Sage as a method of downvoting a thread is insane and encourages even more shitposting. 4chan actually does have a "karma" that manifests in the way of replies to your posts/threads. So when you reply to a thread using sage as a downvote, you encourage the poster by giving him replies. Using sage is just a flag to the other guy that his post is irritating enough for you to sage it.
This used to be a huge problem when it was popular to post troll pony threads on macho boards like /v/, /sp/, or /fit/. What would happen is there would be 10 replies in the first minute, all sages, calling the OP a retard and reminding everyone to sage and report the thread. These replies would just feed him, to which he would reply to the sages and egg people on even more - to which he would receive even more replies.
The only acceptable analogue to "downvoting" on 4chan is to not reply to the thread. Nothing can dissuade a shitposter more than having put some effort into writing a good baity OP post, and not getting a single reply before the janitors delete it.
If you're determined enough to sage bomb the thread to image limit, especially now that there's a captcha, sorta, but not really.
Also cheers to moot. I've noticed the improvement in moderation first hand recently, even getting banned myself, whereas previously that board felt like it had zero mods.
So, using sage as a way to 'downvote' is just a way of adding towards the thread limit without bumping the thread. It's a round-about way to do it though (vs. direct downvoting).
"sage" originates from 2chan (aka Futaba Channel), which was the inspiration for 4chan. 'sage' is short for sageru.
If this is true, sage can not be used to downvote at all, EXCEPT if there are enough sages to make the thread expire. However, that limit is something in the 100s. No one has the time and dedication to "sage a thread into non-existence," even though they sometimes call for it.
Ahhh, memories.
Also the introduction of some of those boards was simply to get shitposts out of other boards (e.g. /soc/ was created to cleanup /b/ and /r9k/). Worked great.
However, I have to disagree with the sage thing. While originally the term was used to not bump a thread (implying that your own post was not worthy of bumping a thread back to the front page), in the last five years (and before that, to some extent) it HAS been used as a way to 'down vote' a thread.