Minimum Reversals Domains : A Link between Median Rules, Veto Power and Monotonicity

We show that any monotonic, anonymous, unanimous and tops-only rule defined on a MD-Connected domain must be a generalized median voter rule. Moreover, we also show that a generalized median voter rule is monotonic if and only if the domain is a Minimum Reversals domain. These two results are combined to obtain a set of necessary and sufficient conditions for the existence of monotonic, anonymous and unanimous rules on a MD-Connected domain. We show that Minimum Reversals domains are a weakening of known preference domains. Lastly, we uncover a connection between veto power and the weakening of Single-Peaked restrictions for domains with monotonic median voter rules