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 an impact.
My suggestion is thus a) that the votes of people who vote a lot (either up or down) would get diluted and b) that the votes of people with little Karma would get diluted.
One possible drawback is that there might be people who read a lot, are good at distinguishing good posts from bad, but which don't post and hence have little Karma. Such people's votes would get heavily diluted in this system. But I suppose that's a minor thing and all systems have their drawbacks after all.
I'm not sure that last one is really a drawback. It amounts to encouraging more active participation from people with good judgement. That would be a good thing.
I think I was unclear in my earlier comment: when I wrote "I suppose what you'd want is ..." I didn't actually mean I thought that was what you were proposing. I was ruminating on what happens if one takes seriously the idea of estimating how much evidence a given vote from someone with a given historical voting pattern provides.
I agree that just restricting the amount of voting each user can do is a simpler way to achieve something along similar lines.
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.)