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Chapter 13: Problem 39
What is a preference ballot?
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What is the plurality-with-elimination method? Why is it advantageous to rank the candidates when using this method?
Your class is given the option of choosing a day for the final exam. The students in the class are asked to rank the three available days, Monday (M), Wednesday (W), and Friday (F). The results of the election are shown in the following preference table. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 4} & \mathbf{8} & \mathbf{3} & \mathbf{1} \\ \hline \text { First Choice } & \text { F } & \text { F } & \text { W } & \text { M } \\ \hline \text { Second Choice } & \text { W } & \text { M } & \text { F } & \text { W } \\ \hline \text { Third Choice } & \text { M } & \text { W } & \text { M } & \text { F } \\ \hline \end{array} $$ a. How many students voted in the election? b. How many students selected the days in this order: \(\mathrm{F}, \mathrm{M}, \mathrm{W} ?\) c. How many students selected Friday as their first choice for the final? d. How many students selected Wednesday as their first choice for the final?
A country has 200 seats in the congress, divided among the five states according to their respective populations. The table shows each state鈥檚 population, in thousands, before and after the country鈥檚 population increase. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { Total } \\ \hline \begin{array}{l} \text { Original } \\ \text { Population } \\ \text { (in thousands) } \end{array} & 2224 & 2236 & 2640 & 3030 & 9870 & 20,000 \\ \hline \begin{array}{l} \text { New Population } \\ \text { (in thousands) } \end{array} & 2424 & 2436 & 2740 & 3130 & 10,070 & 20,800 \\ \hline \end{array} $$ n thousands) 2424 2436 2740 3130 10,070 20,800 a. Use Hamilton鈥檚 method to apportion the 200 congressional seats using the original population. b. Find the percent increase, to the nearest tenth of a percent, in the population of each state. c. Use Hamilton鈥檚 method to apportion the 200 congressional seats using the new population. What do you observe about the percent increases for states A and B and their respective changes in apportioned seats? Is this the population paradox?
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 $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { District } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\ \hline \text { Original Population } & 1188 & 1424 & 2538 & 3730 & 8880 \\ \hline \text { New Population } & 1188 & 1420 & 2544 & 3848 & 9000 \\ \hline \end{array} $$
Why is it important to choose a voting system before an election takes place?
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