Re: Opinions as Evidence: Should Rational Bayesian Agents Commonize Priors

Date: Mon May 07 2001 - 21:23:04 MDT

In a message dated 5/7/01 6:11:22 PM, writes:

>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.

As I understood the paper you recently referenced on this list, you and Tyler
were saying people did not act as truth-seeking Bayesians because they
continued to disagree after extensive exchange of information. From this
you conclude people usually don't behave as TSB's. Isn't this reasoning
at odds with my derivation that Bayesian agents with initially differing
priors will usually disagree even after full exchange of information?

Your paper was indeed based on the assumption of common priors.
I don't disagree with the conclusion above, given the cp assumption.
But, we all know people often act as if they have differing priors.
You do attempt to justify that people *should* have common priors.

"If John and Mary have different priors, then they should realize some
physical process produced that difference. And if that difference was
produced randomly or arbitrarily, it is not clear that John and Mary
should retain it."

That's what I was addressing. If John and Mary do not retain their
priors, the under most circumstances they aren't acting as rational
Bayesian agents. That seems a legitimate reason to maintain
differing priors.

Actually, by my analysis, it is precisely when John and Mary's
priors are *most* arbitrary that they should disagree most. The
better-based the priors are, the more encountering each other will
lead to agreement.

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