X-Message-Number: 19840
Date: Mon, 19 Aug 2002 12:52:54 EDT
Subject: probability problems

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The answer to Thomas Donaldson's conundrum (below) is as follows.

The most basic assumption of probability theory is that the sample tends to 
be representative of the population (and larger samples tend to be more 

In other words, what we see is typical of what is. This is sometimes not the 
case--one could make a good argument that it is almost never the case, except 
in situations of unusual simplicity, such as games of chance or gas 
mechanics--but it's the only starting point we have. 

In any event, this (a) does not tell us how to define the population, and (b) 
it does not guarantee anything about a particular case. Also, of course, (c) 
probabilities are sometimes contingent and subject to feedback, i.e. bets and 
related actions can be self-fulfilling or self-negating, as Donaldson, 
Bozzonetti and many others have noted.

We know that bad experimental design is possible, because professional 
scientists are often guilty of it. We know that invalid arguments can seem 
persuasive to some, becaust this often happens. But that is a far cry from 
concluding that there is no such thing as good design or valid argument.

Even in mathematics, supposedly the most rigorous and least vulnerable of 
disciplines, there can be "proofs" that seem persuasive to some but not to 
others. It doesn't happen often, but it happens. If nothing else, there can 
always be disagreement on axioms or postulates or definitions or undefineds. 
So there is no iron-clad security anywhere, but there is still the reasonable 
and the unreasonable. 

And who is to judge?  You and I, of course.

Robert Ettinger

> OK, so when an event
> hasn't happened, we can try to work out its probability by putting it
> in a class of events many of which HAVE happened, and work out its
> probability that way. But clearly we can't use just any class of 
> events, as Haftka just showed. So we need more information about
> how to properly choose the class of events we're going to use, or
> --- as Haftka's note has shown --- we become lost among the various
> choices, some of which say yes and others of which say impossible.


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