Use alignment of interests. The Captain must sink with the ship.
Those in power and their immediate families must be forced by law to use only the services available to the lower classes while they are in office:
Live in public housing.
Use no private healthcare . Social healthcare is ok.
Send their children only to state schools ( I think singapore enforces this).
Mandatory conscription for their families if they send troops abroad.
Use only public transport.
This will be a system of government where the fate of the elite is aligned with the lower half of the population. You cannot be allowed to take up a civil or political post if you do not agree. you can always resign and go back to your previous lifestyle at any point. I think that this way the standard of living will be raised for all. A lot of the elite are not evil, they simply lack any undertanding for the fate of those at the bottom. Being forced to live like common people may help them develop some empathy.
To summarise—the design of incentives is just as important as design of the laws and structure of government.
Even a fetus has stimulus. Sound, pressure, movement, touch. Without stimulus and the ability to react you would develop no intelligence, your brain networks cannot be trained. Life would be a fuzzy haze until you die.