So this would be an open invitation to people to game the system by simply writing a lot of reviews? (this is the sort of pattern that would get quickly spotted and shared). Seems like if I had an agenda, like systematically driving up the reviews for restaurants for which I am (say) the linen supplier, I'd have a reason to write a lot of good reviews. Or if I owned a chain, I'd systematically write a lot of bad reviews of all competing chains?

Anything with such an obvious way to game the system is probably not defensible. You do NOT want any predictable way to get a benefit other than "quality." For the same reason that you do not want to predictably always go "rock" in a game of rock, paper, scissors. If there is any action that has a predictable effect regardless of quality, it is a game-able exploit. And the fewer people it takes to game something, the faster it will be gamed. This one takes only one person to game. Voting systems take multiple people.

I don't use Yelp, so I don't know what they actually do.