Intuitively, I'd say it's some sort of logarithm or quadratic curve - if one person tells me they say a black dog the next street over, that bumps up my belief a lot; if two people tell me it, it still increases, but not nearly as much; and so on to the point where if 2 billion people tell me that, I begin to think this is part of some cult and start lowering credence.
Something I've been hearing a lot lately (specifically from Orthodox Jews, although it comes up a lot in debates about religion) is that having a large number of people telling a story makes it more likely the story is true, because multiple witnesses can call each other out for deviating from the truth.
My gut reaction is that this is extremely false. But it's a point that should be scientifically testable, and I figure that someone should have done a study on it by now. Does anyone know of such a thing?
A related issue is the argument that oral tradition meant something very different thousands of years ago, when it was the ONLY form of historical record. Oral historians were duty-bound to preserve the story. This sounds plausible. It probably ISN'T as easily testable since we can't compare oral history from pre-writing times against... well, much of anything. (Well, I guess archaeological evidence, if the events being described would have left enough archaeological evidence). Is there an official, accepted scholarly opinion on this?