From: Robin Hanson (rhanson@gmu.edu)
Date: Tue Jun 03 2003 - 15:12:19 MDT
Eliezer Yudkowsky wrote:
>>>>>... You can go forward from the discovery of new evidence; I'm not
>>>>>sure it makes sense to selectively eliminate evidence you were born
>>>>>with and ask what your "priors" were before that. ...
>>>>
>>>>... most babies have no idea what their name is, how many humans have
>>>>lived before them, ...
>>>
>>>I was born with the evidence. I hadn't yet processed that evidence, but
>>>at birth, I was human. There was never a point at which I started doing
>>>anthropic calculations knowing I was a sentient being, but not that I
>>>was human.
>>
>>But that is the situation with pretty much all the evidence we ever get
>>or ever could get. The universe knew it when we were born, but we did
>>not know it. ...
>
>Let's say that we have a doctor, a patient who may or may not have cancer,
>and a mammogram. Before the doctor sees the mammogram, we can calibrate
>the doctor's pointer state directly by figuring the frequency of that
>pointer state next to patients with the environmental fact of cancer.
>After the doctor sees the mammogram, we can, if we like, recalibrate the
>doctor's pointer state directly by figuring the frequency of that pointer
>state next to patients with the environmental fact of cancer. If the
>doctor knows the correct probabilities throughout, the relation between
>the doctor's calculated probabilities will obey Bayes' Theorem, just as
>the actual correlation between the pointer states and the environment
>obeys the naturalistic version of Bayes' Theorem.
I'm not sure what you mean by "pointer states", but it sounds like you are
being a strict frequentist about the interpretation of probability, so that
you refuse to assign a probability to an event, such as the US invading
Iran in the next two years, where there won't be a large number of similar
events. I hope you realize just how few events you can assign
probabilities to when you take this approach.
>It looks to me like you're trying to extrapolate back my pointer state to
>a prior that I never actually had, that is poorly defined (what is the set
>of observers?), and where many of the members of the so-called "reference
>class" may not yet exist, or may not exist at all, or may exist or not
>exist depending on present-day choices. Why should I extrapolate back to
>this prior I never had, to this non-naturalistic object, especially if it
>is ill-defined?
I do not defend analysis in terms of a "reference class", and dislike its
ambiguity just as you do. But this is a separate issue from whether it
makes sense to talk about what priors would make sense for baby-Eliezer,
who did not know many of the things that you do now, or what other contexts
it might make sense to think about priors in.
>... "What were your priors before you were born?" questions are often
>ill-defined, and so they often give ill-defined answers. Asking whether
>pointer state recalibrations obey Bayes' Theorem when they are
>extrapolated backward in time to before my birth strikes me as an
>unnaturalistic thing to do. Should I really give a hoot whether I was a
>good Bayesian before I actually existed? ...
I'm not sure what you mean by "unnaturalistic"; it is such a bad thing to
be? Probability, decision, and game theory are choc full of
counterfactuals. If you are going to be disinterested in something because
it is counterfactual, you might as well give up on all of it. Of course
people do seem to find it easier to make more sense of some counterfactuals
than of others. FYI, the following paper of mine seems to go farther into
counterfactual territory than most theorists are willing to.
----------------------------------------------------------------------------
http://hanson.gmu.edu/prior.pdf or .ps
Uncommon Priors Require Origin Disputes
by Robin Hanson
If two Bayesians believe that the causal process which produced their priors
was just as likely to have assigned them each the other Bayesian's prior,
those priors must be the same. Also, if two Bayesians agree on how much
some event changes the chances that they would have been created with the
same or different priors, those priors must assign the same probability to
that event. Thus Bayesians who agree enough about the causal origins of
their priors must have the same priors.
----------------------------------------------------------------------------
Robin Hanson rhanson@gmu.edu http://hanson.gmu.edu
Assistant Professor of Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-4444
703-993-2326 FAX: 703-993-2323
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