Not only that they can't increase their own salary and total compensation at all, but rather for their salary and total compensation to be increased, somebody from the board members has to suggest it first, and bring it up to voting with the whole board assembly.
This is a problem that takes thought, I don't really think it has to do with the magnitude of their pay. It has to do with how they get paid.
I believe if companies were not allowed to use stocks which they fabricate out of thin air to pay executives, executives would not be paid nearly as well.
The reason is pretty straightforward. By creating $100M in stocks and giving them to the executives, corporations aren't actually paying a dime out of the corporate coffers. This makes it too easy for them to do, it makes executive pay 'cheap' from their perspective.
But nothing is free. The ones that pay for it are the shareholders, who see the value of their shares diminished by this.
Now if that 100M came off the bottom line, hurt their profit, emptied their bank account, they'd think quite differently. It would become far more competitive, and executive 'compensation' would almost certainly drop.
Just pay them the same way normal people are paid - payroll - and for one it becomes subject to payroll tax (37%) and not capital gains tax (20% max). There's also big incentive to make people compete for top jobs, just like regular people.
They can still get bonus', just like normal people. Just keep in mind, that bonus comes out of profits, not out of the shareholders equity. And full normal taxes need to be paid on it.