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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

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?

Three people pool their money to buy 30 shares of stock. The amount that each person contributes is shown in the following table. Use Adams's method to apportion the shares of stock. (Hint: Find the standard divisor. A modified divisor that is greater than this standard divisor will work.) $$ \begin{array}{|l|c|c|c|} \hline \text { Person } & \text { A } & \text { B } & \text { C } \\ \hline \text { Amount } & \$ 795 & \$ 705 & \$ 525 \\ \hline \end{array} $$

Four professors are running for chair of the Natural Science Division: Professors Darwin (D), Einstein (E), Freud (F), and Hawking (H). The votes of the professors in the natural science division are summarized in the following preference table. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Number of Votes } & 30 & 22 & 20 & 12 & 2 \\ \hline \text { First Choice } & \text { D } & \text { E } & \text { F } & \text { H } & \text { H } \\ \hline \text { Second Choice } & \text { H } & \text { F } & \text { E } & \text { E } & \text { F } \\ \hline \text { Third Choice } & \text { F } & \text { H } & \text { H } & \text { F } & \text { D } \\ \hline \text { Fourth Choice } & \text { E } & \text { D } & \text { D } & \text { D } & \text { E } \\ \hline \end{array} $$ Who is declared the new division chair using the plurality method?

Throughout this Exercise Set, in computing standard divisors, standard quotas, and modified quotas, round to the nearest hundredth when necessary. A small country is comprised of four states, \(A, B, C\), and \(D\). The population of each state, in thousands, is given in the following table. Use this information to solve Exercises $1-4 . $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\ \hline \begin{array}{l} \text { Population } \\ \text { (in thousands) } \end{array} & 138 & 266 & 534 & 662 & 1600 \\ \hline \end{array} $$ According to the country's constitution, the congress will have 80 seats, divided among the four states according to their respective populations. a. Find the standard divisor, in thousands. How many people are there for each seat in congress? b. Find each state's standard quota. c. Find each state's lower quota and upper quota.

What is the plurality-with-elimination method? Why is it advantageous to rank the candidates when using this method?
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