Where does the Libertarian Party perform best? In 2012, they received 2.14 percent of the vote in Wyoming; not enough to affect the outcome of this Republican state. In 1980, they received 12 percent of the vote in Alaska. Again, since Alaska is a solid red state, the expected outcome was not changed. However, if the 2016 contest is close and if the Libertarian Party receives enough votes in some of the current swing states such as Colorado, Nevada, New Mexico, Utah or New Hampshire, they could make a difference in the outcome.