A review manager should act like an impartial judge through the process, not like the library’s lawyer.
When I first joined the Boost mailing list, years ago, I also thought that the review manager is supposed to impartially reflect the community opinion, as expressed in the form of formal reviews. But it turned out that I was wrong. The review manager's role was, as I later figured out by observing the process, to decide whether the library should be accepted, and the reviews were helping him with this, rather than deciding for him. It was common, for instance, for the review manager to actually write a review, usually prefaced with "this is my review of the library which I submit independently of my role as a review manager." This doesn't make much sense if the review manager is only supposed to impartially tally votes. I didn't particularly agree then with that process - for me the review manager was, in fact, supposed to tally votes - but the process was what it was, and it worked.