Bayesian democracy
I was reading today about liquid democracy, which is a kind of improvement on direct democracy. Most of what makes direct democracy difficult, aside from the logistical difficulties of holding so many votes, is just that most people don't need to have an opinion on most issues. In liquid democracy you can just delegate your vote to someone else when you want. That can be a friend or a community leader all the way up to a traditional-style professional politician.
But of course you still have the problem of knowing who to delegate to. In some cases you can rely on there being a public figure whose opinion you trust. However, for many issues that process could be just as onerous as figuring out which way to vote. Some of the liquid democracy systems also seem to suggest that you could delegate certain topic areas, ie you have an environment delegate and an economy delegate. Though it's not clear exactly who would decide how things fall into those categories, or what would happen if an issue falls into both.
I think there's a more elegant solution to this: use Bayesian inference. Every vote is option, and by default you're assumed to vote with the majority on any given issue. However, you can at any time change that default vote and that updates the prediction of your future votes. If you vote in a pattern that is similar to a bloc of other voters, your default votes will become more similar to theirs. Essentially, it's the same algorithm you might use for any recommendation engine, it just recommends a vote.
I call this idea Bayesian democracy. I think it could be a pretty interesting generalisation of liquid democracy, allowing you to delegate your vote, not to another person, but rather to a statistical model of your own preferences.