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Chapter 13: Problem 27

Describe how to find a standard divisor.

Short Answer

Expert verified
The standard divisor is calculated by dividing the total population or quantity by the number of parts or sections. The steps to find the standard divisor includes identifying the total population or quantity, identifying the number of parts or sections and then using the formula to calculate the standard divisor.

Step by step solution

01

Identify Total Population/Quantity

Firstly, the total population or quantity that needs to be divided or apportioned should be identified. This could be the total population of a country, total sales volume, etc.
02

Identify Number of Parts

Secondly, the total number of parts or sections that the quantity will be divided into should be identified. This could be the number of available seats in a legislative body, number of sales regions, etc.
03

Calculate Standard Divisor

Finally, the standard divisor is found by dividing the total population or quantity (Step 1) by the number of parts or sections (identified in Step 2). This is done using the formula: Standard divisor = Total Population / Number of Parts.

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Most popular questions from this chapter

Three candidates, A, B, and \(\mathrm{C}\), are running for mayor. Election rules stipulate that the pairwise comparison method will determine the winner. In the event that the pairwise comparison method leads to a tie, the Borda count method will decide the winner. The election results are summarized in the following preference table. Under these rules, which candidate becomes the new mayor? $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{6 0 , 0 0 0} & \mathbf{4 0 , 0 0 0} & \mathbf{4 0 , 0 0 0} & \mathbf{2 0 , 0 0 0} & \mathbf{2 0 , 0 0 0} \\ \hline \text { First Choice } & \text { A } & \text { C } & \text { B } & \text { A } & \text { C } \\ \hline \text { Second Choice } & \text { B } & \text { A } & \text { C } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { B } & \text { A } & \text { B } & \text { A } \\ \hline \end{array} $$

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.

MTV's Real World is considering three cities for its new season: Amsterdam (A), Rio de Janeiro (R), or Vancouver (V). Programming executives and the show's production team vote to decide where the new season will be taped. The winning city is to be determined by the plurality method. The preference table for the election is shown at the top of the next column. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 2} & \mathbf{9} & \mathbf{4} & \mathbf{4} \\ \hline \text { First Choice } & \text { A } & \text { V } & \text { V } & \text { R } \\ \hline \text { Second Choice } & \text { R } & \text { R } & \text { A } & \text { A } \\ \hline \text { Third Choice } & \text { V } & \text { A } & \text { R } & \text { V } \\ \hline \end{array} $$ 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 town has 40 mail trucks and four districts in which mail is distributed. 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 $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { District } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\ \hline \text { Original Population } & 1188 & 1424 & 2538 & 3730 & 8880 \\ \hline \text { New Population } & 1188 & 1420 & 2544 & 3848 & 9000 \\ \hline \end{array} $$

The winner by the plurality method violates the head-tohead criterion.
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