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Luce Arbitrates: Stochastic Resolution of Inner Conflicts

Abstract I propose and axiomatically characterize a multi-attribute stochastic choice model that simultaneously generalizes the standard model of deterministic choice and the Luce rule. Attributes are cardinal, independent measures of desirability that are endogenously inferred from observed choices, and thus subjective. An alternative is chosen with a positive probability from a menu if and only if it is undominated attribute-wise in that menu. The model leads to the context-dependent evaluation of alternatives by assigning every menu a distinct reference point against which the menu alternatives are re-evaluated. The reference point of every menu takes the minimum values of attributes in that menu. The model can accommodate the well-known attraction and compromise effects by linking them to diminishing sensitivity to the attributes and complementarity between them. At the end, I discuss an application of the model in strategic settings and derive an analogue of the attraction effect in games.