[EM] Saari's Basic Argument

[Alex Small]

Steve Barney said:
> IF YOU DO THE DECOMPOSITION WITH THESE
> MATRIXES, IT DOES NOT MATTER  IF YOU FIND THE REVERSAL TERMS OR THE
> CONDORCET (CYCLIC) TERMS FIRST.

That approach gives us profiles where -12 voters or whatever have a given
preference order.  It is undoubtedly a mathematical fact that order does
not matter if you use those matrices and allow for negative numbers of
voters having a given preference order in the final decomposition.

The only question is, what mathematical approach gives the most
useful/interesting description of reality.  I do not doubt the validity of
the statement that order of operations does not matter when you use
Saari's approach.  I just question the importance of his ideas when you
want to understand real situations.

So, in the end, Saari's statements are correct as mathematical statements.
 Whether they provide useful/relevant insights is the question where you
and I will just have to agree to disagree.  Remember that even the most
rigorous math in the world is irrelevant if it doesn't provide a useful
description of what you're trying to study and understand.



Alex


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