The ideals of Libertarianism and Socialism are not mutally exclusive. You could be libertarian in certain aspects but Socialist in others. You might, for instance, be opposed to Authoritarian governments when it comes to policy but feel they have an obligation to grant/enable everyone equal rights. You may beleive in the importance of the free market and self ownership, as many Libertarians do, but still feel capitalism needs to be regulated so as not to allow monopolies, etc.. I consider myself very Libertarian but was also a supporter of Bernie Sanders (social democrat).
What these ideals primarily share in common is an anti-authoritarianism, a skeptisism towards crony capitalism, neoliberalism, and the striving towards equal opportunity and liberty for all.
To look for a key example of both - Noam Chomsky is a good example of a Libertarian Socialist/social democrat. Dennis Kuscinich also somewhat embodies both these ideals as a politician.
"We hold these truths to be self-evident - all men and women created by the, go-you know.. you know the thing!" - Joe Biden
