To solve this problem using the pairwise comparison method, we compare each pair of options (Warehouse (W), Park (P), and Beach (B)) head-to-head to determine the preferred option. Here's the step-by-step breakdown:

Step 1: Organize the information from the ballot table.

• Number of ballots cast: [6, 6, 7, 16]
• Choices and ranks:
  • Ballot 1 (6 votes): 1st = P, 2nd = B, 3rd = W
  • Ballot 2 (6 votes): 1st = P, 2nd = W, 3rd = B
  • Ballot 3 (7 votes): 1st = B, 2nd = W, 3rd = P
  • Ballot 4 (16 votes): 1st = W, 2nd = B, 3rd = P

Step 2: Compare each pair using pairwise comparison.

We compare each pair by counting the votes where one option is ranked higher than the other.

Pairwise Comparisons:

1. W vs. P:

   • Ballot 1: P > W (6 votes for P)
   • Ballot 2: P > W (6 votes for P)
   • Ballot 3: W > P (7 votes for W)
   • Ballot 4: W > P (16 votes for W)
   • Total Votes:
     • W: 7 + 16 = 23
     • P: 6 + 6 = 12
   • Winner: W

2. W vs. B:

   • Ballot 1: B > W (6 votes for B)
   • Ballot 2: W > B (6 votes for W)
   • Ballot 3: W > B (7 votes for W)
   • Ballot 4: W > B (16 votes for W)
   • Total Votes:
     • W: 6 + 7 + 16 = 29
     • B: 6
   • Winner: W

3. P vs. B:

   • Ballot 1: P > B (6 votes for P)
   • Ballot 2: P > B (6 votes for P)
   • Ballot 3: B > P (7 votes for B)
   • Ballot 4: B > P (16 votes for B)
   • Total Votes:
     • B: 7 + 16 = 23
     • P: 6 + 6 = 12
   • Winner: B

Step 3: Determine the overall winner.

• W vs. P: W wins.
• W vs. B: W wins.
• P vs. B: B wins.

Final Ranking:

1. Warehouse (W): Wins against both P and B.
2. Beach (B): Wins against P, loses to W.
3. Park (P): Loses to both W and B.

Winner: Warehouse (W)

Would you like further details or clarification on any step?

Related Questions:

1. How is the pairwise comparison method different from the plurality method?
2. Can pairwise comparison result in a tie? If so, how is it resolved?
3. What are the limitations of using pairwise comparisons in decision-making?
4. How does the ranking order affect the final result in pairwise comparisons?
5. Could another voting method lead to a different winner in this scenario?

Tip:

When using the pairwise comparison method, always ensure you track the total votes for each pair to avoid miscounting.