We demonstrate that no set of neutral and different social choice correspondences exists, so that, if proposed to a group of individuals, it leads to a uniquely defined society, stable in an intuitive sense. Weakening this latter condition makes it possible to reintroduce possibility. This...

Parikh and Krasucki [1990] showed that if rational agents communicate the value of a function f according to a protocol upon which they have agreed beforehand, they will eventually reach a consensus about the value of f, provided a fairness condition on the protocol and a convexity condition on...