[EM] Intermediate Ratings Never Optimal?

[Stephane Rouillon]

It means that a non-extreme range votes ballot can be optimal, but if it is
the case,
at least two extreme range votes ballot should be optimal too.

So if the linear optimum theorem applies and you have found some case where
a non-extreme rating contributes to an optimal ballot strategy, thus you
should be able to obtain the same results
with this rating either to 0 or maximal value.

If it is not the case, the counting that leads to a winner is not equivalent
to an
linear optimization problem.

Steph.

Abd ul-Rahman Lomax a écrit :

> I could imagine that I understand this post from Mr. Simmons, but I
> would then conclude that something is off, or that the application of
> this theorem to the present subject is somehow improper, so I'll
> retreat to asking someone to, please, explain this in ordinary
> language, as well as how it applies to intermediate Range ratings.!
>
> At 06:59 PM 7/22/2007, Forest W Simmons wrote:
> >One of the basic theorems of Linear Programming is that when there is
> >an optimal value of a linear objective function it will occur at least
> >one corner of the feasible region.
> >
> >In the rare cases that it occurs at two corners of the feasible region,
> >it will also occur at every point on the line segment connecting the
> >two corners.
> >
> >In infinite precision Range voting the set of feasible votes (i.e. ways
> >of marking a ballot) form an hypercube of dimension N if there are N
> >candidates.  The corners of this hypercube are the points where all
> >ratings are at extreme values.
> >
> >It is possible (but unlikely) that a linear objective function could be
> >maximized along a entire line segment on the boundary of this feasible
> >region.
>
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