A theory of iterative choice in lists

In a list, alternatives appear according to an order and the decision maker follows this order to evaluate alternatives. He records the first alternative as the initial survivor and then at every stage, he compares the current survivor with the next alternative in the list to determine whether the next alternative replaces that to become the new survivor. When the entire list is exhausted in this manner, the agent chooses the survivor in the last stage. We call this procedure “iterative” and provide an axiomatic characterization for it when the order in every list is observable. Then, we also study characterizations of the iterative procedure that is prone to the well-known primacy and recency effects. Finally, we analyze situations where the order of alternatives is unknown to an outside observer and provide a characterization result that enables such an outsider with limited information to understand whether the decision maker can indeed be an iterative list chooser for some order.