Rationalizing Choice with Multi-Self Models∗† Attila Ambrus‡

This paper shows that in situations in which the preferences of multiple selves are aggregated into a collective decision, even if the researcher has a fully specified theory of how preferences get aggregated, there are typically no testable implications of the theory unless there is an a priori restriction on the number of selves. This result has implications in both interpersonal and intrapersonal decision-making, calling attention to the importance of collecting reliable infor-mation on the number of selves (motivations, in the interpersonal context) participating in the decision. We establish our main result by finding a linear relationship between the number of selves and the set of choice functions that a given aggregator is guaranteed to rationalize with the given number of selves. The latter set is connected to the number of IIA violations implied by the choice function, a new measure of the amount of irrationality a choice function exhibits