The thing you need to look into is "What is Democracy"?
Basically, what people who believe in "democracy" generally regard as democracy is liberal democracy.
This means that you try to design a legal system which protects minorities from the majority.
A true democracy would the example of "2 wolves and a sheep voting over what to have for dinner".
If you read up on the foundation of the US and the development of the Bill of Rights etc., you'll find a lot about how they intentionally sought to protect minorities and individuals from the "tyranny of the majority".
http://www.answers.com/topic/tyranny-of-the-majorityhttp://en.wikipedia.org/wiki/Tyranny_of_the_majorityThe German post WWII Constitution - the Grundgesetz - gets around the tyranny of the majority by putting the power to change the Constitution into the hands of a Constitutional Court (to avoid the Germans voting for another Hitler).
The doctrine of the Separation of Powers also plays a part in this.