so·cial·ism (sō′shə-lĭz′əm)
n.
1. 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.
2. The stage in Marxist-Leninist theory intermediate between capitalism and communism, in which the means of production are collectively owned but a completely classless society has not yet been achieved.
If you want an example of a real socialist nation--by the common definition, not by your own original definition--you can look at North Korea or Venezeula today, or Cambodia or the Soviet Union of the past, among other examples which you can find here:
https://en.wikipedia.org/wiki/List_of_socialist_statesThere is a reason the wiki link says it is "a list of self-declared socialist states". There are many definitions for socialism. But if it includes that production and distribution is owned by the people, through a government or not, it doesn't make sense to say the soviet union was socialist for example. The people had no say on how things were done. The capitalists were replaced by government appointed agents. And if the people had power over government ok. But that wasn't the case. It was an authoritarian government. A better description is it was a form of state capitalism. The state owned and controlled companies and laws managing them without responding to the people.