No third party has ever won the electoral college majority since Teddy Roosevelt days in 1912, though in 1948 George Wallace’s anti civil rights party carried five states. It is the electoral college vote that elects the president, not the popular vote. Polling show that while the Libertarian Party could influence the outcome of this election in a state's electoral college vote, their candidates have no chance to be elected to the White House, nowhere reaching the 15% popular vote mark.
The vote for president is by state. All but a few have rules that the winner of the state popular vote takes all electoral college votes allotted to that state. Your vote for a third party may withhold enough votes from your second choice in a very close election to cause the one you hate the most to win all of your state’s electoral votes, possibly resulting in determining the national vote in the electoral college. There are those who believe it happened in 2000 in the close Florida vote, causing Ralph Nader/Green Party to take away votes from Democrat Al Gore, resulting in his defeat. It may have also contributed to a Republican loss of the White House in 1996 with Ross Perot’s independent candidacy. The Obama coalition would have lost the 2012 election if the under 35 age groups' votes had not been heavily supportive of him. As both President Obama and Michelle Obama said Wednesday, no vote, or a vote for a third party by this important group is a vote for Donald Trump. Given what is stake in both administration of laws and in appointments to the supreme court, the impact of a Trump election could set back for a generation reproductive rights and environmental protections.