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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Definitions:

Indorsement

A signature, usually on the back of a check or other negotiable instrument, that transfers the rights of the document to another party or specifies conditions for its use.

Federal Reserve Board

The governing body of the Federal Reserve System, responsible for the United States' monetary policy.

Restrictive Indorsement

An endorsement on a negotiable instrument that limits the way the instrument can be further transferred or conditions under which it can be cashed.

Personal Defenses

Legal strategies individuals use to challenge accusations or claims brought against them in court.