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A computer company is considering opening a new branch in Atlanta (A), Boston (B), or
Chapter 13, Problem 4(choose chapter or problem)
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.
\(\begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & \mathbf{2 0} & \mathbf{1 9} & \mathbf{5} \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } \\ \hline \text { Second Choice } & \text { B } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { A } & \text { A } \\ \hline \end{array}\)
a. Which city is favored over all others using a head-to-head comparison?
b. Which city wins the vote using the plurality method?
c. Is the head-to-head criterion satisfied? Explain your answer.
Questions & Answers
QUESTION:
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.
\(\begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & \mathbf{2 0} & \mathbf{1 9} & \mathbf{5} \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } \\ \hline \text { Second Choice } & \text { B } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { A } & \text { A } \\ \hline \end{array}\)
a. Which city is favored over all others using a head-to-head comparison?
b. Which city wins the vote using the plurality method?
c. Is the head-to-head criterion satisfied? Explain your answer.
ANSWER:
Step 1 of 5
Let us suppose that a company took votes for opening new branches in three cities: Atlanta (A), Boston (B), Chicago (C) .
Preference table for the three brands is as follows,
\(\begin{array}{|l|c|c|c|} \hline \text { Number of Votes } & \mathbf{2 0} & \mathbf{1 9} & \mathbf{5} \\ \hline \text { First Choice } & \text { A } & \text { B } & \text { C } \\ \hline \text { Second Choice } & \text { B } & \text { C } & \text { B } \\ \hline \text { Third Choice } & \text { C } & \text { A } & \text { A } \\ \hline \end{array}\)