[EM] weighted pairwise (was: recommendations)

James Green-Armytage jarmyta at antioch-college.edu
Sat Sep 4 04:23:07 PDT 2004

```Dear Kevin,
Thank you for taking a look at my paper! I appreciate the feedback. Some
replies follow.
>
>in order and
>didn’t read every word, but I read enough to know exactly what you are
>proposing).  You made some good points but I’m afraid I was unconvinced.
>One
>aspect of your plan seems disjointed to me.  The first of your
>provisions” states, “If the winning side of one defeat constitutes a
>majority (of the
>valid vote), and the winning side of another defeat does not constitute a
>majority,
>then the majority defeat is necessarily considered to be stronger.
>Otherwise, the
>weighted magnitude is always the determining factor in relative defeat
>strength.”
>I think if weighted magnitude should be the determining factor in the
>relative
>defeat strength of a 53% to 44% pairwise win and a 51% to 46% pairwise
>win,
>then it should also be the determining factor in the relative defeat
>strength of a
>51% to 46% pairwise win and a 49% to 48% pairwise win.  I used those
>pairs of
>percentages, all of which leave 13% of the vote for equal rankings, so as
>to reach
>out to backers of both margins and winning votes while making my point.

Okay, you might be right here. First, let me say that the two "additional
provisions" are not essential to the proposal. I am comfortable advocating
the method both with and without them.
And yes, I share your sentiments that a sudden cutoff at a majority point
can be described as "disjointed". I share your discomfort for that sudden
discontinuity. Would you accept a version of WP which did not have this
provision?
Basically, the reason for it is to avoid allowing truncation to serve as
an "effortless" form of strategic manipulation. This is pretty much taken
from the Mike Ossipoff anti-margins school of thought, and I think it has
some usefulness. But again, the discontinuity is not so nice.

>That
>said, I don’t think weighted magnitude should be used at all.  I don’t
>have any
>mathematically-based reason why.  I think it may give voters a greater
>range of
>options then they are willing to take the time to make.

If voters fill out the rankings but don't bother to fill out the ratings,
then it is easy enough to fill in the ballot with evenly-spaced default
ratings.

>You would likely have
>some voters who rank one candidate ahead of another but give the second
>candidate a higher rating.

My method doesn't allow this. Assuming a computer interface, the computer
would simply not allow voters to enter an inconsistent value, and would
inform them that they should make a correction before the entry would be
considered valid.
Or, an alternative version of the proposal is to forget about the
separate rankings ballot, and to just infer the rankings from the ratings.
I'm okay with this, as long as voters are allowed to use a relatively fine
grain, e.g., to vote a candidate at 99.99/100.

>While the introduction of any new voting method
>would likely lead to the results of some elections being taken to court,
>as
>happened in Ann Arbor Michigan when IRV was introduced and the plurality
>winner in the three-way mayoral election sued after narrowly losing when
>the
>third candidate’s votes were redistributed, I think the introduction of
>would lead to multiple court cases and Florida 2000-type controversies.

This criticism is not applicable to my method any more than the other
alternative methods we discuss here.

>I must
>admit, though, that some of my aversion to the use of ratings in
>Condorcet
>completion methods is ascetic,

Aesthetic? Yes, that's a common response. What I am hoping to convince
people of is that this response arises out of prejudice rather than out of
a full understanding of the method's properties. I request that you go
beyond prejudice and give the principle a true hearing. I don't believe
that I have a record of making a lot of frivolous voting methods proposals
on this list, so I hope that people will take the time to look at this one
which I find so promising.

>which probably stems from years of thinking
>mostly about purely ordinal voting methods.  Still, you deserve credit
>for
>exploring an area that few, if any, have explored in conjunction with
>Condorcet
>methods.

Thanks. Some have explored it before me, surely, but I (obviously) agree
that this is an under-explored area so far. Chris Benham introduced an
ordinal-cardinal Condorcet method about 1 year ago. We now refer to it as
the compressing ranks method.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-September/010899.html
Of course, I prefer weighted pairwise (or else I would just be pushing
for compressing-ranks now instead), but I think that compressing-ranks is
quite interesting. Compressing-ranks predates weighted pairwise.
>
>In some possible outcome-based Condorcet-flavored multiple-winner
>election
>methods, ratings could be useful in determining what outcome in a
>pairwise
>contest to attribute the voter’s votes to if it could not be determined
>based on the
>voter’s ordering of the candidates.  If, for example, in a method like
>CPO-STV
>except that it is non-proportional, if two outcomes varied by two
>candidates and a
>voter preferred one of the candidates in just one of the outcomes ahead
>of both of
>the candidates just in the other outcome, who the voter in turn preferred
>over the
>other candidate who was just in the first outcome, the ratings of the two
>mentioned candidates in each outcome could be added up and the voters
>vote in
>that pairwise contest attributed to the outcome whose candidates had the
>higher
>combined rating.  If the combined ratings of the two candidates were
>equal, then
>the voter would be deemed to have no preference between the two outcomes.
>
>Obviously, if the mth ranked candidate of those who are in one of the
>outcomes
>but not the other was ranked greater (and perhaps, even equal if at least
>one
>candidate was ranked greater) than his/her counterpart in the other
>outcome, than
>the voter’s vote would go to the first outcome.  Come to think of it, you
>could
>make this method arguably as proportional as CPO-STV by having votes that
>rank
>a candidate in both outcomes first (among the candidates in either or
>both
>outcomes) go to that candidate initially.  If any candidates had more
>the quota, you would use your favorite surplus method to determine the
>portion of
>each vote that is transferred, and those portions would go to one outcome
>in the
>pairwise contest or the other or neither based on what I have described
>above.
>
An example might help me here, in explaining your idea.
I don't know if you got to it, but there is a section in my proposal
where I apply the principle of weighted pairwise to (fully proportional)
CPO-STV. I believe that the application is sound, but I have not yet