§ The Population and New-States Paradoxes; Jefferson’s Method

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)

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)

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.

PLANETANDO RIA EARTHTELLA R VULCA N TOTAL POPULATI ON in billions STD. QUOTA LOWER QUOTA FRACTION AL PART EXTRA SEATS 11 FINAL APPORTIO NMENT 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.

PLANETANDO RIA EARTHTELLA R VULCA N TOTAL POPULATI ON in billions STD. QUOTA MODIFIED QUOTA POP.  FINAL APPORTIO NMENT 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.

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.

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

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.

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

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 an upper-quota violation.)