(A) Using the Pairwise Comparison Voting Method, Determine the Winner

question 48

Short Answer

$$\begin{array}{l}\text { The results of an election are summarized in the preference table below. }\\\begin{array} { l | c c c c } \text { Number of votes } & 15 & 2 & 20 & 10 \\\hline \text { First choice } & \mathrm { X } & \mathrm { X } & \mathrm { Z } & \mathrm { Y } \\\text { Second choice } & \mathrm { Y } & \mathrm { Z } & \mathrm { Y } & \mathrm { X } \\\text { Third choice } & \mathrm { Z } & \mathrm { Y } & \mathrm { X } & \mathrm { Z }\end{array}\end{array}$$ (a) Using the pairwise comparison voting method, determine the winner. (b) If candidate X drops out and the votes are recounted, does this election violate the irrelevant alternative criterion?

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Definitions:

Modest Means

Referring to a situation or condition where individuals or families possess limited financial resources, often associated with lower income or wealth levels, affecting their standard of living.

Bloody Sunday

Refers to several events in history where unarmed civilians were killed or injured by military or police forces; notable instances include events in Russia (1905) and Northern Ireland (1972).

Peaceful Protesters

Individuals or groups who engage in protests without violence, often to express opposition to an action or policy, aiming for change through non-violent means.

Decembrist

Refers to members of a Russian revolutionary movement in the early 19th century, known for their attempt to overthrow the autocratic government in December 1825.