I like the "jury duty" model for elections.
Everyone who's eligible (citizen, over 18, not currently in jail, what have you) has a chance of being picked randomly to serve on your city council/county council/state or provincial legislature/federal legislature or parliament. Those chosen then have to work together within the framework of a constitution and existing laws to figure out how to run things.
Sounds crazy, but it just might work. If you like SF, Kim Stanley Robinson's "Mars Trilogy" (the three novels Red Mars, Green Mars, Blue Mars) outline a hypothetical society of Mars colonists from Earth who do indeed implement such a system. (I think it's mostly in Green Mars where it's discussed, but I haven't read them in a while and don't remember for sure.)
It's a great way to avoid partisan bickering and extremism, at least.