Dual Random Utility Maximisation (dRUM) is Random Utility Maximisation when utility depends on only two states. This class has many relevant behavioural interpretations and practical applications. We show that dRUM is (generically) the only stochastic choice rule that satisfies Regularity and two new properties: Con- stant Expansion (if the choice probability of an alternative is the same across two menus, then it is the same in the merged 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 merged menu). We extend the theory to menu-dependent state probabilities. This accommodates prominent violations of Regularity such as the attraction, similarity and compromise effects.