Our idea of 'democratic market neo-communism' or a liberalism remorphed as (neo-)communism (or neo-socialism) and vice versa requires seeing that democracy in fact requires a kind of socialism, as this article from CP makes clear.

The supreme value of democratic republicanism is freedom, which can only be possible if the whole population enjoys the material conditions of freedom. Since poverty also entails dependence on the arbitrary dictates of others, social isolation, and the resulting vicious circle of physical and mental damage, it's more than a matter of a bit of redistributive justice but must be actively eradicated. And freedom isn't just about equality of resources. It requires reciprocity in freedom, which is only possible in a society where the political institutions recognize the civil equality of all its members who, then, must all have the status of materially independent social actors or equality of conditions.

Source: Republicanism For The Anthropocene - CounterPunch.org