> There is not gradient. If society is socialist then as per definition and as explained there must be authoritarianism to suppress any private initiative.

This logic works both ways. There is authoritarianism to enforce private ownership in capitalism. The police is a tool of the capitalist class, designed to suppress any protest against the capitalist system. It even extends internationally, to Imperialism. One only needs to think of banana republics, or more recently, Coca Cola murdering union leaders.