Opinions as Evidence: Should Rational Bayesian Agents Commonize Priors

From: Robin Hanson (rhanson@gmu.edu)
Date: Mon May 07 2001 - 19:05:47 MDT

Curt Adams today offered a derivation purporting to show that if two agents
start with different priors, and then each update their beliefs on the fact
that the other one was assigned the prior they got, then the posteriors of
the two agents will not be the same except under unusual circumstances. I
agree that Curt has in fact show this.

I suspect that Curt thinks that his result contradicts something that I
have said, but I do not see any contradiction. The standard agreeing to
disagree literature starts with agents who have the same priors, and show
that updating on statements of opinions produces common beliefs. I also
have a paper on the causal origins of priors
(http://hanson.gmu.edu/prior.pdf or .ps) which shows how updating on the
fact that you were assigned the prior you got can imply common priors. But
neither of these contradict Curt's derivation.

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