Interesting - obviously I've never heard of the Libertarian party since I'm from the UK, but I took a quick look at their website and did their "Are you a libertarian" quiz. The (unsurprising) results follow:
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According to your answers, your political philosophy is left-liberal.

Left-Liberal
Left-Liberals prefer self-government in personal matters and central decision-making on economics. They want government to serve the disadvantaged in the name of fairness. Leftists tolerate social diversity, but work for economic equality.

Your Personal Self-Government Score is 90%.
Your Economic Self-Government Score is 40%.
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(which apparently puts me one step away from being on the border line between Libertarian and Left-liberal).

I'm a sucker for these online political quizzes.

Interestingly enough, the Libertarian Party website has the following to say on the subject of Authoritarianism, and it helpfully describes their definition of a fascist as right-wing:

"Authoritarian
Authoritarians want government to advance society and individuals through expert central planning. They often doubt whether self-government is practical. Left-authoritarians are also called socialists, while fascists are right-authoritarians."