Perfect representation: Difference between revisions

Perfect representation is not compatible with strong monotonicity. Consider the following election with two winners, where A, B, C and D are candidates, and the number of voters approving each candidate are as follows:

A method passing the perfect representation criterion must elect candidates C and D despite near universal support for candidates A and B. This demonstrates that methods passing perfect representation can at best be only weakly monotonic, and could therefore be seen as an argument against perfect representation as a useful criterion.