When I was writing Cat President, I threw in a couple of the weird election scenarios that popped up on the Internet, like "What if one person is secretly funding all candidates?" and "What if the Republican nominee and Democratic nominee are secretly working together?".
(The last one is the bad ending to the Frisky storyline. He falls in love with the female candidate from the other party and picks her as his VP. She picks him as her VP. Now everyone is stuck with both of them no matter what.)
So here's a new election scenario that someone has kicked around. What if neither Trump nor Clinton wins the election? What if they tie at 269 electoral college votes? Or, more likely, what if a third party candidate gets 10% of the vote, which prevents Trump and Clinton from getting the magic number of 270 votes?
This is basically the brokered convention scenario, on a national scale. When that happens, the incoming Congress gets to pick the President. Voting starts with the House of Representatives, I think. The laws covering the "no winning President" scenario--the 20th amendment--were mainly written for the scenario of someone killing the President-elect before they take office, but they apply if no one wins the election, too.