Assignment 1 Lasa 2 The Apportionment Problem You Are 134505

Assignment 1 Lasa 2 The Apportionment Problemyou Are A Census Office

Assignment 1: LASA 2: The Apportionment Problem You are a census officer in a newly democratic nation and you have been charged with using the census data from the table below to determine how 100 congressional seats should be divided among the 10 states of the union. State Population Being a fan of United States history, you are familiar with the many methods of apportionment applied to this problem to achieve fair representation in the US House of Representatives. You decide that apportionment (chapter 11, sections 1-4 in your textbook) is the best approach to solving this problem, but need to compare several methods and then determine which is actually fair. Using the Hamilton method of apportionment, determine the number of seats each state should receive. Using the numbers you just calculated from applying the Hamilton method, determine the average constituency for each state. Explain your decision making process for allocating the remaining seats. Calculate the absolute and relative unfairness of this apportionment. Explain how changes in state boundaries or populations could affect the balance of representation in this congress. Provide an example using the results above. How and why could an Alabama Paradox occur? Explain how applying the Huntington-Hill apportionment method helps to avoid an Alabama Paradox. Based upon your experience in solving this problem, do you feel apportionment is the best way to achieve fair representation? Be sure to support your answer. Suggest another strategy that could be applied to achieve fair representation either using apportionment methods or a method of your choosing. You may perform your own calculations or use either the Excel spreadsheet or the Excel 2013 Spreadsheet to assist you. You must show some calculations in your document to demonstrate that you know how to perform these tasks. Be sure to compile your work in a Word document.

Paper For Above instruction

The apportionment of congressional seats among states is a fundamental aspect of representative democracy, ensuring that populations are fairly represented in legislative bodies. Historically, methods such as the Hamilton method, Huntington-Hill method, and others have been employed to distribute seats proportionally based on population data. In this context, as a census officer charged with dividing 100 seats among 10 states, the application of the Hamilton method offers a systematic approach that mitigates bias and promotes fairness. This paper discusses the process of apportionment using the Hamilton method, explores the implications of apportionment inaccuracies, examines phenomena such as the Alabama Paradox, and considers alternative approaches for achieving equitable representation.

Introduction

The principle of fair representation in a legislative assembly relies heavily on accurate apportionment methods. The Hamilton method, also known as the method of largest remainder, has historically been used to allocate seats by initially assigning each state its lower quota based on the exact raw quotient, then distributing remaining seats according to the largest fractional remainders. This approach aims to balance the proportionality of representation with the practical necessity of assigning whole seats. In this context, applying the Hamilton method requires careful computation and analysis of the resultant distribution to assess fairness and stability.

Applying the Hamilton Method

To employ the Hamilton method, the first step involves calculating the standard quota for each state by dividing its population by the total population, then multiplying by the total number of seats (100). These quotas are then truncated to their lower integer parts, assigning each state that many seats initially. Remaining seats are then distributed sequentially to states with the largest fractional remainders until all seats are allocated. For instance, if State A has a quota of 12.7, it initially receives 12 seats, with 0.7 remaining to be considered for the distribution of leftover seats. This method ensures that the initial allocation respects the proportional population share, with the remainder distribution fine-tuning the final apportionment.

Determining the Average Constituency Size

Once the seats are apportioned, the average constituency size within each state can be computed by dividing the state's population by its allocated number of seats. Smaller congruence between population and seat allocation indicates a more equitable representation. This metric allows us to evaluate the fairness of the apportionment — the lower the average, the better the representation for each constituent within that state. Variations in these averages reveal disparities and highlight potential issues in fairness or disproportionate influence.

Decision-Making Process and Allocation of Remaining Seats

The allocation of remaining seats based on fractional remainders involves ranking these remainders from largest to smallest. Seats are then assigned sequentially to the states with the largest remainders until all quotas sum to the total number of seats. This process prioritizes states with the highest fractional parts, aiming to approximate proportional representation accurately. However, the approach requires careful evaluation to prevent possible biases, ensuring that no state disproportionately benefits from the distribution process, and that the total number of seats remains fixed at 100.

Unfairness in Apportionment: Absolute and Relative

Assessing fairness involves quantifying the deviation between the ideal proportional representation and the actual seat count. Absolute unfairness can be measured by summing the absolute differences between each state's assigned seats and its exact proportional share. Relative unfairness considers these differences relative to the actual population or the ideal quota, highlighting proportional deviations. High unfairness indicates that some states are over- or under-represented, compromising the legitimacy and perceived fairness of the apportionment system.

Impact of Changes in Boundaries and Populations

Alterations in state populations or boundary adjustments can significantly influence representation. For example, if a state's population increases substantially, it may warrant additional seats for fair representation. Conversely, boundary changes that decrease a state's population may result in fewer representatives, altering the balance of power. These dynamics emphasize the need for periodic reapportionment to maintain equitable representation. An illustrative example is if State B's population doubles, its increased demographic weight could shift seat allocations, potentially affecting overall legislative decisions and power dynamics.

The Alabama Paradox and Apportionment Stability

The Alabama Paradox occurs when an increase in the total number of seats results in a state losing seats, which appears counterintuitive. It exemplifies the potential instability in certain apportionment methods where redistributions across states can produce paradoxical outcomes. The Huntington-Hill method addresses this issue by employing a geometric mean criterion for seat allocation, thereby reducing the likelihood of the paradox. This method ensures that the relative sizes of constituencies are preserved more accurately when the total seat count changes, maintaining overall fairness and stability in apportionment.

Evaluating Apportionment Methods and Fairness

While apportionment methods like Hamilton and Huntington-Hill are designed to promote fairness, they are not without limitations. The Hamilton method can give rise to paradoxical results and unfair advantages in some scenarios. The Huntington-Hill method offers improvements by reducing such issues, providing a more stable and equitable distribution framework. Nonetheless, whether apportionment alone can guarantee perfect fairness remains contentious. Some scholars advocate for alternative approaches, such as proportional representation systems or mixed methods, which could potentially address disparities more comprehensively. For example, combining district-based voting with proportional list systems could better balance constituency interests and overall fairness.

Conclusion

In conclusion, apportionment remains a crucial process in ensuring fair political representation within legislative bodies. The Hamilton method, while historically significant, exhibits limitations that the Huntington-Hill approach aims to mitigate. Changes in population and boundary configurations necessitate regular reapportionments to uphold fairness. Although no system is perfect, integrating multiple strategies, such as proportional representation, could complement traditional methods and enhance fairness. Ultimately, the choice of apportionment system reflects societal values regarding fairness, stability, and democratic legitimacy.

References

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