I would keep the House, Senate, and President, but what I would change is that the positions would be filled by lottery. Every citizen would be up to serve, and by a random drawing you would have to serve the country. Now this would mean you'd get a cross section of the citizens, nobody could influence and election, nobody could buy an election.
Let me understand this idea. I guess this lottery would be conducted among every citizen who would declare their interest for running for the office, right? Now, what happens if these are bad people, or just complete idiots?
Nope, everyone even if you didn't want to serve it would be your duty, like jury duty. Now you ask if they are bad people or complete idiots, well don't we have those now? Heck I can point to presidents who's family made their money illegally. And we aren't getting the brightest bulbs in the pack now.
Think about it, under this plan nobody can buy an election, corporations can spend all the money they want, of course they won't because they can't influence the election. Being a random selection you would have more women, minorities, more people from diverse walks of life. And since they wouldn't be beholding to a political party they would be free to co-operate with anyone they choose. Yes, you'd have people going after them once they are in office, but given the short amount of time they would serve 6 years max, most could resist the temptations that they could offer. Of course we would still have corruption laws.
I feel given a chance most people would try and do the right thing, even if two people were far left and far right, given a little time they could find common ground, but as it stands now those two people don't dare talk to each other, much less try to work out some kind of deal, they have corporations, their parties, their constituents, screaming for blood from the other side, then the other side is screaming that they aren't willing to talk, etc. by being picked by lottery, much of that goes away. I know the local papers, news, would blast them but again I feel a person would stand on their principals and do what they think is right. It's only when a person get elected and wants to stay in office that they won't vote their principals.