Fixing the way representation works, or anything else really about the democratic process, will not fix it (although I am partial to doing away with gerrymandering). Improving democracy is a red herring. As long as people can vote themselves a ride on the backs of the minority, a government by the majority is destined to failure.
Although we're taught that America was a brave and innovative experiment in self-government, it ain't true. The Pilgrims ran away from the Netherlands -- which was already a representative democracy. Ages before 1776, even
pirate ships were run according to democratic principles. Heck, the ancient Greeks had a pure democracy. Nothing new or interesting on that front.
The *only* reason the USA is still a going concern (and arguably the stongest and most stable in the world) is that its Constitution is constructed based on a philosophy of a limited government built of strictly enumerated powers.
We (the Americans) dig ourselves deeper into trouble every time we cede to the government greater authority. They always tell us that a given power is necessary to fix a given problem, and they may even be sincere. However, in the end, these powers
always wind up being subverted. Indeed, there's a whole branch of economics (
Public Choice Theory) that deals with this. There's a phenomena called "
regulatory capture", manifested in things like
rent seeking, that describes how the regulated eventually become the regulators -- not through corruption, but through perfectly natural and rational progression.
If you think that things in America are broken, the way to fix it is
not to give the government more power to deal with the issues -- that's just digging a deeper hole. The solution is to strip the government of its power, so all those powers that have been co-opted by interest groups are returned back to the people.