I have a much simpler solution that doesn't require any of that inconvenient unconstitutional investigation and draconian punishment garbage, as it takes away any incentive for politicians to get elected, stay elected, or even be politicians; it takes away representatives' entire basis for graft, which by the way, isn't so much about the small-scale crap like bus stops and parking garages snow removal, as about remaining embedded in office under the sway and pocketbook of lobbyists, corporations, and campaign financiers. It also keeps the government representative; it makes the government far more representative; in fact if it was implemented, it would be the most representative government to ever exist.
There would be some details to iron out over the logistics of it, differences with offices, judiciary, etc. but I think it's completely feasible.