I would not say you have no clue. You can still compute a probability in
the latter case.
If we just call long run averages `relative frequencies' instead of
`probabilitites' the difference in knowledge in all such examples becomes
more apparent.
Sincerely,
Rich
At 10:01 AM 6/7/99 -0400, Joseph Halpern wrote:
>I think Uschi is completely right. To give a concrete example, if I
>have a coin and I believe P(heads) = 0.5, my degree of belief that there
>will be between 450,000 and 550,000 in the next million coin tosses is
>practically 1. (I certainly would be prepared to bet large sums of
>money on that event.) On the other hand, if I have no clue of the
>probability of heads, then I also have no clue of the probabilty that
>there will be between 450,000 and 550,000 heads in the next 1,000,000
>coin tosses. -- Joe
>
>
>-----------
>
>As this is my first mail on this list: I am a PhD-student in Germany working
>with/on Bayesian networks, and with a lot of interest in more or less
>philosophical discussions on probability etc.
>
>There is one point in the reasoning of David Poole that makes it not very
>convincing to me: The reasoning depends on the question "What will be the
>outcome of the next press?". This is not the only valid question.
>
>> 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)?
>
>As far as I can see it, there are as many different meanings as there are
>different questions. As long as the question is, what the outcome of the
>next press will be, the reasoning shows there is no difference between
>ignorance and P(Q)=0.5. But if - for example - the question is about the
>average in the next y presses, there is a difference. Thus, whether or not
>it is important to make a distinction will be dependent on the question(s).
>
> Uschi Sondhauss
>
>
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