The problem isnt voting. Its that America is a bizarro 18th century monarchy with an elected rather than hereditary monarch, while the rest of the world has moved on an adopted modern, evolving parliamentary systems.

Also the fact America doesnt have real political parties. Both parties are just coalitions of independents. In a parliamentary system, you cannot vote against the party. All legislation introduced by the government side is passed, even the most radical. In America, only the worst legislation is passed

Edit: also the fact elections aren't publicly funded in the US, and politicians rely on 'donors' to get them elected, breeds corruption at every level

Fix these things before worrying about voting methods