Mathematically provable that we can’t satisfy a bunch of desiderata simultaneously.
However, one particular constraint both causes a lot of problems and really isn’t that justified: the independence constraint
The collective belief on a particular proposition is uniquely determined by opinions of the members of the group on that belief alone.
Our intuitive sense of collective belief is sensitive to the reasons for belief.
Example:
Two panels: all believe that government and parliament should be in same city, also all believe it should be in Berlin. Other is split on which city things should be on, but all believe it should be in same city.
Independence would say that both panels agree ‘equally’ on whether government+parliament should be in same city.
Intuitively we know that the second group has undermining/inconsistent reasons for their agreed-upon belief, so their aggregate belief should be strictly weaker than first panel.
Independence is usually involved in the unsatisfiable subsets of constraints.