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We consider a server that simultaneously streams multiple video channels. Each video channel is delivered to a set of receivers using peer-to-peer (P2P) live multicast. We propose a framework for allocating server bandwidth to minimize distortion across the peer population, across all channels. The optimization problem considers rate, distortion, the audience size, and peer-churn associated with each channel. Network simulations demonstrate reduction of mean distortion across the peer population due to the proposed server bandwidth allocation. We also highlight the general scope of the proposed framework which makes it applicable to scenarios beyond the one considered in this paper. Other optimization metrics rather than average distortion can also be accommodated in the proposed framework.