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I beg to differ with Rolf Haenni when he writes:
> Let me illustrate this by considering the question "Does God exists?".
> There are two possibilities G and �G (G = "God exists", �G =
> "God does not
> exist"). Following the arguments of David Poole, it would be
> necessary to
> assign a prior probability, that is to say
> P(G) = P(�G) = 0.5,
> which is completely absurd (even to speak about "probability that God
> exist" is absurd).
Those with the temerity to speak about the probability that God exists are
in distinguished company. Blaise Pascal, often claimed as the father of
probability, was much concerned with God's probability. "Pascal's wager", as
you may recall, is about the decision of whether to live life in the manner
which God ordains. If you do so, and it turns out God doesn't exist, you may
have only wasted your life. But, if you don't, and it turns out that he
does, you experience eternal damnation (according to Pascal's Catholic God).
So, however small the probability that God exists, you should behave as if
He does, and so avoid the risk of an infinitely negative outcome. (Predating
von Neuman and Morgenstern by three centuries, Pascal saw no need to
transform utilities onto a bounded scale.)
This wager was no idle thought experiment for Pascal. At the age of 31, he
abandoned mathematics, physics, as well as gambling and high-living, and
retired to a monastery. Fortunately for us, the Reverend Bayes had no such
qualms about the godliness of mathematics.
One may quibble with Pascal's argument: Nowadays, a Bayesian might demand a
clarity test for the "existence of God." And what about the possible
existence of the Goddess Anica, who provides eternal bliss to all _except_
those who abide by Catholic teachings?
Be that as it may, there remain some serious points for us:
1. Not everyone thinks it absurd (or even blasphemous) to talk about the
probability that God exists - and, by extension, the probability of other
more mundane facts or events.
2. Making decisions and taking action in the World implies a commitment to
degrees of belief, even about facts or events about which we feel very
ignorant.
3. Probabilistic reasoning can often be a useful basis for action, even
without assigning numbers to the probabilities.
Cheers
Max
___________________________________________
Max Henrion, Director of the Decision Lab
Ask Jeeves, Inc
59 N. Santa Cruz Avenue, Suite Q,
Los Gatos, CA 95030
408-354-1841 x27, fax 408-354-9562
NEW EMAIL: [EMAIL PROTECTED]
www.ask.com
> -----Original Message-----
> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of
> Rolf Haenni
> Sent: Monday, June 07, 1999 8:38 AM
> To: [EMAIL PROTECTED]
> Subject: Re: Bayesian Networks and Belief Functions
>
>
> Dear UAI Community,
>
> thanks to Ursula, Jonathan, and Wang Pei for their help to clarify the
> problem of representing total ignorance.
>
> Let me add the following answer to David Poole's question:
>
> DAVID POOLE wrote:
> >For those people who would like to distinguish ignorance for
> the outcome
> >of a binary variables and probability 0.5, I would like to
> know how many
> >different meanings are there to "I don't know" (for a binary random
> >variables)?
>
> There are two different meanings of saying "I don't know" to
> the outcome of
> a (binary) variable Q:
> 1) I DON'T KNOW the outcome of Q, but I KNOW (from my experience on
> earlier or similar events or processes) a prior probability P(Q).
> 2) I DON'T KNOW the outcome of Q, and I have no experience allowing
> me to assign any prior probability.
> Total ignorance corresponds to the 2nd case.
>
> Let me illustrate this by considering the question "Does God exists?".
> There are two possibilities G and �G (G = "God exists", �G =
> "God does not
> exist"). Following the arguments of David Poole, it would be
> necessary to
> assign a prior probability, that is to say
> P(G) = P(�G) = 0.5,
> which is completely absurd (even to speak about "probability that God
> exist" is absurd). In contrast, I think it makes perfectly
> sense to say
> that
> Bel(G) = 0, Pl(G) = 1,
> Bel(�G) = 0, Pl(�G) = 1, and
> Bel(G or �G) = Pl(G or �G) = 1,
> which corresponds the agnostical point of view of a person
> who thinks that
> nothing can be known about God (= total ignorance).
>
> A similiar situation is the example given by Jonathan Weiss: at the
> beginning, when nothing is know about the deck of cards and
> about the color
> of the first card dealt, I think it does make sense to assign
> probabilities
> P(red), P(green), etc... In contrast, it makes perfectly sense to say
> Bel(red) = 0, Pl(red) = 1
> Bel(green) = 0, Pl(green) = 1
> ...etc,
> Bel(red OR green OR blue OR yellow OR "something else") = 1.
> Note that from the point of view of probabilistic
> argumentation systems,
> Bel(Q)=0 means that there are no arguments in favor of Q,
> while Pl(Q)=1
> means that there are no arguments against Q. In my eyes, this reflect
> perfectly to nature of total ignorance.
>
> Finally, let me add what Lao Tse said: "Knowing Ignorance is
> Strength".
>
>
> Best wishes,
>
>
> Rolf Haenni
>
>
>
>
>
>
>
>
>
>
>
>
> **************************************************************
> **********
> *
> *
> * Dr. Rolf Haenni __/ __/ __/ __/
> _______/ *
> * Institute of Informatics (IIUF) __/ __/ __/ __/
> __/ *
> * University of Fribourg, Switzerland __/ __/ __/ __/
> _____/ *
> * Phone: ++41 26 300 83 31 __/ __/ __/ __/ __/
> *
> * Email: [EMAIL PROTECTED] __/ __/ ______/ __/
> *
> *
> *
> **************************************************************
> **********
> * World Wide Web: http://www2-iiuf.unifr.ch/tcs/rolf.haenni
> *
> **************************************************************
> **********
>
>
>
