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Gentlemen, it is not my intention to encourage dissention, but rather
cooperation. I am interested in all your approaches; it seems to me that a
reliable theory would start with a method similar to George's, and finish
with Derek's 'nail down everything' concept, moving from expert
judgement to plugging in numbers. 

Both these extremes, expert judgement and plugging in numbers, have flaws:
one is not reproduceable, and the other is not possible from where we are
now. This cannot stop us from doing our best to use them both as parts of
a program to investigate piece values. I think our first efforts must
necessarily be qualitative; the quantitative cannot come at the beginning
of the investigation, as we don't have enough facts to make meaningful
measurements of values that can be 'plugged in'.

Time has marched on since I wrote the above 2 paragraphs, so I'll wrap
this up quickly. 
George, I will be happy to have you use the 'Game Design Analysis
criteria' you've used previously and post any piece values you would. Or
any other comments you care to make. 
Derek, I'm still working my way through your calculations paper, but if I
can figure out how to do them, I'll stick the numbers here and the calcs
in the wiki. A set of calculations that handles more than 1 class/type of
piece is a good start on a deeper 'theory'. Is Jeremy right about the
paper's URL? I thought I saw something different the last time I looked.
I agree with Jeremy that even guesses are valuable in the beginning, if
they are evaluated properly. Some strategies use the refining of an
initial guess to gain an answer. A discussion of criteria can follow.