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Chapter 13: Problem 35

Describe the difference between how modified quotas are rounded using Jefferson's method and Adams's method.

Short Answer

Expert verified
The main difference between Jefferson's and Adams's methods lies in their rounding rules and the party they favor. Jefferson's method rounds down all fractional quotas, benefiting smaller parties, while Adams's method rounds up all fractional quotas, favoring larger parties. Additionally, Adams's method uses a smaller divisor than Jefferson's method.

Step by step solution

01

Understanding Jefferson's Method

Jefferson's method, also known as the method of greatest divisors, involves taking the total population of all districts to be represented, dividing by the number of representations, to get a quota. If the total population doesn't divide equally, Jefferson's method involves rounding down all fractional quotas. This generally benefits smaller parties.
02

Understanding Adams's Method

Adams's method, on the other hand, involves the similar process of calculating quotas, but the method rounds up all fractional quotas instead of rounding down, this generally tends to favor large parties. It's also significant that it uses a modified divisor that is smaller than the one used in Jefferson's method.
03

Comparison

After describing both methods, the difference between Jefferson's and Adams's methods can be summarized as follows: Jefferson's method rounds down all fractional quotas, which generally benefits smaller parties or groups, while Adams's method rounds up all fractional quotas, tending to favor larger parties or groups. Furthermore, Adams's method uses a smaller divisor than Jefferson's method

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Most popular questions from this chapter

In Exercises 27-30, 72 voters are asked to rank four brands of soup: \(A, B, C\), and \(D\). The votes are summarized in the following preference table. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & 34 & 30 & 6 & 2 \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } & \text { D } \\ \hline \text { Second Choice } & \text { B } & \text { C } & \text { D } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { D } & \text { B } & \text { C } \\ \hline \text { Fourth Choice } & \text { D } & \text { A } & \text { A } & \text { A } \\ \hline \end{array} $$ Determine the winner using the Borda count method.

Fifty-three people are asked to taste-test and rank three different brands of yogurt, \(A, B\), and \(C\). The preference table shows the rankings of the 53 voters. $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & 27 & 24 & 2 \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } \\ \hline \text { Second Choice } & \text { C } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { B } & \text { A } & \text { A } \\ \hline \end{array} $$ a. Which brand has a majority of first-place votes? b. Suppose that the Borda count method is used to determine the winner. Which brand wins the taste test? c. Is the majority criterion satisfied? Explain your answer.

A computer company is considering opening a new branch in Atlanta (A), Boston (B), or Chicago (C).Senior managers vote to decide where the new branch will be located. The winning city is to be determined by the plurality method. The preference table for the election is shown. $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & 20 & 19 & 5 \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } \\ \hline \text { Second Choice } & \text { B } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { A } & \text { A } \\ \hline \end{array} $$ a. Which city is favored over all others using a head-tohead comparison? b. Which city wins the vote using the plurality method? c. Is the head-to-head criterion satisfied? Explain your answer.

A university is composed of five schools. The enrollment in each school is given in the following table. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { School } & \begin{array}{c} \text { Human- } \\ \text { ities } \end{array} & \begin{array}{c} \text { Social } \\ \text { Science } \end{array} & \begin{array}{c} \text { Engi- } \\ \text { neering } \end{array} & \text { Business } & \begin{array}{c} \text { Educa- } \\ \text { tion } \end{array} \\ \hline \text { Enrollment } & 1050 & 1410 & 1830 & 2540 & 3580 \\ \hline \end{array} $$ There are 300 new computers to be apportioned among the five schools according to their respective enrollments. Use Hamilton's method to find each school's apportionment of computers.

An HMO has 70 doctors to be apportioned among six clinics. The HMO decides to apportion the doctors based on the average weekly patient load for each clinic, given in the following table. Use Jefferson's method to apportion the 70 doctors. (Hint: A modified divisor between 39 and 40 will work.)$$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { Clinic } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\ \hline \begin{array}{l} \text { Average Weekly } \\ \text { Patient Load } \end{array} & 316 & 598 & 396 & 692 & 426 & 486 \\ \hline \end{array} $$
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