I'm glad you've opened a discussion about this, BTW, even if it turns out you are wrong.

I was wrong. Hansen's 2002 proof was much, much easier for me to understand than the other ones, but I was reluctant to generalize it past 2 voters until I wrestled with homunq's example. Even after seeing it in the 3 voter case, I had to resist an impulse that said "but surely there's an n such that an n voter situation works!"