I doubt it would work the first time. For just as you describe.
However, the new group of 80% of the population will get to see what happens when the person/team they voted for trashes the office, lies to them, treats them as garbage, etc. The new voters can no longer sit on the fence, as they have always done so, and bitch and complain about politicians and politics. Because now, it is their fault. They voted for them.
So next time, more of them will pay attention to the details that affect them. Hopefully, eventually, they start to think beyond themselves.