Chapter 13: Problem 51
Research and present a group report on a brief history of apportionment in the United States.
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Chapter 13: Problem 51
Research and present a group report on a brief history of apportionment in the United States.
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The theater society members are voting for the kind of play they will perform next semester: a comedy (C), a drama (D), or a musical (M). Their votes are summarized in the following preference table. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { Number of Votes } & 10 & 6 & 6 & 4 & 2 & 2 \\ \hline \text { First Choice } & \mathrm{M} & \mathrm{C} & \mathrm{D} & \mathrm{C} & \mathrm{D} & \mathrm{M} \\ \hline \text { Second Choice } & \mathrm{C} & \mathrm{M} & \mathrm{C} & \mathrm{D} & \mathrm{M} & \mathrm{D} \\ \hline \text { Third Choice } & \mathrm{D} & \mathrm{D} & \mathrm{M} & \mathrm{M} & \mathrm{C} & \mathrm{C} \\ \hline \end{array} $$ \(\text { Which type of play is selected using the plurality method? }\)
Research and present a group report on how voting is conducted for the Academy Awards. Describe the single transferable voting method, a variation of the pluralitywith-elimination method, in the nomination stage for best picture. (Members of the Irish Senate are also elected by this method.) Be sure to describe some of the more bizarre occurrences at the Oscar ceremonies.
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 plurality method.
Voters in a small town are considering four proposals, A, B, \(C\), and D, for the design of affordable housing. The winning design is to be determined by the Borda count method. The preference table for the election is shown. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & 300 & 120 & 90 & 60 \\ \hline \text { First Choice } & \text { D } & \text { C } & \text { C } & \text { A } \\ \hline \text { Second Choice } & \text { A } & \text { A } & \text { A } & \text { D } \\ \hline \text { Third Choice } & \text { B } & \text { B } & \text { D } & \text { B } \\ \hline \text { Fourth Choice } & \text { C } & \text { D } & \text { B } & \text { C } \\ \hline \end{array} $$ a. Which design has a majority of first-place votes? b. Using the Borda count method, which design will be used for the affordable housing? c. Is the majority criterion satisfied? Explain your answer.
Research and present a group report on how voting is conducted for one or more of the following awards: the Heisman Trophy, the Nobel Prize, the Grammy, the Tony, the Emmy, the Pulitzer Prize, or any event or award that the group finds intriguing. Be sure to discuss how the nominees are selected, who participates in the voting, the voting system or systems used, and who counts the results.
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