Electoral ties in Nevada are settled by the candidates drawing from a deck of cards. High card wins. Works very well.
There is a well-known anecdote about Abraham Lincoln (I say "well-known anecdote" because I'm not a historian and have no idea if it's an acutal quote or not) in which he claims that just about anybody can do an effective job of governing (at least that's how I read it). Maybe injecting a little randomness into our election process wouldn't be a bad thing. It would sure as heck be more fun, and would clean up all the nasty advertising and pandering and weak positions.