Advanced Reasoning Strategies / Multi-Path Reasoning

Self-Consistency

Advanced [4/5]
Self-consistency decoding Majority voting CoT-SC

Definition

Self-consistency samples multiple reasoning paths from the model and selects the most common answer through majority voting. Instead of relying on a single chain-of-thought, this technique leverages the diversity of reasoning approaches to improve accuracy.

This method significantly improves performance on complex reasoning tasks by reducing the impact of individual reasoning errors.

Key Concepts

  • Multiple sampling: Generate several different reasoning chains
  • Diversity through temperature: Higher temperature creates varied paths
  • Majority voting: Select the most frequent final answer
  • Error averaging: Random errors cancel out across samples

Examples

Concept
How Self-Consistency Works
Question: "If a store sells 3 items at $5 each with a 20% discount, what's the total cost?" Path 1: 3 × $5 = $15, 20% of $15 = $3, Total = $15 - $3 = $12 ✓ Path 2: $5 - 20% = $4 per item, 3 × $4 = $12 ✓ Path 3: 3 × $5 = $15, discount = $15 × 0.2 = $3, $15 - $3 = $12 ✓ Path 4: 20% off means 80% paid, 3 × $5 × 0.8 = $12 ✓ Path 5: (calculation error) 3 × $5 = $15, 20% = $2, Total = $13 ✗ Majority vote: $12 (4 out of 5 paths) Final answer: $12
Implementation
Python Code
from collections import Counter def self_consistency(prompt, model, n_samples=5, temp=0.7): answers = [] for _ in range(n_samples): # Sample with higher temperature for diversity response = model.generate( prompt=prompt + "\nLet's think step by step.", temperature=temp ) # Extract final answer from reasoning answer = extract_answer(response) answers.append(answer) # Majority vote vote_counts = Counter(answers) final_answer = vote_counts.most_common(1)[0][0] confidence = vote_counts[final_answer] / n_samples return final_answer, confidence

Interactive Exercise

✎
Apply Majority Voting

Given these 5 sampled answers for "What is 15% of 80?", which answer should be selected?

Paths: Path 1: 12, Path 2: 12, Path 3: 15, Path 4: 12, Path 5: 12

Pro Tips
  • Use temperature 0.5-0.7 for good diversity without chaos
  • 5-10 samples usually sufficient; more helps with close votes
  • Works best when answer is discrete (number, category, yes/no)
  • Confidence = vote_count / total_samples gives uncertainty estimate

Related Terms

Chain of Thought Tree of Thought Temperature Sampling