[EM] Approval vs. CR (again)

[Forest Simmons]

On Wed, 28 Jan 2004, wclark at xoom.org wrote:

>
> I think CR deserves a lot more attention than it's received.  In many
> ways, it's a generalization of various other systems.  By restricting the
> range of values in one way, CR can be made to simulate Approval.  By
> restricting them in another way, it can simulate Borda.  There are entire
> classes of variants that, to my knowledge, haven't been explored at all --
> because CR is dismissed as being "not worth pursuing."
>

Any scoring method has to have some constraint on the ballot to keep the
election from degenerating into the "who can name the biggest number
game."

CR constrains the L_infinity norm, Cumulative voting constrains the L_1
norm. Constraining the L_2 norm has also been studied, but perhaps not as
much as it needs to be.

Note that the corners of the L_1 ball represent the optimal strategies in
that case, too; i.e. cumulative voting is strategically equivalent to
plurality.

Note also that every Borda ballot (when fully ranked) has the same L_p
norm for all p.

This Borda constraint is so limiting that the only way to exercise your
voting power is to vote insincerely, like a teenager with domineering
parents that make rebellion inevitable.

On this list we have suggested many uses for CR ballots besides the
standard usage.  CR ballots can be scored pairwise as well as ranked
ballots, for example, and yet they have natural built in (nominal)
approval cutoffs, unlike ranked ballots.  And since clones will tend to be
rated nearer each other on CR ballots, it is easier to reduce their
untoward influence, etc.

Another big use of CR ballots is in methods that convert them into
approval ballots, since that is Approval's weak point (i.e. it can be
difficult for the voter to know where to put the approval cutoff).

So join the fun of finding other ways to score CR ballots; it's addicting!

Forest