  We consider elections where the voters come one at a time, in a streaming
fashion, and devise space-efficient algorithms which identify an approximate
winning committee with respect to common multiwinner proportional
representation voting rules; specifically, we consider the Approval-based and
the Borda-based variants of both the Chamberlin-- ourant rule and the Monroe
rule. We complement our algorithms with lower bounds. Somewhat surprisingly,
our results imply that, using space which does not depend on the number of
voters it is possible to efficiently identify an approximate representative
committee of fixed size over vote streams with huge number of voters.
