On the Complexity of Chamberlin-Courant on Almost Structured Profiles

The Chamberlin-Courant voting rule is an important multiwinner voting rule. Although \(\mathsf {NP}\)-hard to compute on general profiles, it is known to be polynomially solvable on single-crossing and single-peaked electorates by exploiting the structures of these domains. We consider the problem of generalizing the domain on which the voting rule admits efficient algorithms.