What we have now is clearly not working well, and no matter what are the reasons you vote for someone initially, they still end up doing their own back-deals that many times it's not what the people voted them for. How do we fix this?
Somebody said it. Swiss-style combination of direct and representative democracy. So you can let political parties do their jobs, but there is a corrective measure if they try to sneak in a lwa against the people. In a pure representative democracy, there is absolutely no (practical) way to prevent politiciens to lie during elections but to make an U turn after the elections and to let influential stakeholders literaly purchase laws. There are no "checks and balances" between politicians and people, to a extent that allows the ruling parties literaly team up and form a cartel against the same people who vote them in.
Partial direct democracy. If people think they should have a direct say on something, even if its a swiss style mosque ban, nobody has the right to deny it to them, under no possible justification.
It is easy to add over our current system, it is democratic, it respects all institutions. I don't understand why this idea doesn't have more followers.
I tend to believe that, in the US at least, most congressmen are not overtly corrupt; rather, SIGs and political news organizations exert influence by drowning out other, often more reasonable or correct sources of information. A steady stream of meetings with constituents may serve to re-ground politicians in a way that's faster and arguably more genuine than trying to cut through a wall of special-interest noise by throwing up our own wall of special-interest noise, no matter how much wiser we believe our (individual and collective) positions to be.
It also seems a relatively inexpensive strategy to test.
[1] That is, who spend most of their time in non-political activities.
[2] Or your capitol of choice.