I'm considering the computational hardness of winner determination under two well-known rules, i.e., the Monroe and Chamberlin-Courant rules. Skowron et al. have mentioned in Achieving fully proportional representation: Approximability results that:
Procaccia, Rosenschein and Zohar were the first to show the hardness of these two rules for the case of a particular approval-style dissatisfaction function. Their results were complemented by Lu and Boutilier who proved the hardness of the Chamberlin–Courant rule for the case of Borda satisfaction function.
Thus, I was wondering whether there is any reference on the hardness of computing Monroe rule for the case of Borda satisfaction function?