[EM] Approval vs. CR (again)

[Forest Simmons]

Note that "optimal" is not the same as "optimum" .  The difference is that
"optimal" allows for lack of uniqueness.

For example, in linear programming we have the well known "corner
principle" which says that if we search among all of the corners we will
find an optimal solution.

There may be another solution (not at a corner) that yields the same value
for the objective function and so is also optimal. In particular, if two
adjacent corners yield the optimum value, then all of the points on the
edge connecting the two corners are optimal solutions.

If we have three candidates, then the set of allowable CR ballots is
(geometrically) a cube in three dimensional space. The ballots that are
marked only at the extremes are represented by the corners of that cube.
It is not impossible for two adjacent corners to be optimal (or in
practice, indistinguishable from optimal) solutions.  In that case the
voter may feel more comfortable in voting the midpoint of the edge than
voting either of the end points.

Forest

On Tue, 27 Jan 2004, Bill Lewis Clark wrote:

> In reading through some of the archives, I've come across a point that
> apparently needs some clarification.
>
> (A) The optimal strategy in CR is to always vote the maximum or minimum.
>
> (B) CR is strategically equivalent to Approval.
>
> Now, the point I would like to make clear is that A and B are not
> synonymous, nor does A logically imply B.
>
> It's conceivable that the optimal strategy for CR may, in some cases,
> require the voter to assign maximum values to a candidate that wouldn't be
> approved under Approval's optimal strategy (and similarly, minimum values
> for a candidate that *would* be approved.)
>
> Now, it may be that these cases never actually come about (because they
> require unrealistic assumptions about how to convert sincere CR ballots
> into sincere Approval ballots) but the point is that A and B cannot be
> assumed to equivalent simply in virtue of the meaning of the statements
> (which seems to have been the case on at least a few occasions in the
> past.)
>
> -Bill Clark
>
> --
> Dennis Kucinich for President in 2004
> http://www.kucinich.us/
>
>
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