To determine the winner using the pairwise comparison method, we need to compare each candidate (Nestle Crunch, Snickers, Milky Way, and Twix) against each other based on the rankings provided by voters.

Here is the plan for solving the problem:

1. Perform pairwise comparisons between each pair of candidates.
2. For each comparison, the candidate that is ranked higher by more voters wins.
3. Count how many pairwise comparisons each candidate wins.

Let's break this down step by step:

1. Pairwise comparison: Nestle Crunch vs Snickers

• Nestle Crunch wins among:
  • 14 voters (ranked 1st) and 17 voters (ranked 2nd) = 31 voters
• Snickers wins among:
  • 39 voters (ranked 1st) and 28 voters (ranked 2nd) = 67 voters
• Winner: Snickers (67 vs 31)

2. Pairwise comparison: Nestle Crunch vs Milky Way

• Nestle Crunch wins among:
  • 14 voters (ranked 1st) and 17 voters (ranked 2nd) = 31 voters
• Milky Way wins among:
  • 28 voters (ranked 1st) and 39 voters (ranked 2nd) = 67 voters
• Winner: Milky Way (67 vs 31)

3. Pairwise comparison: Nestle Crunch vs Twix

• Nestle Crunch wins among:
  • 14 voters (ranked 1st) and 17 voters (ranked 2nd) = 31 voters
• Twix wins among:
  • 39 voters (ranked 3rd) and 28 voters (ranked 3rd) and 17 voters (ranked 3rd) = 84 voters
• Winner: Twix (84 vs 31)

4. Pairwise comparison: Snickers vs Milky Way

• Snickers wins among:
  • 39 voters (ranked 1st) and 14 voters (ranked 2nd) = 53 voters
• Milky Way wins among:
  • 28 voters (ranked 1st) and 17 voters (ranked 2nd) = 45 voters
• Winner: Snickers (53 vs 45)

5. Pairwise comparison: Snickers vs Twix

• Snickers wins among:
  • 39 voters (ranked 1st) and 28 voters (ranked 2nd) = 67 voters
• Twix wins among:
  • 14 voters (ranked 4th) and 17 voters (ranked 3rd) = 31 voters
• Winner: Snickers (67 vs 31)

6. Pairwise comparison: Milky Way vs Twix

• Milky Way wins among:
  • 28 voters (ranked 1st) and 39 voters (ranked 2nd) = 67 voters
• Twix wins among:
  • 14 voters (ranked 4th) and 17 voters (ranked 3rd) = 31 voters
• Winner: Milky Way (67 vs 31)

Summary of Pairwise Wins:

• Snickers: 3 wins (vs Nestle Crunch, Milky Way, Twix)
• Milky Way: 2 wins (vs Nestle Crunch, Twix)
• Twix: 1 win (vs Nestle Crunch)
• Nestle Crunch: 0 wins

Winner: Snickers

Number of pairwise comparison wins: 3

Would you like further clarification on any part of the process?

Here are 5 related questions to explore:

1. What happens if two candidates tie in pairwise comparisons?
2. Can the pairwise comparison method result in a cycle where no clear winner exists?
3. How does the pairwise comparison method differ from other voting methods like the plurality system?
4. What are the strengths and weaknesses of the pairwise comparison method?
5. How can the pairwise comparison method be modified for elections with more candidates?

Tip: When using the pairwise comparison method, it is important to always compare all candidates against each other, as one candidate can perform better against one but worse against another, revealing more nuanced preferences.