[EM] Saari's Basic Argument

[Steve Barney]

Forest:

In message # 10970, why did you say "wisely," as follows?:

> Kemeny (wisely) doesn't believe in cyclic symmetry removal
[...]


Do you mean to imply that the KR tie between A>C>B and B>A>C is more 
reasonable than the A>B>C outcome yielded by both Saari's and your 
decomposition of 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



SB

--- In election-methods-list at yahoogroups.com, Forest Simmons <fsimmons at p...> 
wrote:
> 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
=

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