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Robin Hanson's avatar

The honesty of Hal's scenario depends on whether "privately believing" means that you haven't also publicly indicated that belief.

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Overcoming Bias Commenter's avatar

Hal Finney: You'd be pushing a strong position while privately believing that the other side may well be right. As long as you're honest about it, that seems fine.

Honest as the term is used colloquially, but not as required for Aumann's theorem. In general people don't express their beliefs as honestly assessed probabilities; the natural human tendency is to argue for the belief which you want the other person to believe more strongly in, while hiding doubts. Note that it is rational to discount the expressed opinions of someone who may be "playing devil's advocate". I suspect that in practice this may be as much a barrier to the real world applicability of Aumann's theorem as human irrationality.

Of course, I myself do play devil's advocate sometimes, and you should be less convinced by my opinions because of this.

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