People will often cheat or lie. But if you ask them to sign a document that they are telling the truth, the cheating/lying goes WAAAAAY down. Crazy, I know. Economists would say no way, but social scientists/psychologists have found it to be true. You effectively "wake people up" to their morality and make them think about it. And when they think about it, they usually want to be honest.

There would still be cheaters/people lying, but you can get a lot of mileage out of the cheap method of just asking them to tell the truth.