Don't just the two parties have a chance?. No, take a look at the 1968 and the 1860 elections. Most especially, look at the 1824/25 election where someone that didn't have a majority and wasn't even #1 in electoral votes won.
We also still have what is left of the electoral college. Any of the top 3 POTUS Candidates can win if none get 270 electoral votes. Yes, someone with just a few electoral votes could be POTUS. The electoral college makes sure the candidates don't just target the large cities in the country, but actually look at all the states.
This link below shows who the Utah choices are currently to vote on. You can't just write in anyone for POTUS and have it count. They have to have filed and be listed.
More on the Electoral College:
If we don't get 270 votes, it goes to the US House of Representatives, one vote per state from the top 3. Who is the 3rd candidate going to be If they can't get a majority? We may get the VP Candidate voted on from the US Senate out of the top 2 electoral votes if the House can't decide. IF the House fails to pick a President and the Senate fails to pick a Vice President, then under 3 USC 19, the Speaker of the House can resign and become the President.
If he doesn't, we get Sen. Hatch. Yes, I know....
While this was for a different purpose, it has some good info:
What we have now with the 12th Amendment:
The Electors shall meet in their respective states, and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves; they shall name in their ballots the person voted for as President, and in distinct ballots the person voted for as Vice-President, and they shall make distinct lists of all persons voted for as President, and all persons voted for as Vice-President and of the number of votes for each, which lists they shall sign and certify, and transmit sealed to the seat of the government of the United States, directed to the President of the Senate.
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.
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.
From the 20th Amendment for the section crossed out above:
20th Amendment "Section 3. If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified."
IF the House fails to pick as President and the Senate fails to pick a Vice President, then under:
3 USC 19: Vacancy in offices of both President and Vice President; officers eligible to act
(a)(1) If, by reason of death, resignation, removal from office, inability, or failure to qualify, there is neither a President nor Vice President to discharge the powers and duties of the office of President, then the Speaker of the House of Representatives shall, upon his resignation as Speaker and as Representative in Congress, act as President.
By the way, in Utah, someone can run as a write-in candidate for POTUS, but they must file by September 9th. It doesn't cost. You could, if you qualify.
To show up on the ballot as an unaffiliated candidate for POTUS, The filing must be received by August 15th with $500 and 1000 signatures. You can't just write in anyone on your ballot and have it count.
From the Lt. Gov.
Candidates who do not wish to affiliate with a ballot-approved political party may appear on the ballot by submitting a petition. Candidates for the office of President or US Senator must submit a petition with the signatures of at least 1,000 registered Utah voters. The names on the petition must be verified by the county clerk(s) as registered voters.
Presidential candidates (or a designated agent) must file the petition and a certificate of nomination between March 11, 2016 and 5pm on August 15, 2016. Unaffiliated candidates are required to pay the same filing fees as all other federal office candidates.
Write-in CandidatesTo become a valid write-in candidate for a federal office, an individual must file a Declaration of Write-In Candidacy no later than 5pm on September 9, 2016. Individuals filing for President may have a designated agent file for them.
Federal office candidates must file the declaration in person with the Lt. Governor's Office. Write-in candidates must meet the qualifications required for the federal office they are seeking. Filing the Declaration of Write-In Candidacy means that write-in votes for the candidate will be counted. The candidate's name will not appear on the ballot.