Anonymity in large societies

We formalize the notion of coalition measure as a primitive of social choice with a countably infinite number of agents. An example would be a dynamic setting with an infinite horizon, where it may be convenient to consider separately each individual’s preferences at every moment of time. In this setting, there are some “equal size” coalitions that a social choice rule should treat in the same manner. We therefore introduce a new property of equal treatment with respect to a coalition size measure and explore its interaction with other common axioms of social choice. We observe that, provided the measure space is sufficiently rich in coalitions of the same measure, the new axiom can play a role similar to that of anonymity.