Abstract Arrowian aggregation

In a general framework of abstract binary aggregation, we characterize aggregation problems in terms of the monotone Arrowian aggregators they admit. Specifically, we characterize the problems that admit non-dictatorial, locally non-dictatorial, anonymous, and neutral monotone Arrowian aggregation, respectively. As a consequence of these characterizations, we also obtain new results on the possibility of strategy-proof social choice and the “concrete Arrowian” aggregation of preferences into a social ordering on generalized single-peaked domains.