Consistent rights on property spaces
December, 11th 2019
Chair of Economic Theory
In many aggregation problems, subgroups of agents have the right to predetermine certain properties of the aggregate. Yet, such rights may be inconsistent. In preference aggregation, for example, the liberal paradox refers to the fact that no aggregation rule can grant two individuals the right to fix the social ordering over two alternatives each while staying true to the Pareto principle (a right to society as a whole). We show that, in general, rights to properties are consistent if and only if the following simple condition holds. Whenever rights are given to a minimally inconsistent combination of properties, the respective rights holding groups must intersect to at least one common member. We show that rights are consistent with monotone independent aggregation (voting by properties) if and only if this holds under a suitable generalization of criticality. Our property formulation allows us to study a wide range of applications in social choice theory and in judgment aggregation.