Voting over sampled answers

If each sampled chain of thought is right with probability p, how often is the most common answer among n samples right?

One sample is right (p)40%

Samples per question (n)9

Possible answers

2 answers4, spread4, one tempting

One sample right40%

Vote of 9 right (exact)59.9%

Simulated, 1,000 votesNot run yet

Voting helps: the correct answer is the most likely single answer. Setup: four options, wrong answers spread evenly.

Try this

With 2 answers, compare p = 60% with p = 40% as n grows.
With 4 answers, keep p below 50% and compare spread-out wrong answers with one tempting wrong answer.
Run 1,000 votes and check the simulation against the exact curve.

The curve assumes independent samples. Real samples from one model make correlated mistakes, so real gains are smaller.