The complexity of fully proportional representation for single-crossing electorates (Q2513672)

This paper investigates the complexity of winner determination under Chamberlin-Courant's and Monroe's rules. A polynomial-time algorithm for Chamberlin-Courant's rule for single-crossing elections is presented. This algorithm can be modified to work for elections that are close to being single-crossing in the sense of having bounded single-crossing width. An NP-hardness proof for Monroe's rule for the same setting is added. Under single-peaked single-crossing preferences, an efficient algorithm for the egalitarian variant of this last rule is provided. See also [Zbl 1319.91074] for a previous version of this article.