Chapter 13: Problem 47
Playwright Tom Stoppard wrote, "It's not the voting that's democracy; it's the counting." Explain what he meant by this.
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Chapter 13: Problem 47
Playwright Tom Stoppard wrote, "It's not the voting that's democracy; it's the counting." Explain what he meant by this.
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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?
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 (G), Julia Roberts (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. $$ \begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & 12 & 8 & 6 \\ \hline \text { First Choice } & \text { S } & \text { R } & \text { G } \\ \hline \text { Second Choice } & \text { G } & \text { G } & \text { R } \\ \hline \text { Third Choice } & \text { R } & \text { S } & \text { S } \\ \hline \end{array} $$ 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.
The winner by the plurality method violates the head-tohead criterion.
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? $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{6 0 , 0 0 0} & \mathbf{4 0 , 0 0 0} & \mathbf{4 0 , 0 0 0} & \mathbf{2 0 , 0 0 0} & \mathbf{2 0 , 0 0 0} \\ \hline \text { First Choice } & \text { A } & \text { C } & \text { B } & \text { A } & \text { C } \\ \hline \text { Second Choice } & \text { B } & \text { A } & \text { C } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { B } & \text { A } & \text { B } & \text { A } \\ \hline \end{array} $$
Describe the Borda count method. Is it possible to use this method without ranking the candidates? Explain.
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