Name Chapter 14 Apportionment. 1. What was the Great Compromise in 1787? Populations of 15 states in 1790 as in your book on page 506:

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1 Name Chapter 14 Apportionment 1. What was the Great Compromise in 1787? Populations of 15 states in 1790 as in your book on page 506: State Population Number Number Number Number Virginia 630,560 Massachusetts 475,327 Pennsylvania 432,879 North Carolina 353,523 New York 331,589 Maryland 278,514 Connecticut 236,841 South Carolina 206,236 New Jersey 179,570 New Hampshire 141,822 Vermont 85,533 Georgia 70,835 Kentucky 68,705 Rhode Island 68,446 Delaware 55,540 Total 2. If the House of Representatives has 105 members, how many representatives should each state get? Fill your answer in the table above. There are 4 columns for you to use to explore the possibilities.

2 s = standard divisor h = house size (number of representatives) p = total population p i =state s population q i = state s standard divisor - total population divided by house size, s = p h - the exact share that would be allocated if a whole number were not required, to obtain a states standard, divide its population by the standard divisor. q i = p i s 3. Now apportion 30 teaching assistants to the following courses: Course Enrollment Hamilton s Method 1. Calculate each state s standard. 2. Give to each each state (for the time being) its lower (round down). 3. Give away all the surplus seats (one at a time) to the states with the largest fractional parts.

3 Hamilton s Method i. Calculate each state s standard. ii. Give to each each state (for the time being) its lower (round down). iii. Give away all the surplus seats (one at a time) to the states with the largest fractional parts. 1. Find the apportionment of 30 teaching assistants using Hamilton's Method. i. the standard divisor is. Course Enrollment lower surplus result Jefferson s Method i. Find a divisor such that when each state's (state's population divided by divisor) is rounded downward ( lower ), the total is the exact number of seats to be apportioned. Give to each each state its lower. 2. Find the apportionment of 30 teaching assistants using Jefferson's Method. i. the standard divisor is, the divisor is lower

4 Adam s Method i. Find a divisor such that when each state's (state's population divided by divisor) is rounded upward ( upper ), the total is the exact number of seats to be apportioned. Give to each each state its upper. 3. Find the apportionment of 30 teaching assistants using Adam's Method. i. the standard divisor is, the divisor is upper Webster s Method i. Find a divisor such that when each state's (state's population divided by divisor) is rounded the conventional way (to nearest integer), the total is the exact number of seats to be apportioned. Give to each each state its conventionally rounded. 4. Find the apportionment of 30 teaching assistants using Webster's Method. i. the standard divisor is, the divisor is rounded

5 Huntington-Hill Rounding Rules (H-H RR) If the standard falls between L and L+1, then the Huntington-Hill cutoff point for rounding is H = L (L + 1). If the is below H, then round down, otherwise round up. If a is between 1 and 2, then H = 1 (1 + 1) = Round the following s using the Huntington-Hill rounding rules. a. 1.4 b c d. 1.5 If a is between 2 and 3, then H = 2 (2 + 1) = Round the following s using the Huntington-Hill rounding rules. a. 2.4 b c d. 2.5 If a is between 3 and 4, then H = 3 (3 + 1) = Round the following s using the Huntington-Hill rounding rules. a. 3.4 b c d. 3.5 Huntington-Hill Method i. Find a divisor such that when each state's (state's population divided by divisor) is rounded according to H-H RR, the total is the exact number of seats to be apportioned. Give to each each state its rounded using H-H RR. 8. Find the apportionment of 30 teaching assistants using Huntington-Hill Method. i. the standard divisor is, the divisor is H-H rounded

6 population paradox- A situation when state A gains population and loses a congressional seat, while state B loses population (or increases population proportionally less than A) and gains a seat. (can happen with Hamilton's method) condition - A requirement that an apportionment method should assign to each state either its lower or upper in every apportionment. (violated by divisor methods) Alabama paradox - A state loses a representative solely because the size of the house is increased. (can happen with Hamilton's method) new-states paradox - The situation when the addition of a new state and its fair share of seats causes another state to lose one of its seats. (can happen with Hamilton's method) geometric means:

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