Apportionment

Question 1

Apportionment problem

Answer 1

Congress seats are given in whole numbers. Need to determine method for rounding standard quotas into whole numbers so the sum of the numbers is the total of allocated items.

Question 2

Lower quota

Answer 2

Standard quota rounded down to nearest whole number.

Question 3

Upper quota

Answer 3

Standard quota rounded up to nearest whole number.

Question 4

Standard divisor

Answer 4

Found by dividing total population by number of items to be allocated.

Question 5

Standard quota

Answer 5

Found by dividing that groups population by the standard divisor.

Question 6

Hamilton’s method of apportionment

Answer 6

1- calculate each group’s standard quota
2-round each standard quota Down to nearest whole # (finding lower quota)
3-give the surplus items, one at a time, to groups with largest decimal parts in standard quota

Question 7

Quota rule

Answer 7

A group’s apportionment should be either its upper quota or its lower quota. An apportionment method that guarantees that this will always occur is said to satisfy the quota rule

Question 8

Jefferson’s method

Answer 8

1- find modified divisor.

2- apportion each group its modified lower quota

Question 9

Adam’s method

Answer 9

Begin with a modified divisor that is slightly greater than standard divisor.

• modified quotas are rounded up and are called modified upper quotas.
• apportion to each group its modified upper quota

Question 10

Websters method

Answer 10

Modified divisor can be less than, greater than or equal to standard divisor.

Question 11

Hamilton’s divisor

Answer 11

Standard divisor = total population
Divided by number if allocated items.
Apportionment= round each standard quota down to nearest whole number. Initially give each group its lower quota. Give surplus items to groups with largest decimal.

Question 12

Jefferson’s divisor

Answer 12

Modified divisor is less than the standard divisor.

Apportionment- round each group’ modified quota down to nearest whole number. Apportion to each group’s lower quota.

Question 13

Adams’s divisor

Answer 13

Modified divisor is greater than standard divisor.
Apportionment- round each group’s modified quota UP to nearest whole number. Apportion to each group’s modified upper quota.

Question 14

Webster’s divisor

Answer 14

Modified divisor may be less, greater or equal to standard divisor.
Round each group to nearest whole number. Apportion to each group to its modified rounded quota.

Question 15

Huntington Hill method

Answer 15

Apportion method currently being used in US house of representatives.

Question 16

Alabama paradox

Answer 16

An increase in total number of items to be apportioned results in loss of an item for a group.

Question 17

Population paradox

Answer 17

Group A loses items to group B, even though population of group A grew at faster rate than group B.

Question 18

New states paradox

Answer 18

Addition of new group changes apportionment of other groups.

Question 19

Balinski and Young’s impossibility theorem

Answer 19

No perfect apportionment. Any apportion method that does not violate quota rule must produce paradoxes. And vice versa.

Question 20

Which method of apportionment might produce the Alabama paradox?

Answer 20

Hamilton’s

Question 21

Which methods of apportionment may not satisfy the quota rule? (3)

Answer 21

Jefferson, Adams, Websters

Question 22

Which method of apportionment may produce the population paradox? (1)

Answer 22

Hamilton

Question 23

Which method of apportionment may produce the new-states paradox? (1)

Answer 23

Hamilton

Question 24

In the house of representatives, which apportionment methods favor large states? (2)

Answer 24

Hamilton and Jefferson

Question 25

In house of representatives, which method of apportionment favors small states? (2)

Answer 25

Adams and Webster

Question 26

Hamilton’s apportionment method produces Which paradoxes?

Answer 26

Alabama paradox, population paradox, new state paradox.

Only rule that Hamilton’s does not break is the Quota Rule.

Question 27

Jefferson’s apportionment method violates which paradoxes?

Answer 27

None- only may violate the quota rule.

Question 28

Jefferson, Adams and Webster’s apportionment methods Violates which paradoxes?

Answer 28

None. They only violate Quota rule.

Question 29

Quota rule is only satisfied by Which method of Apportionment?

Answer 29

Hamilton’s method