The Mathematics Department Is Holding an Election for Department Chair

question 37

Multiple Choice

The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The voter profile below shows the results of the preliminary Nonbinding ballots with candidates Clark (C) , Jones (J) , and Smith (S) .
$\begin{array}{c|l}\text { Number of Voters } & \text { Ranking } \\\hline 7 & \mathrm{~J}>\mathrm{S}>\mathrm{C} \\10 & \mathrm{~S}>\mathrm{J}>\mathrm{C} \\4 & \mathrm{~J}>\mathrm{C}>\mathrm{S} \\8 & \mathrm{C}>\mathrm{S}>\mathrm{J}\end{array}$

A second election is then held with the following voter profile:
$\begin{array}{c|l}\text { Number of Voters } & \text { Ranking } \\\hline 7 & \mathrm{~J}>\mathrm{S}>\mathrm{C} \\11 & \mathrm{~S}>\mathrm{J}>\mathrm{C} \\3 & \mathrm{~J}>\mathrm{C}>\mathrm{S} \\8 & \mathrm{C}>\mathrm{S}>\mathrm{I}\end{array}$

Use the Pairwise Comparison Method to determine the winner, and determine if the Monotonicity Criterion is violated in this selection process.

• A) Smith, no
• B) Jones, yes
• C) Jones, no
• D) Smith, yes

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