You're all going at this from the wrong direction.
The problem isn't that we have corruptible politicians--that's as old as history. The problem is a government that has accumulated so much power in so many arenas that the human failures in politics become catastrophic.
Reduce and decentralize that power, and things will improve. Pournelle said once it used to be more important to the average American who their mayor was than who the president was. That was before the Federal government somehow became in charge of almost everything in America.