Math IN THE MODERN WORLD 100_Lecture 7.pdf
- 2. Apportionment -a method of dividing a whole into various parts. Apportionment Methods 1. Hamilton Plan 2. Jefferson Plan 3. Huntington-Hill Method
- 3. Hamilton Plan 1. Determine the total population and the number of people to apportion. 2. Find the Standard Divisor. 3. Divide the population of each state by the standard divisor and round the quotient down to the whole number. Each whole number quotient is called the standard quota. 4. Compute the total standard quota. Assume that the total is less than the total number of representatives, revisiting the calculation of the quotients and assigning an additional representative to the state with the largest decimal remainder. This process is continued until the number of representatives equals the number required by the constitution.
- 4. Example 1 Consider the fictitious country of Andromeda, with a population of 20,000 and five states. The population of each state is given in the table at the right. Andromeda’s constitution calls for 25 representatives to be chosen from these states. The number of representatives is to be apportioned according to the states’ respective populations.
- 6. Jefferson Plan 1. Determine the total population and the number of people to apportion. 2. Find the Standard Divisor. 3. Find a modified standard divisor that is less than the standard divisor calculated. 4 Divide the population of each state by the modified standard divisor and round the quotient down to the whole number. Each whole number quotient is called the standard quota. 5. Compute the total standard quota. The sum of the standard quota must be equal to the number of representatives given.
- 26. Paradoxes 1. Alabama paradox- refers to any apportionment situation where increasing the total number of items would decrease one of the shares. 2. Population Paradox-when two states have a populations increasing at different rates, a small state with rapid growth can lose a legislative seat to a big state with slower growth. 3. New State Paradox If a new state is added as well as a proportionsl number of new seats, it seems logical that the number of seats of existing states would not change. This is not always the case. Adding a new state with its fair share of seats can affect the number of seats apportioned to other states. When a state gains or loses a seat in this situation, this is called the new state paradox.