[EM] Weighted voting systems for proportional representation

[Jameson Quinn]

>
>  I probably would *not* support a system that counted ballots in a way
> that is not precinct summable.
>
>
This is a much more restrictive criterion in the PR context, than it is in
the single-winner context. For instance, approval ballots, the
most-easily-summable system possible in the single-winner context, are
almost guaranteed not to be summable for any PR system (unless you do some
averaging trick as is being discussed on other threads).

I personally do not feel that summability is a high priority for PR, though
I can understand those who do.

Basically, I know of only a few ways to get summability in a PR context. The
first is to restrict the ballot types. That means either party list or
mandatory asset, both of which represent a loss of voting freedom. The
second is to average or otherwise clump ballots for summability. That tends
to open the door to nonmonotonicity and perverse strategies, although it may
only be a crack. And it really does not give much more true voting freedom
than the first method. If my A>D vote ends up averaging out to be
effectively an A>B vote, I'd rather know that from the outset through asset
or party lists, rather than finding out after I've already cast the vote.

One way of clumping ballots is to keep the two-way correlation matrix and
the number-of-votes-per-ballot-including-candidate-X tally matrix. Using
this trick, you can get proportional results, at least from approval
ballots; and I suspect the trick could be extended, using 3D matrices, to
rated or ranked systems. However, this trick inevitably involves a large
amount of mathematical/procedural complexity, and it isn't perfect, because
it assumes that 3-way or higher-order correlations are insignificant. So, I
mention it, but don't recommend it.

SODA-PR, specifically, is not summable, because of the option to vote
approval-style. If you removed the optionality (SDA-PR), it would be
summable. It might also be possible for it to be summable if you restricted
approval-style votes in some way - approve at most two candidates? Approval
can only involve candidates within your district? All of these fixes feel
like giving up too much to me, although YMMV. If I had to choose one, I
guess I'd go with approve-at-most-two, even though it is essentially a
retreat almost to plurality for non-delegated votes.

JQ
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20110723/a43b4791/attachment-0004.htm>