"government by the worst element of a society," 1829, coined (by Thomas Love Peacock) on analogy of its opposite, aristocracy, from Greek kakistos "worst," superlative of kakos "bad" (which perhaps is related to PIE root *kakka- "to defecate") + -cracy. Perhaps the closest word in ancient Greek was kakonomia "a bad system of laws and government," hence kakonomos "with bad laws, ill-governed."
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