>but maybe the solution is to allocate a certain amount of reasonable votes (up or down) total that a user can use weekly

Slashdot did this back in the day IIRC.

I was just gonna say that!

Yeah, you had to have sufficient rep on Slashdot, then you were randomly allocated a certain number of votes (5 or so, IIRC) that you could use to vote. There were fixed categories you could vote an item for, such as "funny", or "off topic". Once your votes were gone, that was it until you were randomly awarded more. The max score anything could get was 5, and a minimum was -1. You could use the scores to filter what you saw. (ie: show full text of >3 insightful, and summaries of 1-2, hide <1)

It worked pretty well. Obvious trolling was still down voted, and insightful stuff was up voted. The ability to just show a blurb of lower-voted stuff was nice as well; you could ignore obvious crap, but expand it if it caught your attention.