The Results of an Election Are Summarized in the Following

question 26

Multiple Choice

The results of an election are summarized in the following preference table. If the plurality method is used, determine whether the head-to-head comparison criterion has been violated and explain why.

$\begin{array}{l|lllll}\text { Number of votes } & 5 & 12 & 7 & 14 & 10 \\\hline \text { First choice } & \mathrm{Z} & \mathrm{Z} & \mathrm{X} & \mathrm{X} & \mathrm{Y} \\\text { Second choice } & \mathrm{X} & \mathrm{Y} & \mathrm{Y} & \mathrm{Z} & \mathrm{Z} \\\text { Third choice } & \mathrm{Y} & \mathrm{X} & \mathrm{Z} & \mathrm{Y} & \mathrm{X}\end{array}$

• A) No, because X is the plurality winner.
• B) Yes, because X does not win over Z in a head-to-head comparison.
• C) Yes, because X does not win over Y in a head-to-head comparison.
• D) No, because X wins over Y and Z in a head-to-head comparison.

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