The People's Republic reference article from the English Wikipedia on 24-Jul-2004
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People's Republic

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People's Republic is a title that is often used by Marxist or Communist governments to describe their state.

Examples include:

Other Communist Party-led states are/were sometimes referred to as democratic republics, or democratic people's republics (for example, the Democratic People's Republic of Korea.)

There is also a usage in political conservative sarcasm using People's Republic to refer to any predominantly left or liberal area, especially those cities with a large liberal arts university population.