Yes. you need a minimum of 500 karma to downvote posts or comments.

RossM · on May 28, 2014

Not quite, I have >500 karma but only see downvote links for comments. I've never come across a post with a negative score.

ctdonath · on May 28, 2014

Exactly. Comments can be down voted; articles/links cannot.

ozh · on May 28, 2014

From the FAQ:

Why don't I see down arrows?

There are no down arrows on submissions. They only appear on comments after users reach a certain karma threshold.

valarauca1 · on May 28, 2014

450 karma to down vote comments.

I'm unsure of the value to down-vote links, its >930 based on the fact that I can't and I have 930 karma.

joshstrange · on May 28, 2014

As 30thElement said:

    There are no down arrows on submissions. They only appear
    on comments after users reach a certain karma threshold.