Just out of curiosity, what do you think would be the consequences of being downvoted? Why would it discourage people?
People won't change their posting habits unless they have some reason that's more than, "Oh, look at all those downvotes! People didn't like what I said. Oh, well. *shrug*"
I've explained this too

You can set "levels" in the vB system, so that if you have, say, 0-50 rep you're at Level 0, at 50-100 rep you're at Level 1, 100-150 is Level 2, etc. Your incentive is to level up -- afterall, this is a
computer games forum! We're all addicted to levelling up. Ideally you'd have your level somewhere under your avatar, where you postcount etc is (actually, replacing post count with rep or level would be pretty great...). But Hygro's also pointed out that the incentive is still there (though I believe lessened somewhat) when the level is hidden on your profile page, or even hidden from public view completely.
Even without the levels, people like getting upvoted. Trolls like getting downvoted, but that's okay because it makes them easier to identify and ignore.
It also means that you get some "closure" in deadlocked threads -- you have a safe, relatively harmless way of signalling your "dislike" for someone's posting. Right now, the only way of doing that is by saying it -- and if you are REALLY offended by a post (but the post doesn't cross the line in terms of rules), your only two options are to respond with as much vitriol as you can muster (whilst still staying inside the rules, of course), or to ignore them. The first option leaves you with a little bit of closure, but clearly is detrimental to the forums and helps to destroy the thread. The second option leaves you with no closure, and just makes you less and less happy with the deteriorating quality of the forums.
The other option is the "Like" button I raised before. I believe in vBulletin forums you can "thank" people for their posts? I've seen it on other forums, which I'm pretty sure are vBulletin forums. This would effectively allow "upvotes" but not "downvotes". Has a similar signalling mechanism -- i.e. you upvote people who aren't engaging in incessant tit-for-tat quote wars, or who are trying to stop them and return some sanity to the thread. But it wouldn't effectively stop people from engaging in tit-for-tat quote wars.
The long and the short of it is that there's no way for anyone to break up an incessant quote war. The only thing we can do is wait for one of them to slip up (as inevitably happens) and troll or flame the other person. Then we can report it and they earn a red card, and hopefully some
Moderator Action: text telling them to STFU. That is clearly a situation in which nobody wins. It needs to change.
Please read the forum rules: http://forums.civfanatics.com/showthread.php?t=422889