Transcript 4.5-4.6

§ 4.5 - 4.6 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.
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
PLANET
ANDOHAMILTON’S
EARTH TELLA
VULCA TOTAL
THE
SEATS USING
METHOD.
RIA
R
N
POPULATI 16.2
16.1
28.3
8.9
69.5
ON
in billions
STD.
QUOTA
LOWER
QUOTA
32.4
32.2
56.6
17.8
139
32
32
56
17
137
FRACTION .4
AL PART
EXTRA
.2
.6
.8
2
1
1
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
PLANET
ANDOJEFFERSON’S
EARTH TELLA
VULCA TOTAL
THE
SEATS USING
METHOD.
RIA
R
N
POPULATI 16.2
16.1
28.3
8.9
69.5
ON
in billions
STD.
32.4
QUOTA
MODIFIED 32.89
QUOTA
POP. 
.4925
FINAL
32
APPORTIO
32.2
56.6
17.8
139
32.69
57.46
18.07
141.12
32
57
18
139
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)
Make D smaller
T<M
Start:
Guess D ( D < SD ).
Computatio
n:
1. Divide
State
Populations
by D.
2. Round
Numbers
Down.
Make
D larger.
3. Add
numbers.
T=M
End
T>M
State
Pop. (est.)
Connecticut
236,841
Delaware
55,540
Georgia
70,835
Kentucky
68,705
Maryland
Modified Quota
Example:
278,514
Final Apportionment
New
Hampshire
The first apportionment of the
475,327
House of Representatives used
Jefferson’s Method with M =
141,822
105.
New Jersey
179,570
New York
331,589
North
Carolina
353,423
Pennsylvania
432,879
Rhode Island
68,446
South
Carolina
206,236
Massachusett
s
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 38.59--an
upper-quota violation.)