Impossibilities with Kemeny updating

Impossibility theorems for preference correspondences based on a new monotonicity concept are discussed. Here monotonicity means that if preferences update in such a way that they get closer to an outcome then at the new situation this outcome remains chosen. Strong monotonicity requires further that in those cases the outcome at the new pro\u85le is a subset of the outcome at the old pro\u85le. It is shown that only dictatorial preference correspondences are unanimous and strongly monotone.