But that is not the same as the democracy of the people voting in politicians.
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Why not? Not everyone in the UK government is elected? The house of Lords is full of people who were (a) made lords by some politician deciding they were lords (Blair "made" 16 new lords while he was in - for example) or (b) are Lords because their parents were Lords. Civil servants are not voted in, but they still draft legislation.
In the EU there are 3 bodies which have an input into law:
The ComissionThese people draft the laws, write reports etc (same role as civil servants in the UK), they are nominated from a shortlist provided by their respective heads of state (1 commissioner per country). Pretty much exactly how civil servants are chosen, only somewhat more transparent as we can see who was on the shortlist - if you're sad enough to look.
The ParliamentThese are
directly elected by member states. For example we elected Farage (for me a prime example of the failure of the democratic process
). This body must sign-off on any law drafted by the commission before it can be adopted into law in the member states. Like the House of Commons does for the UK.
The CouncilThis is made up of the head of state of each EU country, or a cabinet minister depending on the area being discussed. They must also sign-off on all EU law before it is adopted - similar to the House of Lords but elected - ie we voted for ours.
I fail to see any meaningful difference between the way we (in the UK) make law and the way the EU does.
EDIT: Sir Tig, I'm not sure what you mean about the EU parliament not legislating? The House of Commons doesn't either? Laws are drafted by somebody's civil servant and then voted on???