# [EM] 12/16/02 - Re: Optimal methods for multimember elections:

Donald E Davison donald at mich.com
Mon Dec 16 02:17:37 PST 2002

```12/16/02 - Re: Optimal methods for multimember elections:

Hi Doug,

The optimal method may not be a method that you can sell to your contact
pushing for districting nor to the public.  What I am going to do here is
to present a series of stages, each an improvement over the one before.  It
will be up to you to decide which stage to propose.

Stage One:  Going to single-seat districts can be regarded as an slight
improvement over Plurality-at-Large.  It is possible that a few new faces
will be elected, depending on how the districts are arranged, but don't
count on it.  If your jurisdiction has a large faction that is able to
currently elect every member, or at least a conclusive majority, it will be
this same faction that will be gerrymandering the districts.

Stage Two:  Try to have the districts be two seat districts.  This will be
a big improvement over single-seat districts.  Two-seat districts have been
used in America for many years, Vermont and Washington states come to mind,
so it is not something new I am asking you to try.  Washington state runs
two separate single-seat elections using two separate fields of candidates.
At first you may think that the majority in a district will be able to
elect both seats, this is not necessarily so.  Not all people belong to one
leading faction or the other, the voters will more likely be divided:  45%
A,  40% B, and 15% independent voters, or otherwise known as `Swing
Voters".  These swing voters will give the election a measure of
proportionality.  I love these swing voters who will vote for the best A
candidate with one vote and then vote for the best B candidate with their
other vote.  This can result in electing both an A candidate and a B
candidate in the same district - much improved proportionality.

Stage Three:  Electing Two Seats from One Field of Candidates:  Same number
and size of districts as in Stage Two and the voter will still have two
votes, but now the votes can be cast for any two candidates running in the
district.  Top two candidates are the winners.  Vermont elects some of its
House members this way.  This stage has the same improvement of stage two
plus this stage also allows the voter to elect the best two candidates in
the district.  In stage two the voter could only vote for one of the best
if the best two were both in the same race.  And, it follows that only one
of the best could be elected, so, stage three is an improvement over stage
two.

Stage Four:  The improvement in this stage is to give the voter only one
vote in the two seat district.  This one vote per voter will assures that a
majority faction of fifty plus one will only be able to elect one seat,
their fair share.  The second seat will go to the next largest faction in
the district.  One vote per person is known as Single Non-Transferrable
Vote (SNTV), which is regarded as a proportional representation method.  It
is also a step to the next stage.

Stage Five:  In this stage we allow the voter to rank his one vote, that
is, he makes choices, one-two-three.  We then eliminate the lowest
candidate and transfer all his votes according to the next choices on the
ballots he received.  We keep eliminating each new lowest candidate until
we only have two candidates remaining - these two are the winners.  Doing
this routine of runoffs allows the voters of the eliminated candidates to
have a say in who the final two candidates are to be.  A higher percentage
of the votes will end up on the last two candidates. This is a method know
as Bottoms Up (Alternative Vote/IRV for multi-seat elections).

In the event one candidate has fifty percent of the vote in this two seat
election, we can say he has his limit, his quota.  The word `quota' means a
proportional share of the whole.  In the context of an election, that means
total votes divided by the number of seats.  This is not to say that
candidates need a quota to be elected, most elected candidates will have
less than a quota, but what about a candidate that has more than a quota,
like sixty percent in a two seat election?   Ten percent is regarded as
being surplus and would be transferred in other methods to help another
candidate.  So, in the next stage I will make a change that will average
all the votes, quota and surplus, of a faction in order to help another
candidate of the faction.  The history of elections shows that this is what
factions want, and being as all factions together have the majority of the
votes in any jurisdiction, factions have had some form of vote averaging
installed into the rules of elections.

Stage Six:  In this stage I introduce my new elimination rule.  Instead of
merely eliminating the lowest candidate we are now going to eliminated the
lowest candidate of the faction that has the lowest average votes per
candidate.  The use of this rule has the effect of averaging all the votes
of a faction, including any surplus votes, and dividing them between all
the candidates of the same faction.  This action uses all the votes to
protect all the candidates of a faction.  This method of averaging the
votes of a party or slate or faction or whatever does the best job of
averaging, right down to as many decimal point as you care to use.  Other
ways of averaging votes are crude.

Now we have improved the proportionality of the election as far as the two
largest factions are concerned, but one measure of proportional
representation is:  `Can a quota of the voters in the entire jurisdiction
elect one candidate?'  The answer to that question is NO!, for any of these
district stages so far, that's the trouble with districts, but if you
suspect that I am going to turn that No into a Yes, you would be correct.

An Yes answer will require some way in which the proportionality of a
faction in the districts can be linked to the proportionality of the same
faction in the entire jurisdiction.  This can be done, it is done in Mixed
Member Proportionality (MMP), but I am not suggesting MMP for your
jurisdiction.  What I am suggesting is one more change so that a quota will
be able to elect one seat, I am suggesting the `Optimal Method' for you.

Stage Seven:  What we are going to do in this stage is to allow the voter
to rank candidates and/or slates in any mix.  This will allow us to
construct a linkage between proportionality in the districts with the
proportionality in the entire jurisdiction.  Inturn, this will allow a
quota of the voters to elect one seat in the entire jurisdiction.

The voter in this stage can only rank slate candidates that are running in
his district, but he can rank any slate that has at least one candidate
running in any district in the entire jurisdiction.  Independent candidates
are treated the same as slates are treated.  The voters can rank any
independent candidate that is running anywhere in any district in the
entire jurisdiction.  Doing this is only fair because the slate candidates
will be getting support from voters in other districts who have ranked
their slates.  Think of an independent candidate as being a small faction
with only one candidate.

After the casting of the ballots, all the data from all the districts is
collected together and tallied as one big Bottoms Up election, using my new
elimination rule of course.  I call this policy `Districts Within
Districts'.  The voter gets his member-link in a small district, but with
the proportionality that comes from the tally being conducted for the
entire jurisdiction - the best of both worlds.

Regards, Donald Davison

-------------- Original Letter -------------
Date: Thu, 12 Dec 2002 18:35:17 -0800
Subject:  Optimal methods for multimember elections

A local government here in NY is debating moving from at large elections to
district based elections.  I'm in touch with one of the parties pushing for
districting.

I need resources and suggestions on better methods.  Please reply to me
directly, or on list if it will further the knowledge base.  Thanks!

Doug

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Regards,
Donald Davison, host of New Democracy at http://www.mich.com/~donald
Candidate Election Methods
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