  Answering an open question by Betzler et al. [Betzler et al., JAIR'13], we
resolve the parameterized complexity of the multi-winner determination problem
under two famous representation voting rules: the Chamberlin-Courant (in short
CC) rule [Chamberlin and Courant, APSR'83] and the Monroe rule [Monroe,
APSR'95]. We show that under both rules, the problem is W[1]-hard with respect
to the sum $\beta$ of misrepresentations, thereby precluding the existence of
any $f(\beta) \cdot |I|^{O(1)}$ -time algorithm, where $|I|$ denotes the size
of the input instance.
