple properties: Constant Expansion (if the choice probability of an alternative is the same across two menus, then it is the same in the combined menu), and Negative Expansion (if the choice probability of an alternative is less than one and differs across two menus, then it vanishes in the combined menu). By extending the theory to menu-dependent state probabilities we are able to accommodate prominent violations of Regularity such as the attraction, similarity and compromise effects.
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