Prestigious scientists can play this role even with anonymous review. They can publicize their support of a new and radical idea through talks at conferences, word of mouth, and other informal channels (like blogging). This will increase attention to their new idea, especially since many scientists like to keep track of what the top researchers in their field are doing. And if other scientists give extra weight to the views of their high status colleagues, they will also raise their probability estimates for the hypothesis. So the new idea can receive a boost before any paper is published. Then when papers supporting the radical new hypothesis are submitted for anonymous review, they will have a better chance of being published whether or not the prestigious scientist is an author.
Previously, Robin Hanson pointed out that even if implementing anonymous peer review has an effect on the acceptance rate of different papers, this doesn't necessarily tell us the previous practice was biased. Yesterday, I ran across an interesting passage suggesting one way that anonymous review might actually be harmful:
(From Richard A. Posner, "Aging and Old Age")
If this hypothesis holds (and Posner admits it hasn't been tested, at least at the time of writing), then blind review may actually slow down the acceptance of theories which are radical but true. Looking up the Peter Messeri reference gave me the article "Age Differences in the Reception of New Scientific Theories: The Case of Plate Tectonics Theory". It notes:
In this light, an older scientist's acceptance of a new, radical hypothesis should tell us to give the new hypothesis extra weight. It might even be appropriate to apply a heavier "reputation weighting" on controversial theories than established ones - we'd expect the established scientist to write papers supporting the established theories, but not controversial ones. However, blind review makes this impossible. The reviewers may even mistake the established scientist as an undiscriminating free thinker, who endorses any controversial theories simply because they're unpopular. This will slow down the acceptance of hypotheses which are, in fact, correct.
A possible objection to this could be that old scientists are unlikely to change their minds, and therefore old scientists not getting enough credit for their achievements won't have much of an effect in the spread of new hypotheses. (After all, if no old scientist endorses controversial hypotheses, then it doesn't matter if those endorsements aren't properly weighted in review.) Not so. Messeri finds that science does actually progress a lot faster than "one funeral at a time" (as Max Planck put it), and old scientists are ready to adopt new theories given sufficient evidence. While the last holdouts for outdated theories do tend to be the old, their increased security also makes them the first who are willing to publicly support new theories: