What if no candidate has a majority of electors in the GE?
the President of the Senate shall, in the presence of the Senate and House of Representatives, open all the certificates and the votes shall then be counted; -- 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 case of the death or other constitutional disability of the President. --]* The person having the greatest number of votes as Vice-President, shall be the Vice-President, if such number be a majority of the whole number of Electors appointed, and if no person have a majority, then from the two highest numbers on the list, the Senate shall choose the Vice-President; a quorum for the purpose shall consist of two-thirds of the whole number of Senators, and a majority of the whole number shall be necessary to a choice. But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.
This is the first election in modern times that this may become a possibility. If Trump runs as an independent and/or Bernie runs as an independent then it is quite possible that the three or four candidates will split the electoral vote to the point that no one has a majority. I believe that both Bernie and Trump have the ability to take whole states and their electors.
The mechanism for resolution is a majority vote in the House, but where each state has one single vote. Note that the electors are simply sent home. I would project that the main-stream Republican candidate would win, given their large majority in the House and majority in the Senate. Suppose the following scenario. The Republican convention is deadlocked and selects Paul Ryan as their candidate. Trump does as he says and runs as an independent. No candidate gets a simple majority in the electoral college. The House meets according to the rules and selects Ryan as President.
If I am correct about this, then Ryan becomes president without having won one single Primary nor a majority of votes in the electoral college.
Although I think that this scenario is a possibility, I don't think that it will happen. I think that Trump will be the GOP's nominee and I think that Bernie will beat him as the obvious anti-Trump candidate. Bernie is honest, visionary, and driven by public service, Trump is, well, an ego trip, nearly devoid of coherent policy and dishonest as hell.