Self Consistency

name: self-consistency description: Solves the same problem multiple times via genuinely independent reasoning paths, then trusts only the parts where the paths converge (majority vote), catching one-off reasoning slips that a single pass would ship as confident-but-wrong. Use this skill when the user poses a tricky math, logic, probability, or estimation problem, asks "are you sure?", says "double-check this" or "verify your answer," when the stakes are high enough that a wrong number is costly, or when a problem is ambiguous enough that any single line of reasoning could quietly go off the rails.

Self-Consistency

Don't trust one chain of reasoning on a hard problem. Solve it several ways, then believe only what the independent attempts agree on.

When to use

• Multi-step math, logic puzzles, probability, unit conversions, or Fermi estimates where a single arithmetic or framing slip flips the answer.
• High-stakes outputs: a number going into a decision, a contract figure, a deadline calculation, a dosage-like "must be exact" value.
• The user explicitly doubts the answer ("are you sure", "double-check", "that seems off").
• Problems with a known final form (a single number, yes/no, one ranking) so answers can actually be compared.

When NOT to use

• Open-ended creative or subjective tasks with no "correct" answer to converge on (essays, brainstorming, design taste).
• Trivial lookups or one-step questions where a second pass adds latency, not safety.
• Tasks where correctness depends on external facts, not reasoning — use a source-checking approach (cite-check) instead; agreeing with yourself three times doesn't verify a fact.
• When the bottleneck is missing information, not reasoning quality — ask, don't re-derive.

The method

1. Lock the question. Restate exactly what's being solved and what form the answer must take (a number? a yes/no? a ranking?). Ambiguity here poisons every path.
2. Generate 3+ independent paths. Solve it a different way each time — e.g. algebra vs. plugging in numbers; forward vs. backward; estimate-then-refine vs. exact. Do NOT peek at the previous path's answer while working the next; the value is in independence, not repetition.
3. Surface each path's final answer plainly, side by side.
4. Compare. Where do they agree? Where do they diverge?
   • Unanimous → high confidence; report it.
   • Majority (e.g. 2 of 3) → report the majority answer but flag that one path dissented, and say why if you can spot it.
   • All disagree → do NOT average or pick a favorite. The problem is harder or more ambiguous than it looked; go back to step 1, find the hidden assumption, or tell the user it's underspecified.
5. Reconcile divergence. When paths split, find the actual error in the losing path(s) rather than just out-voting them — a located bug is stronger evidence than a tally.
6. Report the converged answer plus a one-line note on how many paths agreed.

What good looks like

• The paths are visibly different in method, not the same steps retyped.
• Disagreements are investigated and explained, not silently dropped.
• The final answer carries its agreement count ("all 3 paths gave 42").
• When paths refuse to converge, the response says so honestly instead of faking certainty.

Anti-patterns

• Fake independence: rederiving the same steps three times and calling the echo "agreement."
• Averaging mismatched answers into a number none of the paths actually produced.
• Anchoring: letting path 1's result steer paths 2 and 3.
• Voting away a correct minority path because two sloppy paths happened to share a mistake — investigate, don't just count.
• Burning three passes on a one-step problem.

Example

Q: "A bat and ball cost $1.10. The bat costs $1.00 more than the ball. How much is the ball?"

• Path A (gut): $0.10. Check: bat would be $1.10, total $1.20. Wrong.
• Path B (algebra): b + (b+1.00) = 1.10 → 2b = 0.10 → b = $0.05.
• Path C (test the answer): ball $0.05, bat $1.05, diff $1.00, total $1.10. Holds. Paths B and C converge on $0.05; A was the classic trap and is rejected. Answer: $0.05 (2 of 3 paths agree; the dissenter used intuition and failed its own check).