American English: to organize or convert a government, system, or organization into a federal structure where power is divided between a central authority and regional governments.
American English verb from federal plus -ize suffix (from Latin -izare), meaning to make something federal or organize it on federal principles.
When countries federalize, it's usually because centralized power has stopped working—they're admitting that people in different regions have different needs and want different things, so local governments should handle local issues.
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