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Chapter 13: Problem 34

Explain why Hamilton's method satisfies the quota rule.

Short Answer

Expert verified
In Hamilton's method, apportionment strictly follows the quotas. The first portion of the allocation adheres to the lower quotas and the distribution of leftover seats follows the decimal parts of the quotas. Therefore, the final apportionment is either equal to or very close to the quota, hence, satisfying the quota rule.

Step by step solution

01

Understanding Hamilton's Method

Hamilton's Method is an apportionment method which involves calculating a quota for distribution based on population. It assigns seats strictly based on the quotas and disregards fractions.
02

Applying Hamilton's Method

First, a standard divisor is calculated by dividing the total population by the total number of available seats. The standard quota for each state, party, or group is then calculated by dividing its population by the standard divisor. The lower quota (whole part of the standard quota) is the initial apportion. The leftover seats are distributed to the states, parties, or groups with the highest decimal parts in their quotas.
03

Explaining the Quota Rule

Quota Rule involves assigning an allocation that is as close as possible to the 'deserved' allocation or quota. The deserved allocation or quota is calculated by dividing the total items to allocate by the total number of participants.
04

Proving Hamilton's method satisfies the quota rule

As we see in Hamilton's method, the first part of the apportionment strictly follows the lower quotas. And the distribution of residual seats also strictly follows the decimal part of the quotas. Therefore, the final apportionment is either the floor or the ceiling of the quota, thus satisfying the quota rule.

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Most popular questions from this chapter

A candidate won the election using the plurality-withelimination method, yet lost the election when the votes were counted by the pairwise comparison method.

In Exercises 19-22, suppose that the pairwise comparison method is used to determine the winner in an election. If there are five candidates, how many comparisons must be made?

A town has five districts in which mail is distributed and 50 mail trucks. The trucks are to be apportioned according to each district鈥檚 population. The table shows these populations before and after the town鈥檚 population increase. Use Hamilton鈥檚 method to show that the population paradox occurs. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { District } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { Total } \\ \hline \begin{array}{l} \text { Original } \\ \text { Population } \end{array} & 780 & 1500 & 1730 & 2040 & 2950 & 9000 \\ \hline \text { New Population } & 780 & 1500 & 1810 & 2040 & 2960 & 9090 \\ \hline \end{array} $$

Describe the difference between the modified divisor, \(d\), in terms of the standard divisor using Jefferson's method and Adams's method.

Describe the monotonicity criterion.
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