[EM] Saari's Basic Argument

[Forest Simmons]

To focus on the order is to miss the boat.  Sometimes one order is most
efficient and sometimes another.

In the example you gave me the most efficient order is removal of five
copies of the cycle.

The other order that you suggested did not reduce the ballot set to the
minimum of three ballots.

Forest

On Sat, 1 Mar 2003, Steve Barney wrote:

> 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
>
> Richard M. Hare, 1919 - 2002, In Memoriam: <http://www.petersingerlinks.com/Hare/>.
>
> Did you know there is a web site where, if you click on a button, the advertisers there will donate 2 1/2 cups of food to feed hungry people in places where there is a lot of starvation? See:
> <http://www.thehungersite.com>.
>
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