Selective Attribute Rules

We develop an extension of Luce's (Individual Choice Behavior: A Theoretical Analysis. Wiley, New York, 1959) model to apply multiattributes to stochastic choice. We consider an agent who focuses on selective (salient) attributes standing out in a choice set. These attributes are endogenously determined according to the criterion of Just Noticeable Difference. The criterion selects attributes whose variation impacts the agent enough so that she cares about each of them. When such selective attributes vary with the choice set, we adjust the choice probabilities for the elements of the choice set. We find that all the violations of Luce's axioms can be attributed to a change in selective attributes. When the global choice set is of the product form, selective attribute rules are characterized. In particular, the distinguished case of (non-selective) attribute rules can be characterized by two axioms, Independence from Irrelevant Alternatives and Separability.