With the historically high negative numbers for both major party candidates, Donald Trump and Hillary Clinton both need to worry about third party candidates.
Third party candidates rarely do well. For the most part they take away from major party candidates to act as a spoiler. The last major third party candidate was Ross Perot who ran against Clinton in 1992 and again in 1996. He received almost 20% of the vote in 1992, but only 8% in 1996. It was enough to let Clinton win with less than 50% of the popular vote. However, it is not clear that his entry would have changed the outcome as he drew votes from both major party candidates.
Green Party Candidate Ralph Nader often receives credit or blame for altering the outcome of the 2000 elections. Although he received less than 3% of the vote, the margin that year was so tight that he may have affected the outcome. People often point to Florida which was decided by less than 1000 votes and which decided the outcome of the election. This is an argument you will hear Clinton make often to discourage liberal voters from abandoning the party this year.
Third party candidates mostly run as spoilers with little chance of actual victory. To win any electoral votes, a candidate must in a majority in a State. Candidates with strong support among a minority of voters end up with zero electoral votes, such as Perot who got 20% of the popular vote but zero electoral votes. The last third party candidate to win an electoral vote was George Wallace, who won a few southern States in 1968, when southern Democrats still were not ready to support a Republican, but also rejected the liberal integrationist candidacy of Hubert Humphrey.
The notion that third party candidates cannot win tends to be a self-fulfilling prophecy. Because people think they cannot win, most see a vote for them as a waste, meaning they pick the better of the two less desirable major party candidates. Therefore, third party candidates have a difficult time attracting votes, even if voters tend to favor them. They also tend to get far less media coverage, which is necessary to attract voters.
The last time a third party candidate won (indeed the only time) was when Abraham Lincoln beat three other major candidates in 1860. That turned the Republican party into a major party for the first time. Since then, the only third party ever to beat either major party was when former Republican President Theodore Roosevelt ran as a Progressive against Republican incumbent William Howard Taft. Roosevelt beat Taft in terms of both popular and electoral votes. But the two men divided support and handed the election to Democrat Woodrow Wilson.
Current rules now make it nearly impossible for a third party candidate. First, unless a candidate gets at least 15% in the polls, he or she cannot participate in the debates. Since most people haven't heard of the candidates, let alone what the stand for, it becomes impossible to reach 15%. Further, candidates who have not reached certain thresholds in the prior election need to jump through more legal hoops to get their names on the ballot. Unless a candidate has strong organization in place more than a year before the elections to file the necessary legal paperwork they will not show up on the ballot in most States. Third party candidates also used to be at a disadvantage because they were ineligible for federal funding. But since the major party candidates also now reject such funding, that disadvantage is largely moot.
In 2016, it looks like there will be only two parties that are on the ballots in enough States to win a majority of electoral votes. The Libertarian Party may be able to get on ballots in all 50 States. The Green Party may get on most but not all States.
The Libertarian Party has nominated Gary Johnson for President and William Weld for Vice President. Both men are former Republican Governors from fairly liberal States (Johnson - New Mexico, Weld - Massachusetts). Currently, the Libertarians seem to be reaching out to Sanders supporters by strongly promoting a liberal social agenda, touting their support of abortion rights and gay rights, as well as marijuana legalization They also focus on their desire to reduce military spending and keep America out of foreign wars. Traditionally, Libertarians tend to take their small percentage of votes from Republicans, because of support for lower taxes, and reduced spending on anti-poverty programs. But this year may be more of a wash. If any third party has a chance of affecting the elections this year, it is the Libertarians. Johnson is currently polling at over 10%. If he can get that up to 15%, he might find himself in the debates, which would only increase his presence.
The Green Party's presumptive nominee is Jill Stein. Stein has never won elective office before, despite running for various offices, including President, in past elections. The Greens generally focus on the need for more environmental rules and regulations. Stein has also called for many of the same issues promoted by Bernie Sanders: higher minimum wage, single payer healthcare, and free college tuition. Stein also supports a much reduced military spending and much lower overall US involvement abroad. Although the Green's have failed to crack 1/2 of 1% in prior elections, they could be a home for many disaffected Sanders supporters this year, perhaps reaching results well into the single digits. Almost all Green votes would pull from Clinton's potential support.
With both major parties seemed to focus on playing up the negatives of their opponent, there is room for a third party candidate to win significant numbers this year. If third party numbers improve in the polls, it may at least force the two major party candidates to explain why voters should vote for them, rather than simply why we should not vote for their opponent.