Third-party candidates who manage to carry any states typically impact the map in states which are bases for the party to which that third-party nominee comes across as an Alternative Republican or Alternative Democrat.
Consider:
• 1912: Progressive Party nominee, and former Republican president, Teddy Roosevelt flips six states which backed, in 1908, incumbent Republican president William Howard Taft: California, Michigan, Minnesota, Pennsylvania, South Dakota, and Washington. All of losing 1908 Democratic nominee William Jennings Bryan’s states logically carry for 1912 Democratic pickup winner Woodrow Wilson before he flips 1908 Republican Taft states—leaving a disastrously unseated Taft (who ends up with just two states—Utah and Vermont).
• 1948: States Rights candidate Strom Thurmond, not happy with the Democratic Party, carries base states for the party which include Thurmond’s home state South Carolina plus Alabama, Mississippi, and Louisiana. President Harry Truman wins a full-term election anyway, in a Democratic hold (the fifth consecutive for that party), and becomes the first Democrat elected without having carried those states.
• 1968: With exception of South Carolina, American Independent George Wallace wins the same states as carried 20 years earlier by Thurmond…along with Arkansas and Georgia. 1968 marks a Republican presidential realigning period with election of Richard Nixon, whose Old Confederacy states, among his total 32, were carriage of Florida, North Carolina, South Carolina, Tennessee, and Virginia.
I would anticipate that the next time a third-party nominee brings a color, other than red or blue, to the electoral map…will do so in states which are bases for Republicans or Democrats. That, for a particular election cycle, such base states would be rejecting the nominated Republican or Democrat.
This thread’s question is good. Along with Utah, I would consider Idaho and Wyoming—two more companion states—for discussing Libertarian Gary Johnson and Election 2016.
That line of thinking also seems to work for a hypothetical Bernie run. He'd do well in Vermont, which is part of the mythical freiwal.
What do you think about Alaska? It's been trending D for a while and has voted in high percentages for past Libertarian candidates. I think it could still be considered a base state for Reublicans though.