Assignment 1 Lasa 2: The Apportionment Problem You Are A Cen

Assignment 1 Lasa 2 The Apportionment Problemyou Are A Census Office

Determine how 100 congressional seats should be divided among 10 states using the Hamilton method of apportionment based on provided census data. Calculate the number of seats for each state, the average constituency per state, and analyze the fairness of the apportionment. Discuss potential effects of changes in state populations or boundaries, explain the Alabama Paradox and how the Huntington-Hill method mitigates it, and evaluate the fairness of apportionment. Propose an alternative strategy for achieving fair representation.

Paper For Above instruction

The process of apportionment plays a vital role in ensuring fair representation in legislative bodies, especially in a diverse nation with varying state populations. Employing the Hamilton method, also known as the method of largest remainders, involves assigning seats based on calculated quotas and then distributing remaining seats according to the largest fractional parts. This paper presents an analysis of how 100 seats are apportioned among ten states, assesses the fairness of this distribution, considers the impact of demographic changes, explores potential paradoxes such as the Alabama Paradox, and suggests enhancements to achieve equitable representation.

Initially, to implement Hamilton's method, the first step involves calculating each state's standard quota by dividing the state's population by the total population, then multiplying by the total number of seats (100). Suppose the population data (in hypothetical units) for each state is as follows:

• State A: 10,000,000
• State B: 8,000,000
• State C: 12,000,000
• State D: 9,000,000
• State E: 11,000,000
• State F: 7,000,000
• State G: 6,500,000
• State H: 8,500,000
• State I: 9,500,000
• State J: 10,500,000

Calculating total population yields 92,000,000. For each state, the standard quota is computed as:

Quota = (State Population / Total Population) × 100.

For example, for State A:

Quota_A = (10,000,000 / 92,000,000) × 100 ≈ 10.87 seats.

Applying this approach across all states provides the fractional quotas which form the basis for seat allocation.

Using these quotas, each state is initially assigned the whole number part of their quota: State A gets 10 seats, State B 8, State C 13, etc. After this initial allocation, the remaining seats are distributed to states with the largest fractional remainders. For instance, State A’s fractional part is approximately 0.87, which may be larger than others, giving it priority for an additional seat if seats remain after initial distribution.

The mean constituency size per state is calculated by dividing each state's population by the number of seats allocated to it. For example, if State A receives 11 seats, then its average constituency size is approximately 909,091 persons per representative.

The fairness of this apportionment can be evaluated by calculating the absolute and relative unfairness. Absolute unfairness measures the discrepancy between the ideal and actual representation, while relative unfairness considers the proportional difference. Variations in state populations or boundary changes could shift quotas and alter seat allocations significantly. For example, a population increase in State D might grant it additional seats, thereby shifting the balance of power and representation among states.

The Alabama Paradox occurs when an increase in the total population causes a state to lose a seat, which seems counterintuitive. This paradox can happen with divisor methods like the Hamilton method under certain conditions but is avoided by the Huntington-Hill method. The latter employs a geometric mean to allocate seats iteratively, reducing the likelihood of paradoxes.

In evaluating the apportionment methods, the Huntington-Hill method offers a more stable and fairer outcome, especially in avoiding paradoxes. However, no system is perfect. Alternative strategies include the use of the Webster method, which employs rounding to the nearest integer and tends to favor larger states, or adopting a mixed approach that combines aspects of different methods to improve fairness.

In conclusion, apportionment remains a complex but essential process for ensuring fair representation. The Hamilton method, while straightforward, can produce paradoxes and fairness issues. The Huntington-Hill method offers improvements by reducing such inconsistencies. Ultimately, a combination of methods and continual assessment is necessary to adapt to demographic shifts and maintain equitable representation in a democratic system.

References

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