>It's about not having a solution that gets anywhere near a majority approval.

You'll never get it in any non-gamed environment.

In democratic voting in FPtP systems if there isn't a majority winner you'll take the top two and go to runoffs forcing those that are voting to pick the best of the bad choices.

This is the same thing that will typically happen in the city you're talking about, hence why most democracies are representative and not direct.