Ask HN: Would allowing a down vote on submissions after a comment improve HN?

I don't want to get into the debate about whether HN quality is declining. I just want to explore how to improve the system.

Being the HN noob that I am, I was surprised to find that submissions can't be down voted. I always assumed that you could down vote submissions once you reached a certain karma level.

If the down arrow were hidden until the user posts a comment, it might encourage constructive criticism, partly because their own karma would be on the line (via the comment).