Monotonicity and qualified majority rules

This paper reflects on some results characterizing qualified majority rules using monotonicity as a key axiom. In particular, some errors in the existing literature are detected and ways to fix them are proposed. Then, the role of monotonicity axiom in characterizing majority rules is analyzed. There, among other findings, we show that its marginal contribution in characterizing relative qualified majority rules is the difference between two properties called sum-invariance and sum-monotonicity. Finally, a new class of qualified majority rules where voters exercise a veto power is introduced and axiomatically characterized.