You are right that there is also the scenario that the test givers are lying (which in this case turns out to be the truth). But this is not something Brennan in the story considers, so it can not have affected his decision. So he arrived at the correct answer, but did so by faulty logic. His two errors (not considering one possible scenario, and assigning wrong odds to the two scenarios he does consider) just happen to cancel out. It would certainly be a way to fix this story: Let Brennan first realize that he should trust everybody else over himself, and then realize that the examiner may be lying.
Though there remains a problem. If the conspirators are lying, it is not clear what answer they want. It may be a test to see if he can withstand peer pressure, but it might also be a test to see if he is willing to entertain the notion of being wrong!
Finally, yes, you are absolutely right that holding a believe because others hold it does not constitute proof. So perhaps the most rational answer would be: “My own independent calculation tells me that the answer is 2 in 9, and for the purpose of establishing a consensus opinion on this question, that is my answer. However I do not think that my evidence is enough to shift the consensus opinion away from the answer of 1 in 6, and thus this is what I shall consider the correct answer, despite my own intuition”.
But this is not something Brennan in the story considers,
But it is! He recalculates—aloud, which makes him less likely to repeat a mistake, and more likely to catch it if he does—and then, reaching the same conclusion as before, gives it again. He thinks he might have made a mistake, which is a reasonable thought, so he works it out again.
In other words,
It may be a test to see if he can withstand peer pressure, but it might also be a test to see if he is willing to entertain the notion of being wrong!
but he does the correct thing for both of those scenarios. He entertains the notion of being wrong, and calculates his odds publicly, where anyone could point out to him if he has found that 4 times 5 is 12, but, finding the same conclusion as before, he stands up to peer pressure.
Thanks!
You are right that there is also the scenario that the test givers are lying (which in this case turns out to be the truth). But this is not something Brennan in the story considers, so it can not have affected his decision. So he arrived at the correct answer, but did so by faulty logic. His two errors (not considering one possible scenario, and assigning wrong odds to the two scenarios he does consider) just happen to cancel out. It would certainly be a way to fix this story: Let Brennan first realize that he should trust everybody else over himself, and then realize that the examiner may be lying.
Though there remains a problem. If the conspirators are lying, it is not clear what answer they want. It may be a test to see if he can withstand peer pressure, but it might also be a test to see if he is willing to entertain the notion of being wrong!
Finally, yes, you are absolutely right that holding a believe because others hold it does not constitute proof. So perhaps the most rational answer would be: “My own independent calculation tells me that the answer is 2 in 9, and for the purpose of establishing a consensus opinion on this question, that is my answer. However I do not think that my evidence is enough to shift the consensus opinion away from the answer of 1 in 6, and thus this is what I shall consider the correct answer, despite my own intuition”.
But it is! He recalculates—aloud, which makes him less likely to repeat a mistake, and more likely to catch it if he does—and then, reaching the same conclusion as before, gives it again. He thinks he might have made a mistake, which is a reasonable thought, so he works it out again.
In other words,
but he does the correct thing for both of those scenarios. He entertains the notion of being wrong, and calculates his odds publicly, where anyone could point out to him if he has found that 4 times 5 is 12, but, finding the same conclusion as before, he stands up to peer pressure.