This reminds of sensitivity vs. specificity for medical tests. You essentially have a 2x2 matrix: Error vs. non-error on one axis, and detected vs. not detected on the other. If we assume that a reviewer LLM has 95% accuracy, meaning that it produces the correct result 95% of the time it (identifying errors as errors, and identifying non-errors as non-errors), you get the following: Of 100 cases, the output of 5 is wrong, and the output of 95 is correct. Of the 5 wrong outputs, the LLM correctly identifies 4.75 (95%) as wrong. But it will also create 4.75 false positives (5% of 95). Of the 95 correct ones, the LLM correctly identifies 90.25 (95%) as correct. Therefore it creates 0.25 false negatives. So the positive predictive value is low: When the reviewer LLM flags an error, it's actually only an error 50% of the time. On the other hand, the negative predictive value is high, so in ~99.7% of cases, there will be no error if the reviewer LLM didn't catch one.
All of that is assuming that the actual accuracy of the reviewer LLM is truly a flat 95% and that the base error rate is truly only 5%. I think that in reality, LLMs perform better with a certain type of tasks / errors and 5% error rate is just an average.
