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I have seen polls that indicate that Evan McMullin is statistically even with Trump and Clinton in the state of Utah. With the possibility of six votes taken away by another candidate it is possible that neither Trump nor Clinton secures 270. I've read conflicting explanations of how the election would be resolved in the case that no candidate secures a majority of electoral votes.
How exactly will the election be resolved if no candidate receives the needed 270 electoral votes?
The answer below is from FAQ on National Archives and Records Administration
If no candidate receives a majority of Electoral votes, the House of Representatives elects the President from the 3 Presidential candidates who received the most Electoral votes. Each state delegation has one vote. The Senate would elect the Vice President from the 2 Vice Presidential candidates with the most Electoral votes. Each Senator would cast one vote for Vice President. If the House of Representatives fails to elect a President by Inauguration Day, the Vice-President Elect serves as acting President until the deadlock is resolved in the House.
(Emphasis added)
The Congress meets in joint session on January 6, 2017 to count the electoral votes (this count happens whether the election is close or not). If no candidate has reached 270 Electoral Votes, then the House and Senate take over and elect the President and Vice-President, respectively. Note that the newly elected Congress will be sworn in on January 3rd, 2017. It is that new Congress that takes on this responsibility.
Both Rathony's answer and Brythan's are entirely correct about the authoritative, legal answers as to what would happen if neither candidate received 270 electoral votes. This FiveThirtyEight article takes it a step further, though. It explores the actual, political realities which would influence how the Constitutional laws would be applied in this particular election, rather than the general case. (At least, the realities as of October 13th, anyway.)
Specificially, it's looking at the case where Evan McMullin (or Gary Johnson) win at least one electoral vote (which likely means winning Utah or Nevada) and are thus in the list of "the persons having the highest numbers not exceeding three on the list of those voted for as President" (as per the 12th).
So let’s say the Democrats pick up a couple of states in the election, while Utah and Nevada go for McMullin and persuade a few other Republican states to join them right away, such that the breakdowns goes something like – with 26 needed to win — 19 delegations for Clinton, 23 for Trump and eight for McMullin.
Meanwhile, the vice president would likely be known. Since the Senate can only choose between the top two candidates (presumably Kaine and Pence), it would take a perfect tie for them to remain deadlocked.
So here’s the rub: Whichever side loses in the Senate might have good reason to make a deal with a McMullin contingent in the House. That is, if Kaine is VP and the McMullin contingent holds fast, the party-loyal Republican coalition may be pressured to accept McMullin as better than Clinton (who would win if McMullin states sided with the Democrats) or Kaine (who would become president if the House remained deadlocked). While if Pence wins in the Senate, the Democrats may be pressured to accept McMullin rather than Trump or Pence — especially if they make deals for political appointments or legislative commitments. While this may sound shady by U.S. norms, it’s not unlike what happens in parliamentary systems around the world.
In other words, in the highly unlikely scenario that neither candidate receives an outright majority because a state or two went third-party, and House Republicans have enough gumption to oppose Trump, there is a strong possibility we will end up with the first split White House since 1796.
The authoritative source is the 12th amendment:
The person having the greatest Number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice. And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President.
Note that the fourth day of March text was changed in a later amendment to the 20th of January.
The state delegations in the House of Representatives vote state-by-state. The candidate with a majority of the states wins. If no candidate wins a majority of the states, it goes to the Vice-President. Note that the Vice-President is chosen (possibly by Senate vote) prior to the presidential selection. And both houses of Congress change prior to the vice-presidential and presidential selections.
The Republicans currently have a clear majority of the state delegations. This is likely to continue. They have a stronger control over the state delegations than they do over the House majority. This is because the small states that Republicans dominate count for as many votes (1) as the larger states where Democrats are most likely to gain seats.
That said, Utah is unlikely to keep presidential candidates from 270. It's a clear Republican state in most elections and only has six electoral college votes. Donald Trump would need to make a major comeback to limit Hillary Clinton to 269 or fewer electoral college votes. If he did that, he'd presumably gain votes back from Evan McMullin. It would be more effective for a Democratic state like Maine, Massachusetts, Minnesota, or New Mexico to go for a third-party candidate, as that would reduce Clinton's overwhelming lead.
It's not clear that a McMullin win in Utah would change anything even if it did keep the candidates from winning the electoral college. He might have trouble rallying Democrats behind him to join with Never Trump Republicans to flip state delegations. It's possible, but not decisive. By contrast, Johnson would have a much easier time appealing to Democrats and still has Never Trump appeal to Republicans. And of course, Johnson has actual governing experience, where McMullin is a first-time candidate.
The more likely effect would be to send the election to the House and Trump voters to apply enough pressure to give him the election. But if Utah voted for Trump, he'd win the election anyway. The greater risk seems to be that a four-way split would give Clinton victory in Utah. But that seems unlikely to occur if Trump is anywhere close to 270 electoral votes.
