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David Simmons's avatar

I think the original argument is not completely incorrect, though it is phrased in a confusing manner. When A says "B's hint quality is uniformly distributed in [1/2,1]", he means that the distribution of B's hint quality conditional on the fact that he stuck with his original answer, but not conditional on A's hint quality, is uniformly distributed in [1/2,1]. This is a claim of the same form as the claim made in the first round, in which the assertion that B's hint quality is uniformly distributed in [0,1] is also not conditioned on A's hint or hint quality. The point is that comparing A's hint quality versus B's expected hint quality not conditional on A's hint quality tells you which hint is more likely to be correct.

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Overcoming Bias Commenter's avatar

The analysis is incomplete. Though it gets the right results, it does so using a flawed method.

The problem is that you did not consider the distributions each player has of the other's quality using bayesian reasoning.

Specifically, after observing a disagreement on the first round, the quality of the other player is no longer uniformly distributed. Higher qualities are less likely, but a higher quality also makes it better off to switch, resulting in a cutoff of 1/2. The same value as with naive reasoning, but the reasoning behind it is completely different.

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