  We study committee voting rules under ranked preferences, which map the
voters' preference relations to a subset of the alternatives of predefined
size. In this setting, the compatibility between proportional representation
and committee monotonicity is a fundamental open problem that has been
mentioned in several works. We design a new multi-winner voting rule called the
Solid Coalition Refinement (SCR) Rule that simultaneously satisfies committee
monotonicity and Dummett's PSC as well as one of its variants called inclusion
PSC. This is the first rule known to satisfy both of these properties.
Moreover, we show that this is effectively the best that we can hope for as
other fairness notions adapted from approval voting such as Rank-JR and
Rank-PJR+ are incompatible with committee monotonicity.
