What if Trump and Sanders Both Ran as 3rd Party Candidates?

A friend asked me, what would happen if Clinton and Rubio win the primaries, but Trump AND Sanders both run as 3rd party candidates? We haven't seen an election with four legitimate (in that they each would have large followings and a chance to win) candidates for president in the last hundred years.

I decided to project which candidate would win each state in this theoretical example. My assumptions were that Trump would do well in the Bible belt, Clinton would do well in the Mid-Atlantic states as well as classic Democratic strongholds in the Mid-West, Sanders would do well in New England and California, and Rubio would do well everywhere else. What this led me to was:

So, we end up with:

Trump, 14 States, 88 Electoral Votes
Sanders, 11 States, 124 Electoral Votes
Clinton, 12 States, 152 Electoral Votes
Rubio, 13 States, 170 Electoral Votes

What does this mean? This would mean that for the first time since 1824, the House of Representatives would choose the President of the United States. Under the Constitution, if no candidate gets a majority of the votes, the three highest vote getters would be put before the House of Representatives with each state getting one vote.

To me, in this scenario, there would be no bargain like there famously was in 1824 with Henry Clay and John Quincy Adams. This is because even if Clinton and Sanders formed a coalition around one of them, Rubio would still win. The fact of the matter is, right now, there are more Republican states than Democratic states. There are more Democrats, but they are often concentrated in urban areas. Although it should be said that Donald Trump is the definition of a wild card so it is impossible to say which direction he would send his support.

It would be historic. It would be incredible. But, if all four run, I'd project us to elect President Marco Rubio.