A federation is a large, often multi-ethnic, state originally based on mutual agreement between the participants. Compare with Empire, a term describing a large, multi-ethnic state, whose political structure was originally put together by coercion.
Examples of federal states:
It is arguable that the European Union has some of the attributes of a federal state, although its member states remain separate entities.
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In Star Trek, a collection of science fiction works, the Federation is an alliance of planets, of which Earth is a member. This alliance is loosely modelled after the United Nations.