Market socialism, as fare as I'm aware, is defined by social ownership of the means of production. State capitalism would definitely be more appropriate to describe China. Especially in the marxist sense of the term.
edit:
I spoke with a Chinese student once, whom preferred the term dictatorial capitalism.
Slightly off topic but can you clarify what 'social ownership' means, exactly? I've been trying to figure this out for a few weeks now. I just ask since you seem to know.
Wikipedia says, "The two major forms of social ownership are society-wide public ownership and cooperative ownership." What's the practical difference between 'society-wide public ownership' and government ownership? The government is supposed to represent the people.
What's the practical difference between 'cooperative ownership' and corporate ownership? A corporation is just a group of shareholders, often including millions of individuals and employees of the company.
e.g. In America the government owns parkland, and people can use it. Is that 'social ownership' of the parkland? Or 'government ownership'? What's the difference?
e.g. In the West, many corporations are owned by millions of shareholders. Sometimes the majority of ownership is ultimately from small shareholders, largely through pension funds. Is that 'social ownership' or 'corporate ownership'? What's the difference?
What are some existing, real, sustained examples of 'social ownership' in real history?
I feel like this term is either super general and not particularly meaningful, or it's one of those cases where the definition changes according to the argumentative needs of the moment, or it's just a euphimism for government control without a practical difference.
>What's the practical difference between 'society-wide public ownership' and government ownership? The government is supposed to represent the people.
Typically, socialists (and even market socialists) contend that the current democratic establishment does not represent the people, usually going off Lenin's conception of "bourgeois democracy". This is also behind the most common Marxist rejection of achieving socialism through non-revolutionary means. Compare, for instance, how Lenin described what he figured Soviet Socialism would turn out to be - control by the soviets, not by the state. Of course it didn't really turn out that way, and in Economic Problems of the USSR, Stalin effectively admitted as such.
>What are some existing, real, sustained examples of 'social ownership' in real history?
This is a difficult question because one would either have to draw from pre-capitalist modes of production to answer the question, or one would have to argue that the USSR/Stalinism implemented such social ownership. I have already described why the second is not appropriate (see here[0] too) but the first is also not appropriate because "social ownership" is not a transhoistorical term, it was intended to describe a future mode of production in which it is one of the components of socialism (market or otherwise) - its applicability, therefore, does not encompass pre-capitalist or capitalist modes of production. For the notion of the critique of transhistorical categories, see Marx's discussion on the "Robinsonades"[1] and Patrick Murray's argument on Marx's improvement over David Ricardo and Adam Smith[2]. That said, you would probably have to look deeper into anthropology to find if such a society did indeed exist - that is to say, a society in which as far as we can tell today the will of the producers themselves was actually reflected in the ownership and control of the means of production and its products.
Finally, a note: Marx himself, to my knowledge, never used the term "social ownership". In fact, his argument against Proudhon was that plain "social ownership" results in a state where "society becomes a general capitalist". The term was used by Engels once, but he quotes Marx as follows:
>Marx assumes on page 56 “a community of free individuals, carrying on their work with the means of production in common, in which the labour-power of all the different individuals is consciously applied as the combined labour-power of the community[3]
As such, I tend to avoid using the term, as do most academic Marxists.
[0] "On the Question of Soviet Socialism" (2011) by Paresh Chattopadhyay, a rejoiner to David Laibman's thesis of the USSR having achieved "formal" socialism but not "real" socialism; (Chattopadhyay doubts that it even achieved "formal" socialism in the Marxian sense). https://www.jstor.org/stable/25769087
[2] "Marxs “Truly Social” Labour Theory of Value: Part II, How is Labour that Is Under the Sway of Capital Actually Abstract?" Historical Materialism, Number 7 (Winter 2000)
I think an example of social ownership would be in Karl Marx own family. Karl Marx was cousins with son of the founder of the Philips N.V. through his mothers sister. In the first 100 years of Philips , a lot of decisions made by the Philips family had social underlying motives.
Building affordable housing, sponsor of sport accommodations reflected some of Marx's reasoning with respect to sharing profits with society.
A century ago the silicon valley of the world was around the Philips factories and then somebody came in and decided to move the whole company to another place.
Okay this post went on a little longer than I intended, partly because social ownership is a fairly broad concept, but I hope it answers some of your questions:
The point of social ownership ought to be that the people who either work in or directly rely on the organisation are the people who have meaningful control over it. This immediately excludes any kinds of pure owner who may never interact with the organisation other than for having decision making power over it and extracting profits from it.
Where worker co-operatives are concerned, an important aspect is that workers should have equal say (in the sense that voters in a democracy should have an equal say) over their organisations. Where corporations have 'one share, one vote', worker co-ops are 'one worker, one vote'. Of course in practice the nature of this varies - in smaller co-ops, the workers tend to have a more direct say over the operation of the organisation and in larger ones are more likely to just be able to elect board or committee members at the overall level, and more direct decision making for their organisational unit. All of this happens while workers retain all the same rights and privileges they'd be afforded at a traditional corporation such as the ability to leave and change jobs if they want to, so they get to have their cake and eat it in this respect but the cost is arguably more responsibility in the form of taking informed decisions.
There are also other kinds of co-ops such as consumer co-ops where anybody who shops at a co-op can become a member. You also get community co-ops where residents directly, jointly own their own local accommodation or amenities. Some co-ops are hybrids.
The co-op group in the UK is a large, long running group of consumer co-ops which have been going since the 1840s: https://en.wikipedia.org/wiki/The_Co-operative_Group and they have nation-wide businesses including retail, energy, funeral services and so on.
Sometimes it may be one of the above types of ownership or a combination. Co-ops usually adhere to a set of principles called the Rochdale principles: https://en.wikipedia.org/wiki/Rochdale_Principles which define various rights for members and ultimately a culture that co-ops should adopt.
Building societies and credit unions are another form of social ownership where those saving with them are the members:
Government control, where there is a functioning democracy, can be a form of social ownership. It is just a very dilute kind. It's easy for your voice to get lost in a sea of millions, but that does not mean it isn't there - things like FPTP and the electoral college notwithstanding... Everything owned by a democratic state would be "sort of" social ownership; just a very weak, undesirable kind that puts too much power in the hands of a small group of representatives. Nevertheless, there are certainly some cases where it makes sense such as things which are natural monopolies like water sources, rail networks and indeed in the UK the NHS enjoys wide public support.
In that respect, municipal/local council control is also a form of social ownership but is much closer to home. Municipal libraries, public parks, public restrooms and such for instance are very much in keeping with the principle of social ownership. Municipal socialism as a specific aim has become a goal of some places, for instance in late 2018 Preston was named 'most improved city' in the UK after following a programme with this aim ultimately by leveraging local institutions to improve the area: https://www.theguardian.com/politics/2018/nov/01/preston-nam...
When it comes to social ownership I think sometimes something gets lost in translation, like you get some people who seem to think that just nationalising everything fits the bill - but the truth is that the model you have to choose has to fit the problem the organisation is supposed to be solving at the right scale. Having your local park managed by a centralised state authority by somebody who has never visited is probably a horrible idea in pretty much the same way that having it managed by somebody who only wants to profit from it but has also isn't particularly attached to its use as a park for residents may be a horrible idea (or certainly would be seen as such by those residents, at any rate). All of these approaches are appropriate tools for the goal of enfranchising communities and workers to have decision making power over things that affect their lives provided they're used right.
Nevertheless, none of this matters if you're otherwise operating within the confines of some highly authoritarian nation-state that in practice can totally take the reigns of your organisation, effectively disenfranchising members or constituents from making decisions.