Second-order voting means that the aggregate of everyone who does it votes towards a consensus value of things being the value they think they are; first-order voting means that there's no consensus process, instead getting a double-counting of perspectives, where a post that is easy for many people to evaluate as good gets voted highly because they independently think "this is good, therefore I will upvote it". if they all instead think "this is x amount good" and vote towards that, then it reduces incentive towards popularity contests and the stuff that is harder to evaluate but good stands out better.
I guess, in reality some people are going to be first-order voters no matter what, some people are going to be second-order voters no matter what, and the resulting karma depends on the order they placed their votes.
Imagine an article such that five people think "this is nice", and five people think "this is nice, but does not deserve more than 5 total karma". If the former vote first, the article gets 5 karma, then the latter abstain from voting, so it stay at 5. But if the latter vote first, the article gets 5 karma, then the former vote, and it goes up ...
I'm much more likely to take existing karma into account when strong voting. For weak votes I'll just vote my opinion unless the karma total is way out from what I think is deserved. This comes up mostly with comments that are bad but not so bad I want to beat the dead horse, or that express a popular sentiment without adding much.
If you want Karma to be about more or less of this on LW, then the first strategy seems to match that. And adjust (removing or reversing your vote) if others vote to the level you think is right.
I think there's enough others on the site that #2 tends to happen, regardless of your intent, so maybe don't worry much about that.
In fact, don't worry much about any of it - karma is lightweight and noisy, and it's a mistake to treat it as a particularly fine-grained signal.
Normally I try to use karma votes in a practical way to try to help promote content that I want to see more of on LW, or to downrank content that I want to see less of. (As opposed to using them as a kind of social signal, which is a separate issue.)
One thing I have never quite figured out is which of these two I should be doing to best accomplish that goal:
Look at the current score of a post or comment, and vote so as to adjust its current score towards what I would consider to be fair.
Judge the post independently of its current score, and have some thresholds of goodness in my mind (relative to a general standard of quality for LW posts) that I use to decide how to vote.
I could easily imagine some pros and cons to each approach. Is there any consensus as to which will make better results, either if I apply it independently, or if the community applied it universally?
My intuition is that the second is better, but I haven't really figured out anything concrete.