Earlier, we discovered that the summary of ranked ballots shown in the table below results in the pairwise comparison matrix in Figure 11.12. Use this information to answer the questions.

1. Determine the winner of the election by the pairwise comparison method.
2. Suppose that the 95 voters in the first column increased their ranking of the winner by 1 . Determine the winner by the pairwise comparison method with the new rankings.
3. Does this election violate the monotonicity criterion?
4. Do you think the result of part 3 is true for the pairwise comparison method and the monotonicity criterion in general? Why or why not?

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Number of Ballots 95 90 110 115 Option A 4 4 1 1 Option B 2 2 2 2 Option C 3 1 3 4 Option D 1 3 4 3 Opponent Option A Option B Option C Option D Points Runner AB AC AD Option A wins 3 225 225 225 BA BC BD Option B wins 2 185 320 315 CA CB CD Option C wins 0 185 90 200 DA DB DC Option D wins 1 185 95 210 Figure 11.12 Analyzed Pairwise Comparison Matrix for Sample Summary of Ranked Ballots