There was a Stack Overflow blog post today about Hacker News's lack of downvoting, and how that was bad. There's a great discussion of it over on Hacker News. As a matter of fact there is downvoting, but it's not very evident from a cursory glance.
Both Stack Overflow and Hacker News feature user voting. Users can vote on links, questions, and comments posted by other users. The votes add up for the user, which in turn lets them do more with the site. With the vote systems, the community can decide what's on and what's not. It's community moderation.
Stack Overflow uses this vote system to determine the most interesting questions and answers, which is good because it's a Q&A site. You can upvote after you gain 15 "rep" (points), and downvote after you get 100.
Hacker News is similar. Again, upvotes, but this time you only need to be registered. Downvotes require 100 points. The down arrow isn't shown to users with less than this, which is where Jeff (who wrote the blog entry) admits he didn't catch. Stack Overflow does show the arrow, it just doesn't let people under the threshold use it.
Notice the voting pattern here? Downvotes always seem to require more than upvotes. Why? Is a -1 more dangerous or powerful than it's +1 counterpart?
One theory has to do with the Internet itself. In a place like this, negativity reigns. Hate breeds hate. Vitriol breeds vitriol. Flames fan more flames. Arguments spiral out of control.
Communities tend to decide themselves. Developer mailing lists draw other developers. Fan sites attract other fans. Hackers attract hackers. Trolls attract more trolls. In a community, like attracts like. Because of this, direction at the early stages of a community is vital for its future.
If I had to guess, the upvote/downvote dichotomy has to do with breeding positive interaction over negative, in order to build a uplifting community. Still, from a bits-and-bytes perspective, -1 vs. +9 is the same difference as 0 vs. +10. However, to people, they're very different. Strange but true.
Ultimately, community moderation is scaffolding: the point is to promote discussion and valuable contribution. If people were perfect and exactly the same, we wouldn't need these things; one person's favourite submissions would be everybody else's, everybody would agree, no voting required.
But in the real world, community moderation is a necessity. By arriving at a consensus, it lets us communicate more effectively as a group. The point of these voting systems is to give attention to the links and comments that the community as a whole likes the most.
If the aim of voting is to separate the wheat from the chaff, maybe there's another way. People could still vote on submissions, but rather than merely summing up votes for users, voting would contribute the points of the voter to the voted. The more points a user has, the more trusted their opinion. If a lot of nobodies vote for a user, that isn't worth much, but if an established user who's sent in lots of good comments votes, that's worth a lot. By doing this, there's real incentive to carry on the spirit of the community, because those are the ones most likely to be voted on by the established user base. Like attracts like.
You know, it almost sounds like Google's PageRank.
It wouldn't be free of problems. The simple voting system is more transparent, and thus has a greater element of trustworthiness. People would have to be stopped from voting for themselves. Instead of link spamming, there'd be vote spamming. A sleeper cell could turn the whole thing inside out. But I bet it'd be an interesting experiment.
Edit: Speak of the devil, this book about game theory has a chapter about exactly that. Chapter 27: Manipulation-Resistant Reputation Systems.