pwc-pairwise-comparison-matrix

name	pwc - Pairwise Comparison Matrix
description	Instead of rating each option absolutely (hard), compare pairs
output	{"format":"prose"}

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