Social and Information Sciences Laboratory (SISL) Seminar

Abstract: This paper provides a general characterization of methods of aggregation that are recursive, and shows that recursive aggregation lies behind many seemingly different results in economic theory: spanning social choice, belief formation, and individual decision making. Recursivity means that the aggregate outcome of a model over two disjoint groups of features is a weighted average of the outcome of each group separately. The main result of our paper pins down any aggregation procedure that is recursive: There exist a weight function, and a ranking order over the set of features, such that the outcome of the model conditional on aggregation of a subset of features is the weighted average of outcomes associated with each highest-ordered feature separately.

The result unifies aggregation procedures across many different economic environments, showing that all of them rely on the same basic result. Following the main representation, we show applications and extensions of our representation in various separated topics of economics such as belief formation, choice theory, and social welfare economics. For example, for individual discrete choice, recursivity lies behind the multi-stage Luce (or Logit) model.