[EM] Saari's Basic Argument
Forest Simmons
fsimmons at pcc.edu
Thu Jan 16 17:27:06 PST 2003
On Thu, 16 Jan 2003, Forest Simmons wrote:
> On Thu, 16 Jan 2003, Steve Barney wrote:
>
> > Forest:
> >
> > Isn't that just another way of saying Kemeny's Rule does not respect cyclic
> > symmetry?
> >
>
> Or we could say that "cyclic symmetry" doesn't respect the minimal
> distance criterion, since that is what Kemeny's rule is.
>
> A more neutral statement is that minimal average distance and "cyclic
> symmetry" are incompatible with each other.
>
In physics variational principles give rise to symmetries.
For example Fermat's principle of least time (for light) is an explanation
of why the angle of incidence and the angle of reflection are equal.
In other words, the symmetry of the object and its image in the mirror can
be thought of as a consequence of a minimization principle.
Kemeny's rule is a minimization principle, so for example, we're not
surprised that it satisfies the Reverse Symmetry Criterion.
But it is incompatible with this pseudosymmetry of cycles.
Forest
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