(I'm partial to approval voting (vote "yes" or "no" for each cantidate separately and if the winner doesn't have at least 50% "yes", the office is vacant until the next election), but I suspect the party line would immediately become "you're a traitor if you approve anyone but the Party's candidate".)
Not voting, but it is a real election system, known as Sortition (https://en.wikipedia.org/wiki/Sortition). It was used in ancient Athens.
Also, yes, approval voting is a great approach and we should absolutely use it. We'd still get people who vote party-line, and it'd take a while for people to truly internalize that they can safely vote for other candidates they like, but it'd be a massive improvement.
I vaguely remembered that, but not the name, thanks.
Other countries with other systems don't really do much better.
The fundamental problem is that the people who want this sort of power are the last ones who should ever be allowed to wield it. When people are willing to spend hundreds of millions of dollars to get a job that pays $500K a year, you have to wonder what's really going on.