The more influence politicans have to sell, the higher a price they are able to command.
The only solution to this problem is to take power away from politicians. The way you do that is to keep the federal government powerless so that everything not listed in the Constitution is done on the state level. People can pay more attention to more local government, and if it gets really bad, they have the option of switching to a different state's government (by moving).
Politicians will always try to sell their influence. You keep it down to a dull roar by keeping them as powerless as possible.
That means doing less through politics and more through markets. This is good for markets, too, because it forces corporations to look more to their customers and less to politicians.