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And what is your average error rate per runbook step.

one thing we're experimenting to help with the hallucinations/error rate issue is using a committee framework where we take a majority vote.

If the error rate of 1 expert is 5%, then for a committee of 10 experts, the probability a majority of the committee errors is around 0.00276% (binomial distribution with p=0.05). For 10 steps, this would be an error rate of 0.0276%

Pretty bad maths there. Those committee members are not independent.

They are highly correlated even amongst LLMs from different vendors.

I'm not sure they are highly correlated. A committee uses the same LLM with the same input context to generate different outputs. Given the same context LLMs should produce the same next token output distribution (assuming fixed model parameters, temperature, etc). So, while tokens in a specific output are highly correlated, complete outputs should be independent since they are generated independently from the same distribution. You are right they are not iid but the calculation was just a simplification.

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