CF Dictionary A reference for Critical Fallibilism

CF Dictionary · Decision Making

Multi-Factor Decision

A decision based on multiple factors. CF shows the standard weighted-sum approach doesn't work and proposes pass/fail multiplication.

A multi-factor decision is a decision that depends on multiple factors. "Which car should I buy?" is a multi-factor decision. CF's analysis of multi-factor decisions is one of its most distinctive contributions.

The standard approach fails

Most people (and most decision-making books) suggest:

  1. Score each factor on a 0–100 scale.
  2. Weight each score by importance.
  3. Add weighted scores.
  4. Pick the option with the highest total.

CF shows this fails because:

  • Dimensions don't add. $20 + 5 cuteness = nothing.
  • Weights are made up. Why is "price" weight 0.3 and "color" 0.05?
  • The numbers are arbitrary. What does 7 out of 10 mean for "cuteness"?

CF's solution

CF recommends:

  1. Find the breakpoints for each factor.
  2. Evaluate pass/fail for each option × factor.
  3. Multiply pass/fail factors. All-pass yields 1; any-fail yields 0.
  4. If you must rank, break ties by how far past the breakpoint you are — but only on same-dimension factors.

Why multiplication works for pass/fail

"If you multiply pass/fail factors, it's the same as using 'and' on them. The result is 1 (pass) if every factor works and 0 (fail) otherwise."

This is a meaningful mathematical operation because pass/fail is binary.

When you need more than pass/fail

  • Two options tied on pass/fail. Then look at how close they are to other breakpoints.
  • A single breakpoint is too coarse. Define multiple categories.
  • Diminishing returns matter. Use a piecewise pass/fail.

"the first dog might be -20d + 5c (d being dollars, c cuteness), ignoring for now the dozen other factors. the thing is, you cannot add -20d + 5c. there's literally no way to combine them." — criticalfallibilism.com