Self-Consistency Majority Vote

Background

Self-consistency is the dominant inference-time scaling trick for reasoning LLMs: sample $k$ independent completions, then take the answer that appears most often. Empirically it pushes pass-rate up several points on math and code benchmarks without retraining.

Problem statement

Implement majority_vote(answers, tiebreak=None) returning the mode of answers. Ties broken by the value of tiebreak (a function on candidate answer -> sort key); if None, ties broken by first-occurrence order.

Input

• answers - sequence of hashable answers.
• tiebreak - optional function (answer) -> sortable key. None means first-occurrence.

Output

• The chosen answer (whatever type).

Examples

Input: answers=["A", "B", "A", "C", "A", "B"]
Output: "A"

Constraints

• Empty input raises ValueError.
• The output type matches the input element type.

Notes

• vs Best-of-N. Best-of-N picks by an explicit reward / verifier; self-consistency picks by frequency, no verifier needed.