Dual random utility maximisation

Many prominent regularities of stochastic choice, such as the attraction, similarity and compromise effects, are incompatible with Random Utility Maximisation (RUM) as they violate Monotonicity. We argue that these regularities can be conveniently represented by a variation of RUM in which utility depends on only two states and state probabilities are allowed to depend on the menu. We call this model Dual Random Utility Maximisation (dRUM). dRUM is a parsimonious model that admits violations of Monotonicity. We characterise dRUM in terms of three transparent expansion/contraction conditions. We also characterise the important special case in which state probabilities are constant across menus.