Questions: A travel club is holding a vote for the club's favorite travel destination. The nominations are Benin (B), Saudi Arabia (S), and China (C). A vote of all the club members was held and the results are summarized in the preference table below. Number of Votes: 48, 53, 14, 41, 40, 25 First Choice: S, S, C, B, B, C Second Choice: C, B, B, C, S, S Third Choice: B, C, S, S, C, B Using the pairwise comparison method, determine favorite travel destination of the club. - Benin - Saudi Arabia - China - China and Saudi Arabia tied for first place - Benin and China tied for first place

Solution Steps

To determine the favorite travel destination using the pairwise comparison method, we need to compare each pair of destinations and count which one is preferred by more voters. For each pair, we tally the votes where one destination is ranked higher than the other. The destination with the most wins in these pairwise comparisons is the favorite.

We have the following votes for each preference order: \[ \text{votes} = [48, 53, 14, 41, 40, 25] \] The preferences of the voters are summarized as: \[ \text{preferences} = \{(S, C, B), (S, B, C), (C, B, S), (B, C, S), (B, S, C), (C, S, B)\} \]

We will compare each pair of destinations: \(B\) (Benin), \(S\) (Saudi Arabia), and \(C\) (China). The pairwise comparisons yield the following results:

1. Comparison of \(B\) and \(S\):

   • Votes for \(B\) over \(S\): \(48 + 41 + 40 = 129\)
   • Votes for \(S\) over \(B\): \(53 + 14 + 25 = 92\)
   • Result: \(B\) wins with \(129\) votes against \(92\).

2. Comparison of \(B\) and \(C\):

   • Votes for \(B\) over \(C\): \(41 + 40 + 25 = 106\)
   • Votes for \(C\) over \(B\): \(48 + 53 + 14 = 115\)
   • Result: \(C\) wins with \(115\) votes against \(106\).

3. Comparison of \(S\) and \(C\):

   • Votes for \(S\) over \(C\): \(48 + 53 + 41 = 142\)
   • Votes for \(C\) over \(S\): \(14 + 40 + 25 = 79\)
   • Result: \(S\) wins with \(142\) votes against \(79\).

The total wins for each destination are:

• \(B\): 1 win (against \(S\))
• \(S\): 2 wins (against \(B\) and \(C\))
• \(C\): 1 win (against \(B\))

The destination with the most pairwise wins is \(S\) (Saudi Arabia) with \(2\) wins.

Final Answer