Could you explain how a democratic society can work with a communistic system?
Communism works through state owned companies and redistribution of founds. Due to this fact it's hardly possible without complete integration of market and politics or let me say, the complete integration is the base concept of the communistic or socialistic system.

In democracies is possible to change state ownership to private ownership but this would crash the communistic economical system. In this case the system wouldn't be stable and could be changed through democratic decisions, which is fatal as a new economic system needs years to establish.