There are online fora where downvoting costs you some of your own karma. That might be an effective compromise.
I like in principle the idea of weighting more informative votes more. I suppose what you'd want is that a vote counts for +/- log p where p is the fraction of the voter's votes that are the same as it. (I'm not sure whether you'd want to count "neither up nor down" as a vote for this purpose. Let's say we don't.) So if someone downvotes everything, her downvotes would be worth nothing, but then her first upvote would be worth log N where N is her total number of votes. If we take the logs to base 2, then a vote either way from someone who upvotes and downvotes equally would be worth exactly 1 unit.
That would be kinda fun. I think it wouldn't actually be that hard to implement (provided we didn't want changes in vote frequency to be retroactive -- which I think is correct) but it would complicate things and it might get gamed in ways more harmful than what we have now (e.g., casting a lot of meaningless votes on random comments to increase the power of one's votes in the other direction).
My suggestion is rather like this. A new poster would get the ability to make some upvotes and some negative votes for free (say 20; perhaps you'd get more upvotes than downvotes). I think that's necessary to encourage newcomers; otherwise they'd feel locked out.
As your karma increases, the number of positive and negative votes you can make increases. However, if you only ever give one down-vote, it's not like that's going to give the person receiving it minus 100 karma. There's still an upper limit on -1. Otherwise, single downvotes could have too large a...
To whoever has for the last several days been downvoting ~10 of my old comments per day:
It is possible that your intention is to discourage me from commenting on Less Wrong.
The actual effect is the reverse. My comments still end up positive on average, and I am therefore motivated to post more of them in order to compensate for the steady karma drain you are causing.
If you are mass-downvoting other people, the effect on some of them is probably the same.
To the LW admins, if any are reading:
Look, can we really not do anything about this behaviour? It's childish and stupid, and it makes the karma system less useful (e.g., for comment-sorting), and it gives bad actors a disproportionate influence on Less Wrong. It seems like there are lots of obvious things that would go some way towards helping, many of which have been discussed in past threads about this.
Failing that, can we at least agree that it's bad behaviour and that it would be good in principle to stop it or make it more visible and/or inconvenient?
Failing that, can we at least have an official statement from an LW administrator that mass-downvoting is not considered an undesirable behaviour here? I really hope this isn't the opinion of the LW admins, but as the topic has been discussed from time to time with never any admin response I've been thinking it increasingly likely that it is. If so, let's at least be honest about it.
To anyone else reading this:
If you should happen to notice that a sizeable fraction of my comments are at -1, this is probably why. (Though of course I may just have posted a bunch of silly things. I expect it happens from time to time.)
My apologies for cluttering up Discussion with this. (But not very many apologies; this sort of mass-downvoting seems to me to be one of the more toxic phenomena on Less Wrong, and I retain some small hope that eventually something may be done about it.)