This year's presidential election has the potential to be one of the greatest political trainwrecks in American history.
The founding fathers had a low opinion of the average citizen. That's why Presidents are selected by the Electoral College and not by popular vote.
The founders also didn't believe in partisan politics, which is why there's no mention of political parties in the Constitution, so the present method of primary elections, caucuses, and party conventions evolved erratically over the years.
While most savvy voters know the president and vice president aren't elected by popular vote, and that each party's nominees are selected by delegates attending national conventions, they may not know that, in most cases, those delegates can vote for whomever they want, regardless of the results of their state's primaries or caucuses after the first ballot. There are even five states and territories who don't hold primaries or caucuses, resulting in 112 delegates who can vote according to their personal preferences without direction from voters.
Consider the 1968 Democratic convention. Despite the fact that over 80 percent of primary voters had supported anti-Vietnam war candidates, the "peace" candidate, Senator Eugene McCarthy, was defeated by Vice President Hubert Humphrey, who had not competed in any of the primaries, instead gaining his delegates in caucus states that were controlled by party leaders.
The Humphrey business resulted in many- but not all- states to adopt rules where delegates are bound to vote for the winning candidate during the convention's first ballot. After that, it's a free-for-all.
The worst case scenario to date was the 1924 Democratic convention, a 16-day marathon that required 103 ballots to select a candidate. Wikipedia notes that during his 1960 campaign, John F. Kennedy cited the dilemma of the Massachusetts delegation at the 1924 convention when making light of his own campaign problems: "Either we must switch to a more liberal candidate or move to a cheaper hotel."
What could happen this year? Say Trump is nominated, despite the party's efforts to thwart his campaign. Disgruntled Republicans could put together a third-party ticket, in an effort to prevent any candidate from winning the absolute majority of 270 electoral votes necessary to win the general election.
Should that happen, the president would be chosen by that shining example of civic responsibility, the U.S. House of Representatives, composed of lame duck Congressmen, many with an axe to grind. The U.S. Senate gets to pick the vice president.
Could it come to that? Probably not. But the odds are good the Republicans will have a brokered convention, and the Democrats may have one as well, if Bernie Sanders can convince uncommitted superdelegates to take his side.