The antifederalists were particularly concerned about tyranny of elites whereas federalists were primarily concerned about tyranny of the majority.
Basically, the Anti-Federalism was a political movement that opposed the creation of a stronger U.S. federal government and which later opposed the ratification of the 1787 Constitution.
During these period, the Anti-Federalists who were political coalition of popular politicians, such as Patrick Henry, who unsuccessfully opposed the strong central government envisioned in the U.S. Constitution of 1787 and whose agitations led to the addition of a Bill of Rights.
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