Apportionment Flashcards
Standard quota
A states fair share— found by dividing its population by the total population and then multiplying this value by the number of seats to be apportioned
Standard divisor
The total population divided by the number of seats to be distributed (P/H)
What are the quota methods and describe them
Hamilton and Lowndes.
Hamilton—find the standard quota for each state. Round all of the quotas down (the lower quota) and count how many seats there are. Assign the remaining available seats (1 per state) to states in order of decimal places in the standard quotas. (.89 would get an extra seat before .56). The seats should then equal to H.
Lowndes— (not really necessary) but give each state it’s lower quota then rank the states in decreasing order of the ratio of the fractional part of their standard quota to their lower quota. If a state has a standard quota of 3.1, the ratio is .1/3= 1/30. Give the remaining seats to the states in the order of that ranking.
Jeffersons method
Divide each state population by a modified divisor. The result is a series of modified quotas. Round the modified quotas down and add all the numbers up to see if they add up to H. If they don’t, repeat the process with a new modified divisor until the rounded down quotas add up to the desired H
The modified divisor for Jefferson’s method compares to the standard divisor in what way?
The modified divisor for Jefferson is usually slightly less than the standard divisor.
Adams method
Divide the state populations by a modified divisor to get modified quotas round the numbers up. See if a1+a2+an=H. If not, redo the process with a new modified divisor until the apportionments equal the desired H
Jefferson favors ___ while Adams favors____
Jefferson favors large states while Adams favors small states
Balinski and young impossibility theorem
A neutral method cannot satisfy the quota rule and also population monotonicity
Arrows theorem of voting
A social choice function with at least three candidates that satisfies Pareto and independence must be a dictatorship
Degree of rep and avg district size
Degree of rep:
Ai/pi
Avg district size:
Pi/ai
Neutrality criteria (apportionment)
Changing the input changes the output accordingly
If there are 3,2 and 1, seats for populations 85, 56, and 12, then there should be 1,3 and 2 seats for populations 12, 85, and 56 respectively
(All methods are neutral)
Proportionality criterion
When method is applied to two census that have the same population distributions and the same house size, the outputs of the method are the same
(Population distribution is list of all pi/p+p2/p+p3/p etc
Order preserving criterion
If whenever ai>aj
Then pi>pj
(The only way one state can get more seats than another is if it has a larger population)
Quota rule
A method assigns the state either it’s lower quota or its upper quota (no quota violation)
Upper quota criterion: no state is assigned by the method a number of seats greater than its upper quota
Lower quota: no state is assigned by the method a number of seats lower than its lower quota
House monotone
Whenever h increases, the method does not assign a smaller value of ai for any state (seat doesn’t get smaller)
