I think you are abstracting away some key details of what is more accurately called a "liberal democracy" (vs. just "democracy"). These details are often left out of casual conversation about "democracy" and "freedom". For example:

    * fair and free elections
    * representative form of government (not a "tyranny of the majority")
    * limited government
    * individual rights that can not be usurped by majority  rule
    * separation of powers and checks and balances
    * rule of law

A "democracy" is not just having laws or holding elections. The nature of the laws and the nature of the processes involved in creating the laws are critical elements that distinguish a liberal democracy from other systems of government.