Federalists believed that popular sovereignty was best expressed through a representative government, in which citizens elect representatives to make decisions on their behalf. They argued that the framers of the Constitution had created a system of checks and balances that would ensure that decisions were made with the welfare of the entire country in mind, rather than with the interests of any particular group or individual
Anti-Federalists, on the other hand, were more sceptical of representative government. They argued that ordinary citizens are often swayed by emotions rather than reason, and that they can therefore be easily manipulated by powerful elites. For this reason, Anti-Federalists believed that popular sovereignty was best expressed through direct democracy, in which citizens make decisions directly, rather than through representatives.
Overall, both Federalists and Anti-Federalists supported the idea of popular sovereignty, but they differed in their views on how it should be expressed.