Apportionment Flashcards
Apportionment problem
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.
Lower quota
Standard quota rounded down to nearest whole number.
Upper quota
Standard quota rounded up to nearest whole number.
Standard divisor
Found by dividing total population by number of items to be allocated.
Standard quota
Found by dividing that groups population by the standard divisor.
Hamilton’s method of apportionment
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
Quota rule
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
Jefferson’s method
1- find modified divisor.
2- apportion each group its modified lower quota
Adam’s method
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
Websters method
Modified divisor can be less than, greater than or equal to standard divisor.
Hamilton’s divisor
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.
Jefferson’s divisor
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.
Adams’s divisor
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.
Webster’s divisor
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.
Huntington Hill method
Apportion method currently being used in US house of representatives.
Alabama paradox
An increase in total number of items to be apportioned results in loss of an item for a group.
Population paradox
Group A loses items to group B, even though population of group A grew at faster rate than group B.
New states paradox
Addition of new group changes apportionment of other groups.
Balinski and Young’s impossibility theorem
No perfect apportionment. Any apportion method that does not violate quota rule must produce paradoxes. And vice versa.
Which method of apportionment might produce the Alabama paradox?
Hamilton’s
Which methods of apportionment may not satisfy the quota rule? (3)
Jefferson, Adams, Websters
Which method of apportionment may produce the population paradox? (1)
Hamilton
Which method of apportionment may produce the new-states paradox? (1)
Hamilton
In the house of representatives, which apportionment methods favor large states? (2)
Hamilton and Jefferson
In house of representatives, which method of apportionment favors small states? (2)
Adams and Webster
Hamilton’s apportionment method produces Which paradoxes?
Alabama paradox, population paradox, new state paradox.
Only rule that Hamilton’s does not break is the Quota Rule.
Jefferson’s apportionment method violates which paradoxes?
None- only may violate the quota rule.
Jefferson, Adams and Webster’s apportionment methods Violates which paradoxes?
None. They only violate Quota rule.
Quota rule is only satisfied by Which method of Apportionment?
Hamilton’s method
