  We investigate winner determination for two popular proportional
representation systems: the Monroe and Chamberlin-Courant (abbrv. CC) systems.
Our study focuses on (nearly) single-peaked resp. single-crossing preferences.
We show that for single-crossing approval preferences, winner determination of
the Monroe rule is polynomial, and for both rules, winner determination mostly
admits FPT algorithms with respect to the number of voters to delete to obtain
single-peaked or single-crossing preferences. Our results answer some
complexity questions from the literature [18, 28, 21].
