If there isn't a downvote button, it's hard to see how things could get out of hand.
I don't know how you could say that with a straight face, because I sure couldn't do it. Just because there's no downvote button, the mere presence of an upvote type mechanism will form factions. The only thing the downvote mechanism will do is just make the existing mess bigger. Not having the downvote mechanism will still result in factions who just compete for more upvotes (or as I would say,
<you can't say that here> with whatever mechanism is available to them)