A Club Voted on Whether to Meet on Monday $( \mathrm { M } )$

question 22

Short Answer

A club voted on whether to meet on Monday $( \mathrm { M } )$ , Wednesday $( \mathrm { W } )$ , Friday $( \mathrm { F } )$ , or Saturday (S). The results of the election are summarized in the preference table below.

$\begin{array}{l|lccc}\text { Number of votes } & 6 & 10 & 5 & 8 \\\hline \text { First choice } & \text { F } & \text { W } & \text { M } & \text { F } \\\text { Second choice } & \text { W } & \text { F } & \text { W } & \text { S } \\\text { Third choice } & \text { M } & \text { S } & \text { F } & \text { W } \\\text { Fourth choice } & \text { S } & \text { M } & \text { S } & \text { M }\end{array}$
(a) Using the pairwise comparison voting method, determine the winner. (b) If candidate S is eliminated and the votes are recounted, does this election violate the irrelevant alternative criterion?

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Definitions:

Dormitories

Residential buildings on educational campuses where students live during academic terms.

Cluster Sampling

A sampling technique where the population is divided into clusters, and a random sample of these clusters is then selected for analysis.

Simple Random Sampling

A sampling method where each member of a population has an equal chance of being selected.

Standard Deviation

An indicator of the degree of spread or divergence among values in a dataset.