[EM] Saari's Basic Argument
asmall at physics.ucsb.edu
Wed Feb 19 11:43:26 PST 2003
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.
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