[EM] 12/28/02 - Re: Multi member district methods:

[Donald E Davison]

12/28/02 - Re: Multi member district methods:

Greetings Rick Dietz,

Allow me to walk you through possible options for your three seat election.

 * Limited Voting is your first improvement over Plurality-at-Large.  The
voter is only given a number of votes equal to a simple majority of the
total seats.  In your case of three seats, the number of votes will be two.
As you should be able to realize, the majority party in your city would
only be able to elect a majority of the seats, which is only two.

 * Cumulative Voting is your next improved method to chose from.  The voter
is given the same number of votes as there are seats, but he is allowed to
cast them in any combination, including more than one vote per candidate.

 * Single Non-Transferrable Vote (SNTV) is your next method of improved
proportionality.  Each voter has only one vote.  The top three are the
winners (as simple as that).

 * Bottoms Up is your next method of improved proportionality.  This method
uses Alternative Vote for multi-seat elections.  The voter has only one
vote but he is allowed to rank the candidates, that is, he makes choices,
one-two-three-etc.  The lowest candidate is deemed to have lost in the
results of the first count, so he's eliminated and his votes are
transferred to the next choices on the ballots.  Each new lowest candidate
is eliminated one by one until the number of remaining candidates equals
the number of seats to be filled.

Most election reform people would list Preference Voting/STV as the next
improvement up the ladder of multi-seat election methods, but before you
embrace STV, you need to make a decision.  We have come to a fork in the
road and you and your jurisdiction need to decide if you want to select a
feature that favors the larger political parties.  That feature is some
sort of way to average the votes of two or more candidates such that the
lower candidate may avoid a few elimination cycles and maybe float up and
survive to win a seat and extra representation for his political party.

If a jurisdiction votes not to allow averaging of votes by the rules, then
the method it should use is Hare Preference Voting, which will divide the
total votes into proportional shares.  In the case of three seats, the
shares would be one third - one third - one third.  This is called the Hare
quota.  In STV the word quota means the limit number of votes a candidate
is allowed to receive, any surplus will be transferred to the next choices
on the ballots, but a candidate could win by less votes than the quota.

The results of a Hare STV election can be very proportional, with results
near perfect, perfect being one third of the total votes ending up on each
of three winning candidates.  If your jurisdiction votes not to allow
averaging the votes for the political parties then you should not use the
Droop Quota because the Droop quota is a means of averaging votes.  While
it does a crude job of averaging, it is never-the-less averaging the votes
of political parties.   Besides, the Droop also causes a near quota of
votes to be wasted, which inturn lowers the proportionality of the
election.  In your case of three seats the proportionality will only be 75%
plus three votes.  The balance of 25% less three votes will be wasted votes
of excluded voters.

Other design features of the Hare Preference Voting method should be as follows:
   * Fractional transfer of all surplus votes, original and secondary:
   * Transfer value equal to surplus divided by all the votes of the
     candidate with the surplus, not by the number of fractional papers.
   * Transfer both transferable and non-transferrable ballots.
   * Transfer original surplus votes before eliminating any candidates.

On the other hand, you are going to find that there will be pressure in
your jurisdiction to allow the averaging of votes.  Political factions want
some of the votes of their higher candidates to be spread onto their lower
candidates.  And, being as all the factions together are a majority of the
electorate, it is understandable that something like the Droop quota was
imposed into Preference Voting/STV many years ago.  The Droop quota does
spread votes over more candidates, kind of like averaging the votes.

In the event your jurisdiction does approve the averaging of votes, you
should still reject the Droop quota, there is a better way to average
votes.  The Droop quota is a crude way to average votes.  It will not do
the best job of averaging the votes for each faction, some candidates can
still be left with lower votes than higher candidates in the same faction.
Besides, don't forget, Droop also creates a near quota of excluded voters
and that lowers the proportionality of the election.

The better way of averaging the votes is a new elimination rule that I have
created.  That rule is as follows: `The candidate to be eliminated shall be
the lowest candidate of the party with the lowest average votes per
candidate.'  This rule will average the votes equally across all the
candidates of each faction, plus it does not exclude any voters, and will
maintain proportionality, and it adjusts for exhausted ballots after every
elimination.

My new elimination rule can be added to three of the above methods, SNTV,
Bottoms Up, and Preference Voting/STV.  All three are improved by this new
rule, but Bottoms-Up+rule is the best because it has better proportionality
than SNTV+rule and less math than Preference Voting/STV+rule and with about
the same proportionality.

 * Davison-SNTV is your next method of improved proportionality.  This is
my variant of SNTV.  In this variant, instead of merely eliminating all the
lower candidates at once, this method will eliminate them one by one
according to the following rule:  `The candidate to be eliminated shall be
the lowest candidate of the party with the lowest average votes per
candidate.'  What this rule is doing, when it averages the votes of a
party, is protecting every candidate of that party with the highest number
of votes possible so that maybe the lowest candidate will avoid the next
elimination.

In regular SNTV it is possible for a candidate to receive more votes than
the number of votes needed to be elected.  These extra votes are considered
to be surplus.  In all fairness, these surplus votes should be free to help
elect some other candidate.  In Davison-SNTV, the averaging of a party's
votes does have the effect of using the surplus votes to help the lower
candidates of the party.

There is a feature that can be added to Davison-SNTV that is an additional
improvement to the method.  That feature is to allow the voter to vote for
one candidate or one political party (not both).  The party votes would be
added into the math when the average votes per candidate is calculated.

 * Davison-Bottons-Up is your next and final method of improved
proportionality.  It is a combination of Bottoms Up and my rule of
elimination, which is, to repeat, `The candidate to be eliminated shall be
the lowest candidate of the party with the lowest average votes per
candidate.'  This method will yield 100% proportionality and it will do it
with the least amount of math.

There is also a feature that can be added to Davison-Bottoms-Up that is an
additional improvement to the method.  That feature is to allow the voter
to rank candidates and/or political parties in any mix.  Both the party
votes and the candidate's votes would be used to calculate the average
votes per candidate for each party.

STV has much more math than Davison-Bottoms-Up.  This extra math includes
the transfer of original surplus votes, transfer of secondary surplus
votes, fractional transfer of ballots, and fractional transfer of
fractional ballots (gets hairy).
  Davison-Bottoms-Up has no surplus to transfer, therefore no fractional
ballots.  Davison-Bottoms-Up is superior to regular STV.

Now, it is possible to install my new elimination rule into STV, and I have
done that, I call the method Hare-Davison, and it does give STV 100%
proportinality, but it still has more math than Davison-Bottoms-Up.

Davison-Bottoms-Up is superior to both regular STV and my variant of STV,
Hare-Davison, but I keep Hare-Davison in my stable as a standard to check
if Bottoms Up and Davison-Bottoms-Up have elected the `HD' candidates, that
is, the same candidates as would be elected by Hare-Davison.

Now, one more point:  You used the word `district' in your post.  If this
means that your city is divided into two or more three-seat districts then
that is more reason to use my Davison-Bottons-Up method, because this
method can be converted to the best district method.  A method that will
connect the party proportionality in the districts with the party
proportionality of the entire jurisdiction, which means that the unit of
proportionality will be that of the entire jurisdiction (that is good).

This conversion to a district method is as follows:
 * It will be necessary to allow the voters to rank candidates and/or
political parties in any mix.
 * The candidates still run in the different districts and the voters still
vote in their districts and the first count of the ballots can be done in
each district, but after that all the ballots from all the districts are
collected together and calculated as one jurisdiction election using
Davison-Bottoms-Up.




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