Why do you think that socialism has to involve the government, besides things like enforcing contracts.
From the American Heritage dictionary,
noun
Any of various theories or systems of social organization in which the means of producing and distributing goods is owned collectively or by a centralized government that often plans and controls the economy.
My Credit Union is owned collectively, same with various Co-ops I deal with, though I'm not a member of most of them.
Wiki has much more on it, starting with,
Socialism is an economic and political philosophy encompassing diverse economic and social systems[1] characterised by social ownership of the means of production,[2] as opposed to private ownership.[3][4][5] It describes the economic, political, and social theories and movements associated with the implementation of such systems.[6] Social ownership can take various forms, including public, community, collective, cooperative,[7][8][9] or employee.[10][11] As one of the main ideologies on the political spectrum, socialism is the standard left-wing ideology in most countries.[12] Types of socialism vary based on the role of markets and planning in resource allocation, and the structure of management in organizations.[13][14]
Socialist systems are divided into non-market and market forms.[15][16] A non-market socialist system seeks to eliminate the perceived inefficiencies, irrationalities, unpredictability, and crises that socialists traditionally associate with capital accumulation and the profit system.[17] Market socialism retains the use of monetary prices, factor markets and sometimes the profit motive.
Personally, I like the market forms, which are hopefully more resistant to authoritarianism.