Tiered subreddits. You would need to earn credibility in open discussions, and earn your way up into more serious discussions. So there would end up being multiple layers of credibility, with only vetted accounts participating in the highest levels.
HN user jfc said it better here: https://news.ycombinator.com/item?id=7650975
Moreover, jfc has valid points about negativity and unhelpful responses, but it remains anecdotal. As a counter, my own anecdotal experience has largely been positive on SO, and I rarely run into those problems. I am definitely not part of the cohort that was there first, and think it's a rather fair system. For example, preventing downvotes until a certain level of reputation is reached is a small check on those looking to farm karma by blanketing out competing answers. Obviously it isn't foolproof, but it at least ensures that you have actually contributed to the community at least a few times.
Perhaps his comment speaks more to the quality of the userbase than to the efficiency of the voting system?
After the initial adopters had been outnumbered, but long before reddit was popular enough to attract legions of professional marketers, popular subreddits were dominated by puns, memes, highly biased politics, emoting, etc. It's what people upvote, and it doesn't require a reputation system.
People who are picturing crowds coming in and messing up such a system aren't really getting the idea -- it is a closed system. Above the lowest layer, it is read-only to the public, unless you are given permission to contribute. The other commenter who said people don't want a system like this may be correct... but that might be a good thing. Catering to the crowds isn't the goal here. Finding the much smaller groups that are willing to put in more work to manage themselves, and engage in meaningful dialogue is exactly what might make places like /r/politics meaningful.