An idea I had for a voting system

[minionofmidas]

Condorcet would probably be ideal in the United States, actually, due to the lack of a centrist party to make it boring.

But it's too complex, both in voting and counting. Plus nobody can agree how to count it, or what constitutes a winner. This is far simpler, yet leads to roughly the same outcome.

No, it doesn't. It leads to a fairly random outcome that may or may not be sorta like Condorcet. If you think Condorcet's too complex (although the situations you refer to in which there's any doubt about the winner are not substantially more common than exact ties in fptp, frankly), use IRV.

Or how about not having quite such a powerful single individual, electable by any form of simple majority, in the first place? That would certainly be the most rational choice.