You've hit a nail right on the head here IMHO. I think Socialism has a few different interpretations, all varying in relative degree. Your definition is as valid as any. In some writing your definition of Socialism is referred to as Communism. In other writing, Socialism is referred to as a state somewhere in between your Communism and totally unbridled, Darwinistic Captialism.

to answer your direct question, no, based on your definition I am not an advocate of that type of government.

Based on the definition that Socialism is a state of government whereby the small guy is afforded some protection from the super powerful grip of those that have amassed capitalistic clout, yes I'd advocate that society over one where the more one has, the more power one has to exploit those beneath.

My point is that we live in some nether world between unbridled Capitalism (that system was bridled, for example, with anti-trust laws that didn't allow John D. Rockefeller to charge whatever he wanted for his oil, even though it was HIS OIL), with some government mandated social programs, examples being Social Security, Medicaid, Medicaire.

Given my definition of Capitalism, where the government exerts no control on corporations, regardless of how vital the goods they sell are to the function of society, where the market is king, and if the small suffer, well, it's just not our job to intervene, would you be an advocate of living in that society?

The poison, as they say, is in the dose.