/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 7 A small country is composed of f... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A small country is composed of five states, \(A, B, C, D\), and \(E\). The population of each state is given in the following table. Congress will have 57 seats, divided among the five states according to their respective populations. Use Jefferson's method with \(d=32,920\) to apportion the 57 congressional seats. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline \text { Population } & 126,316 & 196,492 & 425,264 & 526,664 & 725,264 \\\ \hline \end{array} $$

Short Answer

Expert verified
After applying Jefferson's Method, the apportionment of the 57 congressional seats among the states A, B, C, D, and E would be 2, 5, 12, 16, and 22 respectively.

Step by step solution

01

Calculating the Standard Quota

Begin with calculating the standard quota for each state. The standard quota is the population of the state divided by the standard divisor. For state A: \( \frac{126,316}{32,920} = 3.83 \),For state B: \( \frac{196,492}{32,920} = 5.97 \), For state C: \( \frac{425,264}{32,920} = 12.92 \), For state D: \( \frac{526,664}{32,920} = 16.00 \), and For state E: \( \frac{725,264}{32,920} = 22.03 \)
02

Calculating the Lower Quotas

Calculate the lower quota for each state by rounding down the quota from the first step to the nearest whole number. For state A, it is 3,For state B, it is 5, For state C, it is 12, For state D, it is 16, and For state E, it is 22.
03

Distribute the Remaining Seats

Up until now, \(3 + 5 + 12 + 16 + 22 = 58\) seats have been apportioned, which is one over the total 57 seats. As per Jefferson's Method, reduce the quota of the state which has the smallest decimal until the total number of seats matches the given total. Here, the state with the smallest decimal is state A, so reduce the quota of state A by one, making it 2 instead of 3. Now, the total number of seats is 3 + 5 + 12 + 16 + 22 - 1 = 57, matching the total number of seats given.
04

Final Apportionment

Each state's final quota is: State A: 2State B: 5 State C: 12 State D: 16 State E: 22

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

apportionment
Apportionment is the process by which a government or authority distributes something, such as seats in a legislative body, among different entities or regions. In this context, it involves distributing congressional seats among five states based on their population sizes. Each state is allocated a number of seats that corresponds to its proportion of the total population. To achieve apportionment fairly, different methods can be used, with Jefferson's Method being one approach. This method involves using a specific formula and adjustments to ensure that the distribution of seats reflects the population distribution as accurately as possible. Understanding apportionment is crucial because it ensures that representation in governance is balanced and equitable. The goal is to match each state's influence in Congress to its population size, thereby providing equal representation for all citizens.
congressional seats
Congressional seats refer to the allocated positions in a legislative body that representatives occupy on behalf of their constituents. In the exercise, there are a total of 57 congressional seats that need to be distributed among the states. The method used to allocate these seats is important because it affects representation in government. The more seats a state has, the more influence it can exert. Therefore, ensuring fair and accurate representation by distributing seats according to population is essential. The calculation of congressional seats begins with determining standard quotas and then making necessary adjustments to ensure the total matches the predetermined number of seats, utilizing a method like Jefferson's.
standard quota
The standard quota is a crucial calculation in the apportionment process. It represents how many congressional seats each state should ideally receive based on its population relative to a standard divisor.In simple terms, the standard quota is found by dividing each state's population by the divisor. For example, in the exercise, state A's standard quota is calculated as \( \frac{126,316}{32,920} = 3.83 \). This calculation is done for each state to determine how many seats they would get before rounding or adjustments.Once calculated, the standard quota serves as the baseline for further steps in the apportionment process, such as determining lower quotas and making final adjustments to meet the total number of seats available.
population distribution
Population distribution refers to how people are spread across different states or regions, which impacts political representation. In the context of the exercise, it's the distribution of the population across five states that determines each state's share of the total number of congressional seats. Understanding the population distribution is vital because it shapes the apportionment process. With varying populations in each state, the goal is to ensure seats are apportioned fairly relative to each state's share of the total population. This ensures equitable representation of citizens in the legislative body. The method used must take into account both large and small populations, balancing the representation so that even less populated states receive fair representation compared to those with larger populations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A town is voting on an ordinance dealing with nudity at its public beaches. The options are (A) make clothing optional at all beaches; (B) permit nudity at designated beaches only; and (C) permit no nudity at public beaches. The winner is to be determined by the Borda count method. The preference table for the election is shown. $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & \mathbf{2 0 0} & \mathbf{8 0} & \mathbf{8 0} \\ \hline \text { First Choice } & \text { C } & \text { B } & \text { A } \\ \hline \text { Second Choice } & \text { A } & \text { A } & \text { B } \\ \hline \text { Third Choice } & \text { B } & \text { C } & \text { C } \\ \hline \end{array} $$ a. Which option is favored over all others using a head-tohead comparison? b. Which option wins the vote using the Borda count method? c. Is the head-to-head criterion satisfied? Explain your answer.

