A note on the impossibility of a set of constitutions stable at different levels.

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 appearance reveals itself as only transitory if seen as a way to escape the multiplicity of solutions problem in social choice theory. This last result is obtained by generalizing the concept of stability to higher levels.