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From my sister:

kakistocracy

/kăk"T-stök'ra-sẽ, kä"kĩ-/ (*)
noun
1. Government by the least qualified or most unprincipled citizens.
2. Government by the worst men.
3. Government under the control of a nation's worst or least-qualified citizens.
The American Heritage® Dictionary of the English Language, 5th Edition • More at Wordnik