You're correct. I can no longer edit my post, but I should have specified. There's no true "equivalent" of downvoting posts, just the flag system which downweights posts like downvotes do comments. After it reaches a threshold, the post becomes hidden.

It is supposed to be used strictly for posts that violate the guidelines (i.e. off-topic, reposts, incorrect titling, etc). If a user keeps flagging content inappropriately, action may be taken against the user instead.