Final answer:
Hamilton's Method involves using the whole number part of quotas to allocate seats, then distributing remaining seats based on largest fractional remainders, while Jefferson's Method uses a modified divisor and rounds down quotas to the nearest whole number. The three-fifths compromise significantly influenced the apportionment process by increasing the representation for slave-holding states. Both methods reflect the political interests and context of the time during which they were proposed.
Step-by-step explanation:
Hamilton's Method vs. Jefferson's Method of Apportionment
To determine the apportionment of the 120 seats in Congress according to Hamilton's and Jefferson's methods, we need to consider the 1790 census data provided. The apportionment process plays a crucial role in the representation each state receives in the House of Representatives, which according to the Constitution, is based on population. Deciding how to apportion Congressional seats involves a balance of power which historically, has been a contentious issue.
Hamilton's Method
Hamilton's Method of apportionment involves dividing the total population by the total number of seats to find the standard divisor. Each state's population is then divided by this divisor to determine their standard quota, and the initial allocation of seats is according to the whole number part of each state's quota. Remaining seats are then distributed one by one to the states with the largest fractional remainders until all seats are allocated.
Jefferson's Method
Jefferson's Method, proposed by Thomas Jefferson who hailed from Virginia, involved using a modified divisor. The population of each state is divided by this divisor, but the result is then rounded down to the nearest whole number to determine the number of seats for each state. This method tends to favor larger states, as it may assign them more seats than under Hamilton's.
Arguments and Historical Context
Alexander Hamilton, from New York, argued for precise mathematical fairness in representation, while Jefferson, from a large slave-holding state, sought an advantage for states like his. The three-fifths compromise comes into play here, where enslaved individuals were counted as three-fifths of a person for the purposes of both representation and direct taxation. This rule gave Southern states more political power than if the enslaved people were not counted at all but less than if they were fully counted. The compromise was a critical factor in the distribution of political power during that period. For example, Virginia, a large slave-holding state, was given additional seats because it could add three-fifths of its enslaved population to its total count.
Conclusion
Both Hamilton's and Jefferson's methods were rooted in the political realities and conflicts of their time, with each proposal reflecting the interests of their respective states. Apportionment is critical to the fundamental principles of democracy, as it dictates the balance of power among the states and, by extension, their citizens.