The table shows the 1790 United States census. In 1793, at th direction of President George Washington, 105 seats in t House of Representatives were to be divided among the 15 stat according to their 1790 populations. Use this information to sol Exercises 23-26. $$ \begin{aligned} &1790 \text { UNITED STATES CENSUS }\\\ &\begin{array}{|l|r|l|r|} \hline \text { Connecticut } & 236,841 & \text { New York } & 331,589 \\ \hline \text { Delaware } & 55,540 & \text { North Carolina } & 353,523 \\ \hline \text { Georgia } & 70,835 & \text { Pennsylvania } & 432,879 \\ \hline \text { Kentucky } & 68,705 & \text { Rhode Island } & 68,446 \\ \hline \text { Maryland } & 278,514 & \text { South Carolina } & 206,236 \\ \hline \text { Massachusetts } & 475,327 & \text { Vermont } & 85,533 \\ \hline \text { New Hampshire } & 141,822 & \text { Virginia } & 630,560 \\ \hline \text { New Jersey } & 179,570 & & \\ \hline \end{array} \end{aligned} $$ Use Hamilton's method to find each state's apportionment of congressional seats.

What is the quota rule?

Members of the Student Activity Committee at a college are considering three actors to speak at a campus festival on women in the arts: Whoopi Goldberg \((\mathrm{G})\), Julia Roberts \((\mathrm{R})\), and Meryl Streep (S). Committee members vote for their preferred speaker. The winner is to be selected by the pairwise comparison method. The preference table for the election is shown. $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 2} & \mathbf{8} & \mathbf{6} \\ \hline \text { First Choice } & \text { S } & \text { R } & \text { G } \\ \hline \text { Second Choice } & \text { G } & \text { G } & \text { R } \\ \hline \text { Third Choice } & \text { R } & \text { S } & \text { S } \\ \hline \end{array} $$ a. Using the pairwise comparison method, who is selected as the speaker? b. Prior to the announcement of the speaker, Meryl Streep informs the committee that she will not be able to participate due to other commitments. Construct a new preference table for the election with \(S\) eliminated. Using the new table and the pairwise comparison method, who is selected as the speaker? c. Is the irrelevant alternatives criterion satisfied? Explain your answer.

Students at your college are given the option of choosing a topic for which a speaker will be selected. Students are asked to rank three topics: Technology (T), Environmental Issues (E), and Terrorism in the Name of Religion (R). The results of the election are shown in the following preference table. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{7 0} & \mathbf{3 0} & \mathbf{1 0} & \mathbf{5} \\ \hline \text { First Choice } & \mathrm{R} & \mathrm{T} & \mathrm{T} & \mathrm{E} \\ \hline \text { Second Choice } & \mathrm{E} & \mathrm{R} & \mathrm{E} & \mathrm{T} \\ \hline \text { Third Choice } & \mathrm{T} & \mathrm{E} & \mathrm{R} & \mathrm{R} \\ \hline \end{array} $$ a. How many students voted? b. How many students selected the topics in this order: \(\mathrm{T}, \mathrm{E}, \mathrm{R} ?\) c. How many students selected technology as their first choice for a speaker's topic? d. How many students selected environmental issues as their second choice for a speaker's topic?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.