2. § 4.5 - 4.6 The Population and New-States Paradoxes; Jefferson’s Method

3. The Population Paradox The Population Paradox occurs when one state loses a seat to another even though the first state’s population grew faster than the second state’s. (see Example 4.6, pg 145)

5. The New-States Paradox The New-States Paradox occurs when the addition of a new state, with its fair share of seats, causes another state to lose seats. (see Example 4.7, pg 147)

7. Jefferson’s Method  Yesterday we saw that the distribution of surplus seats in Hamilton’s method led to large states being favored over smaller ones.  The Idea behind Jefferson’s method is to modify our standard divisor so that there are no surplus seats.

8. PLANETANDO RIA EARTHTELLA R VULCA N TOTAL POPULATI ON in billions 16.216.128.38.969.5 STD. QUOTA 32.432.256.617.8139 LOWER QUOTA 32 5617137 FRACTION AL PART.4.2.6.82 EXTRA SEATS 11 FINAL APPORTIO NMENT 32 5718139 Example: THE PLANETS OF ANDORIA, EARTH, TELLAR AND VULCAN HAVE DECIDED TO FORM A UNITED FEDERATION OF PLANETS. THE RULING BODY OF THIS GOVERNMENT WILL BE THE 139 MEMBER FEDERATION COUNCIL. APPORTION THE SEATS USING HAMILTON’S METHOD.

9. PLANETANDO RIA EARTHTELLA R VULCA N TOTAL POPULATI ON in billions 16.216.128.38.969.5 STD. QUOTA 32.432.256.617.8139 MODIFIED QUOTA POP. .4925 32.8932.6957.4618.07141.12 FINAL APPORTIO NMENT 32 5718139 Example: THE PLANETS OF ANDORIA, EARTH, TELLAR AND VULCAN HAVE DECIDED TO FORM A UNITED FEDERATION OF PLANETS. THE RULING BODY OF THIS GOVERNMENT WILL BE THE 139 MEMBER FEDERATION COUNCIL. APPORTION THE SEATS USING JEFFERSON’S METHOD.

10. Jefferson’s Method  Step 1. Find a modified divisor D such that when each state’s modified quota is rounded down (this number is called the modified lower-quota) the total is the exact number of seats to be apportioned.  Step 2. Apportion to each state its modified lower quota.

11. Jefferson’s Method: Finding the Modified Divisor (pg. 150) Start: Guess D ( D < SD ). End Make D larger. Make D smaller Computatio n: 1. Divide State Populations by D. 2. Round Numbers Down. 3. Add numbers. Let total = T. T < M T = M T > M

12. StatePop. (est.)Modified QuotaFinal Apportionment Connecticut236,841 Delaware55,540 Georgia70,835 Kentucky68,705 Maryland278,514 Massachusett s 475,327 New Hampshire 141,822 New Jersey179,570 New York331,589 North Carolina 353,423 Pennsylvania432,879 Rhode Island68,446 South Carolina 206,236 Vermont85,533 Virginia630,560 Total 3,615,920 Example: The first apportionment of the House of Representatives used Jefferson’s Method with M = 105.

13. Jefferson’s Method  Jefferson’s Method is nice in that it is paradox-free.

14. Jefferson’s Method  Jefferson’s Method is nice in that it is paradox-free.  However, it violates the quota rule. (In 1832, Jefferson’s method led to New York having 40 seats even though its standard quota was only 38.59--an upper-quota violation.)