I've come across three political quizzes that "place" you on various scales: left-right, authoritarian-libertarian, pragmatic-idealistic, etc. The three quizzes are Political Compass, Political Survey, and World's Smallest Political Quiz.
Political Compass comprises about 40 questions, many of them ambiguously worded. Your score places you on a two-dimensional scale: economic left-right and libertarian-authoritarian. The labels are misleading because libertarianism, in this case, is something akin to anarchism. The author considers those whose scores place them in the lower-left quadrant (libertarian-economic left) to be libertarians, whereas they are in fact pot-smoking, pro-abortion, anti-war adherents of the welfare state -- socialist-anarchist-libertines, if you will. My score, in the upper-right quadrant, makes me "right authoritarian" -- which puts me in some pretty good company with the likes of Dean Esmay, Stephen Bainbridge, Michael Rappaport, Daniel Drezner, and Timothy Sandefur. What it really makes me is a personally conservative free-market capitalist libertarian who believes in a minimal state to protect Americans from force and fraud.
Political Survey comprises 75 questions, which are sharply worded. Your score places you on a two-dimensional scale: left-right and pragmatic-idealistic. The labels of the Political Compass survey would do as well. The scores are distributed similarly, with a strong bias toward the lower-left quadrant. I am, again, in the upper-right quadrant, this time surrounded by a lot of names I don't recognize. (Political Survey has drawn far fewer participants than Political Compass.)
World's Smallest Political Quiz, which is touted on the Libertarian Party's home page, comprises 10 unambiguous questions, five about personal issues and five about economic issues. Your score places you on a two-dimensional grid with two axes: personal issues and economic issues. The surface of the grid is subdivided into five areas: libertarian, conservative, statist, liberal, and centrist. Which of the five areas you land in depends on your score. I've taken the quiz several times and always come out in the libertarian part of the grid. In fact, I took the quiz today and came out "pure" libertarian because there's no longer a question about immigration, which I always got "wrong" in the past.
World's Smallest Political Quiz is the easiest to take, and it places you accurately on a nuanced scale of political persuasions. Try it and see what political flavor you are.