Forest:
No, only the Borda Count completely cancels such symmetric profiles and
produces a complete tie. For example, the plurality outcome for the reversal
profile:
A>B>C
C>B>A
is A~C>B. For the circular profile (what Saari calls a "Condorcet term":
A>B>C
B>C>A
C>A>B
the pairwise vote outcome (Condorcet's method) is a cycle, which is not the
same as a tie. As Rob pointed out, the addition of such a circular profile can
change the outcome; that is, pairwise voting does not completely cancel such a
term and produce a complete tie. That's the difference between a cycle and a
tie.
SB
--- In [EMAIL PROTECTED], Forest Simmons <[EMAIL PROTECTED]> wrote:
> On Tue, 19 Feb 2002, Steve Barney wrote:
>
> > Forest:
> >
> > What do you think of circular triplets, such as:
> >
> > A>B>C
> > B>C>A
> > C>A>B,
> >
> > and reversals, such as:
> >
> > A>B>C
> > C>B>A.
> >
> > If that is all the information that we have to go on (when ordinal
preference
> > ballots are used, it is ), shouldn't either of these profiles cancel out
> > completely and yield a tie? The Borda Count is the only method which always
> > does that, according to Saari's analysis. From that simple fact, argues
Saari,
> > come voting paradoxes such as non-monotonicity, etc.
>
> The two examples that you give yield ties in every serious method of which
> I am aware.
>
> Forest
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