It ensures votes hold equal weight and that "extreme polar" voters don't skew things. It also avoids the opposite problem of "everything is neutral" vote unless horrible/incredible.
RT also handles high brow and low brow well. You get less voting of "eh I didn't love it, but it's sophisticated so I'll give it an extra star."
I'm sold on simple up/down.
So RT is good at predicting "should I watch this movie I haven't watched before", but bad at predicting more sophisticated habits or preferences. I wouldn't buy the Blu Ray off a RT prediction, but I would rent.
So it becomes a question of what are you trying to accomplish? For some issues up/down is a good way to solve a problem, for others it isn't.
It feels like you're mixing together two different arguments. Rotten Tomatoes is good at predicting whether someone will like a movie. What is "ranking"? That is a very undefined concept. Ranking of what? It's clearly not ranking of likelyhood of a person liking a movie because rotten tomatoes already does that.
Later you mention likelihood of repeat watchings of a movie. Rotten Tomatoes thumbs up or down based on whether someone liked a movie, as a result it produces a metric on likelihood of someone liking of movie. Instead if rotten tomatoes immediately after watching a movie, asking "Did you like this movie?", asked "Would you watch this movie again?" then it would produce an indicator of re-watchability.
Up/down doesn't matter - it's the question that's being asked.
note the caveat RT obviously doesn't actually ask critics these questions, they read and judge their reviews and interpret them as answering those questions.
Really this comes down to how terrible one dimensional comparisons are: it only measure popularity, which is a terrible filter for quality.
Recently, however, it seems like more (imo undeserving) movies that are "just ok" - like decent, but nothing special, romantic comedies and big blockbusters - are scoring above 90%. I might be being curmudgeonly about it, but I've nearly stopped checking it because it feels like there's no information there. My theory is that this started happening once Roger Ebert died... without such a leader in the field, no one is willing to say they didn't like a film unless it's obviously very bad.
Amassing a bunch of 4- and 5-star ratings is easy, but leaving nothing for even the most habitual of complainers to complain about? That's an monumental achievement.
If a place has more 5-star ratings than 4-star ratings, it's generally amazing. If it has more 4-star ratings than 5-star ratings, it's generally fine but not something particularly special.
Just thumbs up/down would eliminate what is, to me, the single most useful aspect of Yelp.
It doesn't matter that star ratings are arbitrary -- when you average enough of them out, a clear signal overrides the noise. You can distrust any given user, while still trusting the aggregate.
(Curiously enough, I don't find any equivalent value on Amazon. On Yelp, you're really evaluating an overall experience along a whole set of dimensions, so there's a lot more to discriminate on. On Amazon, it does seem to be more of a binary evaluation -- does the product work reliably or not?)