Math  /  Data & Statistics

Question2. Refer to the following preference schedule to answer parts (a) - (f). Note: See attached page for additional copies of the table. ( 36pts436 \mathrm{pts}-4 pts for each part) \begin{tabular}{|r|c|c|c|c|} \hline First & A & B & D & C \\ \hline Second & B & D & C & B \\ \hline Third & C & A & B & A \\ \hline Forth & D & C & A & D \\ \hline Number of Voters & 30 & 20 & 25 & 10 \\ \hline \end{tabular} a. How many votes were cast? \qquad b. How many votes are needed to receive a majority? \qquad c. Find the plurality winner: \qquad d. Did the plurality winner also receive a majority? \qquad Show work to support the selection process below. e. Find the winner by a single runoff of the top two candidates: \qquad Show work to support the selection process below. f. Find the winner by a sequential runoff: \qquad Show work to support the selection process below. g. Find the winner by a Borda count: \qquad Show work to support the selection process below. h. Find the winner, if any, by the method of pairwise comparisons: \qquad Show work to support the selection process below.

Studdy Solution
Determine the winner by the method of pairwise comparisons:
Compare each pair of candidates:
- A vs. B: A wins (30 vs. 20) - A vs. C: A wins (30 vs. 10) - A vs. D: D wins (45 vs. 30) - B vs. C: B wins (20 vs. 10) - B vs. D: D wins (45 vs. 20) - C vs. D: D wins (45 vs. 10)
D wins the most pairwise comparisons.
The winner by the method of pairwise comparisons is candidate D.

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