Are conservatives more subservient to authority while liberals are more independent and free thinking?

If you read social science claims, the humanities, and certainly the fringes of partisan science media, you would think so; it's a non-stop culture war by people who just happen to not be conservatives and who claim they are not because, well, conservatives are wrong about everything.

Yet reality tells a different story. It is social authoritarians on the left most likely to try and use the force of government to advance their political agenda - banning Big Gulps, gold fish, golf courses, Happy Meals, etc. Those bans affect 80 percent of Americans. Sure, conservatives want to ban gay marriage, but that is 1.6 percent of America (1).

And the recent events in Ferguson, Missouri did not happen because conservatives want a larger, more militaristic police force, they have been the ones concerned about spying and overuse of heavy-handed tactics by governments - the people on the left insist the government are the only ones who should have guns. (2)

Yet both sides claim to care more about freedom and independence than the other. What gives?

Obviously, left and right, conservative and liberal, is too simplistic. Social authoritarian progressives hide behind liberalism, for example, though they want to ban everything they disagree with and pick cultural winners and losers based on their pet beliefs - the exact opposite of liberalism. On the right, religious conservatives do the same thing, though with far less success, given the runaway trains of social authoritarianism in California and New York.

NOTE:

(1) Though that 1.6 percent has terrific public relations. Gallup polling shows Americans assume 25% of the country is gay

(2)  While government has gotten bigger and more controlling, just as liberals have desired, look at the trend in gun murders by individuals versus gun murder by police, compiled by Yoni Appelbaum: