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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Definitions:

Disjoint

Referring to sets that have no elements in common; also used to describe events that cannot occur at the same time.

Proportion

The fraction of times an event occurs relative to the total number of trials or instances.

M&M Candy

A brand of colorful, button-shaped chocolates with a letter "m" printed on them, encased in a sugar shell.

Drawn

A term used to describe an outcome or result that ends in a tie or no clear winner, or the process of extracting or pulling something.