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Each apportionment method is a different way to determine how to distribute remaining seats into subgroups, in our case, the House of Representatives. Every method is flawed but some methods are arguably better than others.
Hamilton method uses the decimal place to determine which states receive the extra seats first. The first state(s) to recieve the remaining seat(s) need to have the highest decimal that is closest to the next whole number.
Hamilton method is subject to:
Alabama paradox, which changes the distribution of seats when they are added, despite no change in population.
Population paradox which does not adequately reflect a state's population growth or population decrease when redistributing seats.
New State paradox which changes the distribution of seats when a new State is added, even though the population of other states hasn't changed.
Jefferson method changes the s until the sum of the lower quotas matches the number of seats.
Jefferson’s method is also flawed.
It does not meet the quota rule which states that a state's apportionment should be either the floor or the ceiling of the quota Pop/s.
Jefferson’s method also favors large states.
In Adams Method, change s until the sum of the upper quotas matches the number of seats.
This is the exact opposite of the Jefferson Method.
In Webster method, change s until the rounding will add up to the number of seats.
This method uses arithmetic rounding so we must find the arithmetic mean to find our rounding cutoff.
Arithmetic mean = ⁽ⁿ⁺⁽ⁿ⁺¹⁾⁾⁄₂ = n + ½
This Method is similar to the Webster Method but instead we use the geometric mean to find our rounding cutoff.
Huntington Hill method is what we use today .
Geometric mean = s √(n(n=1)
The Balinski Young Theorem states that it is impossible for a neutral apportionment system to satisfy the quota rule and be free of the population paradox.
An apportionment method is neutral if switching the populations of two states will result in the switch of their apportionments.
In order to meet the quota rule, a state's apportionment should be either the floor or the ceiling of its ideal quota. The ideal quota is obtained by dividing its population by the standard divisor s.
Mariela Duran - Grace Jackson - Hannah Quiroz
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