Monotonic aggregation of preferences and the rationalization of choice functions

We consider a decision maker that holds multiple preferences simultaneously, each with different strengths described by a probability distribution. Faced with a subset of available alternatives, the preferences held by the individual can be in conflict. Choice results from an aggregation of these preferences. We assume that the aggregation method is monotonic: improvements in the position of alternative x cannot displace x if it were originally the choice. We show that choices made in this manner can be represented by context-dependent utility functions that are monotonic with respect to a measure of the strength of each alternative among those available. Using this representation we show that any generic monotonic rule can generate an arbitrary choice function as we vary the distribution of preferences. Domain restrictions on the set of preferences (e.g. dual motivation models) or consistency restrictions on the aggregator across choice sets reduce the set of admissible behaviors. Applications to positive models of individual decision making with context effects and social choice are discussed