Final answer:
The Federalists promised a Bill of Rights and pointed to the Constitution's system of checks and balances to address the Anti-Federalists' fears.
Step-by-step explanation:
The Federalists countered the Anti-Federalists' fear by promising a Bill of Rights to limit government powers. In the Federalist Papers, particularly Federalist No. 51, James Madison explained how the Constitution's checks and balances and the federal system would prevent tyranny. The division of power among branches and levels of government, plus the addition of the Bill of Rights, assured that no single entity could gain unchecked power.
Ultimately, the inclusion of the Bill of Rights in 1791 and the ongoing emphasis on limiting federal powers through constitutional checks and balances helped alleviate the fears of the Anti-Federalists and paved the way for the ratification of the U.S. Constitution.