It's called representative democracy.

The UK isn't a monarchy...http://en.wikipedia.org/wiki/Constitutional_monarchy Basically the royal family has mostly ceremonial duties not political ones.

You obviously don't understand the relationship of the Queen and the UK government. She is a non-political 'figurehead' head of state. She represents the state. She has to be non-political and neutral, as she is unelected. If she started spouting off her own opinions on various things (even if you might agree with them), then it would undermine this relationship to such an extent that in all likelihood, the monarchy would be abolished.

Basically, the British monarchy continues to exist because it does nothing. The prime minister is elected by the people if he does something the people don't like, they can elect someone else. If the Queen does something the people don't like, their only recourse is to abolish the monarchy.

Alright, people explained stuff to me, now can you stop downvoting my question? It is not a stupid question!