The problem with this is that even the best communities have types of arguments that get plenty of upvotes. That would make it easy for someone who knows how to win upvotes to get all the downvote points they need, while making it hard on people who play fairly.
This was essentially Slashdot's approach to voting. Make mod points a sparse currency, forcing users to be far more cautious in their use of them.
I don't agree with their policy that those who vote in a thread may not comment in that thread but I think a lot can still be learned from Slashdot's model.
It doesn't have to be "downvote points", perhaps it's a limit on downvotes per day, perhaps it's a hit on karma (every downvote means a costs x number of karma points, and below a certain karma you can no longer downvote), etc.
There's always going to be a way for determined users to get around the limits, but if it can reduce the number of reflexive downvotes from most users it could still be a net win.
One tweak to this can be to segregate karma points by category (or sub-reddit). That way, any downvote points that you need will need to be "earned" in the same topic.
