I was asking myself what the right amount of games to rate was and one answer I came up with was this.
(games I rate) > (ratings on my game)
If your game was popular this might be difficult for you lol
You should rate as many as you want to. There should be no obligation to rate a set amount, since such rules would turn Jams into Jobs.
A bigger number of ratings legitimizes the winner. However not everyone will win the prize. I think that real feedback (not the "nice game" variety) is much more valuable than star ratings. When you rate you should concentrate on helping your fellow game dev rather than rate for ratings sake.