Valued Opinions or Opinionated Values: The Double Aggregation Problem

Abstract Within the realm of social choice, the framework originally developed by Arrow can be viewed as applying to two different and distinct aggregation problems. In the first, aggregation takes the form of utilizing information about individual well-being to generate a social ranking of states. This is what is done by a social welfare function. In the second, the purpose of aggregation is to take a collection of social rankings of states that individuals in society may possess and to combine them to create a ‘consensus’ social ranking. This could be done by a voting system. In a general problem of social choice, one could expect to meet both aggregation problems—individuals in society have (perhaps different) views about the well-being of all individuals in society and, using this information, a single social ranking of states is desired.