[EM] Intermediate Ratings Never Optimal?

[Forest W Simmons]

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.

FWS