I think that a decent "rule patch" would be to make a law tying the maximum amount of money someone can legally earn to the lowest wage paid within a company. So if you're the owner/CEO and your lowest paid employee makes $15,080 per year (which ayk is the current federal minimum wage), you can only make N x $15,080, with N being a two-digit number that people can agree on without crashing the government. Under this system, the more you pay your employees, the more you're eligible to make. I don't actually think it's something that could be implemented in my lifetime, I just think it's interesting.
That wouldn't solve anything. The shareholders would just elect a CEO who's willing to work for (relatively speaking) the minimum.
You won't get a good CEO with that. A good CEO can pick whatever company he wants, he/she gets a golden handshake and an amazing contract because companies are competing over which of them the CEO will pick.
CEO's use that argument all the time to peel off as much as the can from the companies that are supposedly getting the most out of their amazing CEO-ness.
Funny how they always manage to organize themselves golden parachutes when their amazing management skills make the company go belly-up!
