This is my current understanding and definition of Socialism.
Can anyone point out gaps or flaws in this so I can refine it?
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Discussion
It's intervention by the state. The mafia does all those things but it's not socialism. Here's Murray Rothbard's definition of socialism:
When government ownership or control extends to the entire productive system, then the economic system is called socialism. Socialism, in short, is the violent abolition of the market, the compulsory monopolization of the entire productive sphere by the State. There are two and only two ways that any economy can be organized. One is by freedom and voluntary choice—the way of the market. The other is by force and dictation—the way of the State.
The Mafia can establish a 'Government' with a set of well-defined laws and coerce people into abiding by them as well.
As can trade unions by overthrowing the Government and 'seizing the means of production'.
As can a group of businessmen looking to maximise profits by establishing monopolies through licenses and permits.
All of the above has coercion and aggression involved, and would amount to Socialism. I generalised my definition to include them.