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Anarcho-socialists often blame capitalism for their problems, but I'm convinced half of them are capitalists and capitalism is the default state of anarchy. You can't have anarchy, and also abolish property; to abolish property you'd need an authority with the power to use force against those who "refuse to share." Therefore anarcho-socialism either becomes capitalistic by nature, or establishes a government to take and give as it sees equal. The latter usually leads to totalitarianism, and becomes either poor (Venezuela), militaristic (Soviet Union), or ironically fascist (China). 

Meanwhile if the capitalists form a government it can be so minimal that its only purpose is to help stop theft and violence (minarchy). The problem in a capitalist society is when the government starts playing a role in business, which is corporatism, fascism, or crony capitalism, but these don't have to be inherent to capitalist society- while it seems any government under socialism inherently becomes tyrannical. 

There is a third option to these political and economic systems, which is religious community. People who simply share, or don't steal, or whatever it be, based on uniform religious conviction. But I've only seen that work for the Amish, and they kinda have the crutch of the outside world providing them with security from invasion as well as a place for excommunicate people to go.