Let's make the following definition:
"Private ownership" of means of production means 3 things:
The profit from selling things produced go to someone dubbed an "owner", who is one or more private person (e.g. NOT government/state)
The "owner" is legally allowed to sell ownership to another person/group of persons.
The "owner" can decide to stop producing if they feel like it, barring absence of contraindicating legally binding contracts.
if you don't think that private ownership of means of production means something different, you can simply mentally call whatever I defined above "SocioEconomic Condition #1" instead. This question is about facts, not semantics.
Are/were there any countries or governments that officially label(ed) themselves "Socialist" but where over 50% of means of production in the country are privately owned as per above definition? (... and there are no official stated plans by the government to drive that share below 50% in the near future)
50% can be measured by GDP produced, or by % of labour force employed.
For the purposes of this question, we will ignore the issues of presence or absence of competitive markets, or density of capital accumulation.