Suppose 8 candidates a, b, c, d, e, f, g, h are involved in a Pairwise Comparison Method election. The number of pairwise comparisons each candidate wins is shown in the table. $$\begin{array} { l | l l l l l l l l l l }
\text { Candidate } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } & \text { f } & \text { g } & \text { h } \
\hline \text { Number of Pairwise Comparisons Won } & 4 & 5 & ? & 3 & 2 & 2 & 1 & 4
\end{array}$$ Which candidate wins the election and how many pairwise points does the winner have?
A)c, with 7 pairwise points
B)c, with 5 pairwise points
C)c, with 8 pairwise points
D)c, with 6 pairwise points

Question

Suppose 8 candidates a, b, c, d, e, f, g, h are involved in a Pairwise Comparison Method election. The number of pairwise comparisons each candidate wins is shown in the table. $$\begin{array} { l | l l l l l l l l l l } 
\text { Candidate } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } & \text { f } & \text { g } & \text { h } \
\hline \text { Number of Pairwise Comparisons Won } & 4 & 5 & ? & 3 & 2 & 2 & 1 & 4
\end{array}$$ Which candidate wins the election and how many pairwise points does the winner have?
A)c, with 7 pairwise points
B)c, with 5 pairwise points
C)c, with 8 pairwise points
D)c, with 6 pairwise points

Quizplus · Accepted Answer

In a pairwise comparison method with 8 candidates, there are 7 comparisons for each candidate. Since the total number of wins must equal the total number of comparisons (7 wins or losses for each of 8 candidates, divided by 2 since each match is counted for two candidates), the sum of all wins is 28. Adding the known wins (4+5+3+2+2+1+4=21) and subtracting from 28 gives 7, which must be the number of wins for candidate c. Therefore, candidate c wins with 7 pairwise points.

Suppose 8 Candidates A, B, C, D, E, F, G