Left-libertarianism (or left-wing libertarianism) names several related, but distinct approaches to political and social theory which stress both individual freedom and social equality. In its classical usage, libertarianism is a synonym for anti-authoritarian varieties of left-wing politics, e.g. libertarian socialism, which includes anarchism and libertarian Marxism, among others.
Left-libertarianism can also refer to political positions associated with academic philosophers Hillel Steiner, Philippe Van Parijs and Peter Vallentyne that combine self-ownership with an egalitarian approach to natural resources. While maintaining full respect for personal property, they are skeptical of or fully against private property, arguing that neither claiming nor mixing one's labor with natural resources is enough to generate full private property rights and maintain that natural resources (land, oil, gold and vegetation) should be held in an egalitarian manner, either unowned or owned collectively. Those left-libertarians who support private property do so under the condition that recompense is offered to the local community. Many schools of thought are communist, advocating the eventual replacement of money with labor vouchers or decentralized planning.
On the other hand, left-wing market anarchism, which includes Pierre-Joseph Proudhon's mutualism and Samuel Edward Konkin III's agorism, appeals to left-wing concerns such as egalitarianism, gender and sexuality, class, immigration and environmentalism within the paradigm of a socialist free market. In the United States, the word "libertarian" has become associated with right-libertarianism after Murray Rothbard and Karl Hess reached out to the New Left in the 1960s. However, until then political usage of the word was associated exclusively with anti-capitalism and in most parts of the world such an association still predominates.