Pairwise Comparison Matrix
Overview
Instead of rating each option absolutely (hard), compare pairs directly (easier). “Is A better than B?” is easier than “How good is A?” Aggregate comparisons to produce ranking.
Goal
Rank options by comparing all pairs and counting wins. Each individual comparison is simple; aggregation is mechanical. Avoids the difficulty of absolute rating.
Steps
Step 1: List All Options
Enumerate all options to be compared. Label them for easy reference (A, B, C… or 1, 2, 3…).
Output: Labeled option list
Step 2: Define Comparison Criterion
Clearly state what you’re comparing on. Can be single criterion or composite.
Single: “Which is more important?” Composite: “Considering cost, quality, and time, which is better?”
Output: Criterion statement
Step 3: Create Comparison Matrix
Create N×N matrix with options on both axes. Diagonal is empty (don’t compare to self). Only need to fill upper triangle (lower is symmetric).
Output: Empty matrix
Step 4: Compare Each Pair
For each pair (i, j) where i < j: Ask: “Is [Option i] better than [Option j] on [criterion]?”
Record:
- “1” in cell (i,j) if i wins
- “0” in cell (i,j) if j wins
- “0.5” each if tie
Be consistent. If A > B and B > C, then A > C (transitivity).
Output: Filled comparison matrix
Step 5: Check for Inconsistencies
Look for intransitive cycles: A > B > C > A If found, reconsider those comparisons. Some intransitivity may be acceptable (different criteria).
Output: Consistency check result
Step 6: Calculate Scores
For each option, sum its wins. Win = 1 point, Tie = 0.5 points, Loss = 0 points Total possible points = N - 1
Output: Score for each option
Step 7: Produce Ranking
Sort options by score (descending). Handle ties by re-comparing or accepting tie.
Output: Final ranking
When to Use
- Ranking options when absolute scoring is difficult
- Prioritizing features/tasks
- Multi-criteria decision making
- Reducing bias from anchoring
- When options are hard to rate but easy to compare
Verification
- All pairs were compared
- Criterion was applied consistently
- No significant intransitivity
- Scores sum correctly
- Ranking reflects scores
Input: $ARGUMENTS
Apply this procedure to the input provided.