[EM] Saari's Basic Argument

[Steve Barney]

Forest:

What do you mean by "the order of removal isn't important as along as you 
recognize that whenever you have two non-adjacent factions left, more symmetry 
reduction is possible."

I showed you with my example:

3:A>B>C
5:A>C>B
0:C>A>B
5:C>B>A
0:B>C>A
5:B>A>C


that the order of those operations matters in some cases. Please show me what 
you mean.



SB

--- In election-methods-list at yahoogroups.com, Forest Simmons <fsimmons at p...> 
wrote:
> On Thu, 27 Feb 2003, Steve Barney wrote:
>
> > Forest:
> >
> > Apparently, as I thought, your method of decomposition is to simply to 
remove
> > cycles first, and then reversals. My point remains, then, that your
> > decomposition method does NOT NECESSARILY yield the same outcome as 
Saari's
> > matrix decomposition method.
>
> Actually, the order of removal isn't important as along as you recognize
> that whenever you have two non-adjacent factions left, more symmetry
> reduction is possible.  In other words, you can reduce the total number of
> ballots in the set by addition and subtraction of cycles and reverse
> pairs.
>
> I don't know if Saari is aware of this or not.
[...]

Steve Barney

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