According to Kurt Gödel second incompleteness theorem there is one statement/element in each system that cannot be proved by rules and proceedings of the system itself. If system is consistent than there has to exist one element that does not fit into that system but at the same time constitute that system. The system is saturated, working, operational, … only if it has an element that does not belong to the system.
Consequently, we have to conclude, that democracy as a system is consistent only if it has an element that does not belong to democracy. If there is one contradiction to democracy, then this is authoritarianism. Democracy without authoritarianism cannot exist.