[EM] 7/14/03 - Single-Seat Method in a Multi-Seat Method:

Donald Davison donald at mich.com
Mon Jul 14 12:21:01 PDT 2003

7/14/03 - Single-Seat Method in a Multi-Seat Method:

Greetings Michael and James,

Michael you wrote:
>and can be used for multi- winner elections (just take the
>top N candidates in the ranking rather than just the top one).

And James you wrote:
Maybe it CAN be used for this purpose, but it never should be.  No
single-seat winner system should ever be used to elect the top N
candidates.  The result will be distorted, except by chance.

Donald here:  "Never say Never"

A Single-Seat Method can be used as a major part of a Multi-Seat Method.
The best known example of this is STV.  Irving is a major part of STV, a
combination of ranked ballots, surplus ballots policy, and Irving.

For partisan Multi-Seat elections, and most of the important elections are
partisan elections, we create the best method when we replace the policy on
surplus ballots with my elimination rule:

`The candidate to be eliminated shall be the lowest candidate of the party
with the lowest average votes per candidate.'

We now have a new Multi-Seat Method, a combination of ranked ballots,
averaging party votes, and Irving:

   *The voter has the option to rank candidates and/or parties in any mix.
   *The votes of each party and its candidates are added together and then
divided by the number of these candidates.  Each party receives the benefit
of averaging all its votes across all its candidates including any votes
that would be regarded as surplus votes in a STV election.
   *The lowest candidate of the party with the lowest average votes per
candidate is eliminated.
   *The votes of this eliminated candidate are transferred to the next
choices on the candidate's ballots/votes.  These transferred votes are free
to cross party lines.
   *The routine repeats, any party that lost or gained votes and/or a
candidate will have a new `average votes per candidate' and again the
lowest candidate of the party with the lowest votes per candidate shall be
   *This routine is repeated over and over until the number of candidates
remaining is equal to the number of seat to be filled.  These are the
winners, the election is over.

This new method will have far less distortion than Bottoms Up and less than
all the distortions that can be found in STV (list below of STV

Regards, Donald Davison

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
A list of distortions of Preference Voting/STV:

Politicans fiddle with the rules of Preference Voting/STV:

Preference Voting is a good proportional election method but over the years
and in different places in the world, politicans have fiddled with the
rules such that there are now a number of questionable practices.  These
questionable practices cause distortions in STV.  The questionable
practices are as follows:

1) The Droop Quota:
The Rejection of the Droop Quota: by Donald Davison

Political factions want some of the votes of their higher candidates to be
spread onto their lower candidates in order to help the lower candidates
avoid a few elimination cycles and maybe survive to gain an extra seat and
extra representation for the faction.

All the factions together are a majority of the electorate, so it is
understandable that something like the Droop quota was imposed into
Preference Voting/STV.  The Droop quota does spread votes of each party
over more candidates, kind of like averaging the votes.

Every jurisdiction should have the right to decide if or not the rules of
its election shall average the votes for the factions.  If the jurisdiction
decides to allow averaging of votes by the rules I can live with that
decision, but I reject the Droop quota because Droop creates a near quota
of excluded voters and that lowers the proportionality of the election
which is a distortion.
Besides, Droop is a crude way to average votes.  Droop will not do the best
job of averaging the votes for each faction, some candidates can still be
left with lower votes than other candidates in the same faction.  Droop
will not protect all candidates of the same party equally.

2) Eliminating Candidates before Transferring Surplus Votes:
The Northern Ireland Electoral Region eliminates candidates before
transferring surplus votes.  This is not a proper thing to do because it is
possible that different candidates could be elected, that is, if the
ballots were available, and a study was made in which both ways were used
to count the same election, we would find that there is the possibility
that different candidates could be elected, if so, then the question must
be asked: `Which set of candidates is the true set to elect?'
The answer is that we must follow the same policy in which no candidates
were transferable at the start.

3) Separating Non-Transferable Ballots from Transferable Ballots:
When a candidate has some surplus votes to be transferred, the transfer
value should be based on all the votes being held by the candidate.  In
some elections the transfer value is only based on the votes of the
transferable ballots and only the fractional parts of the transferable
ballots are transferred.  The non-transferable ballots have been left out
of the transfer, they remain with the candidate.  Doing this is not
correct.  In effect what is being done is that the parts of the
non-transferable ballots are being transfered according to the lower choice
of some other ballot, some transferable ballot of some other voter, and not
via a choice of the voter of the non-transferable ballot.  This policy is
not correct.

4) Averaging the ballot papers:
When a candidate has some surplus votes to be transferred, the candidate
may be holding more ballot papers than votes.  This is caused by the
candidate holding fractional parts of votes.  The transfer value should be
based on the total of the votes and then a proportional part of each ballot
paper is transferred.  In some jurisdictions the transfer value is based on
the number of ballot papers.  This has the effect of averaging all the
ballot papers.  This is bad math and should not be done.

5) Dropping decimal places and inturn losing votes:

6) Not doing some functions when computers are being used:
Cambridge now is using computers, but they are still using radom transfer.
They are forced to do so by their state's law which was enacted when
Cambridge was doing hand counting with, of course, random transfer.

7) Successive Quota Preference Voting STV(SE):
This variant of Preference Voting uses an extreme quota to decide which
candidate is to be eliminated.  The quota is not based on the number of
seats, it is based on the number of remaining candidates as follows:

                Total Voters less any Exhausted Ballots
Quota equals:  -----------------------------------------   plus one
                          Remaining Candidates

The method starts with the quota equal to total votes divided by all the
candidates, then plus one vote is added.  The surplus votes are transferred
and the lowest candidate is eliminated.  A new quota is calculated and
again surplus votes are transferred and again the lowest candidate is
eliminated, etc, etc, until the number of remaining candidates equals the
number of seats.
This method clearly increases the number of surplus votes to be transferred
and being as the larger factions have their surplus transferred first it
follows that the larger factions will be able to fill more of the quotas
and protect more of their candidates from early elimination.

This method is going to be used to determine Ordered Candidate List (OCL)
in New Zealand.  It has also been suggested that it can be used to elect
the chairman of a committee.  The method should not be used for anything.
This method clearly favors the larger factions.  Surplus votes are
transferred first, by increasing the number of surplus votes, the larger
factions will fill all the first quotas and the smaller factions will fill
the later quotas including the last quota, which is to be eliminated.  The
larger factions have been able to cover all their candidates with a quota
so that none of them will face early elimination.  If we start with twice
as many candiates as seats, the votes of the larger factions have been
averaged to a number less than the usual Droop quota (one half the Hare
quota).  This averaging of the larger factions by the increase in surplus
votes will push the candidates of the lower factions into the `chipper' of

8) Stopping Cross Party Voting:
In Malta, some nine years ago, two major parties attempted to have a rule
passed that would disallow transferability between candidates of different
parties.  This would have turned Preference Voting into Party List.
Fortunately this attempt failed, but the attempt does point up the lengths
that politicians will go to in their efforts to fiddle with the rules of
Preference Voting/STV.  It also points up the fact that most people who
make rules for election methods are dishonest, they don't want equality for
everyone in an election, they want an advantage for their faction, as if
they are entitled to more representation than anyone else.

9) The Meek Variant:
The Meek variant recalculates the quota downwards after every transfer of
ballots to allow for the loss of votes due to exhausted ballots.  Meek
would be valid if it used the Hare quota, but not if Droop is the quota.
Meek with Droop is not necessary because the quota has already been lowered
downward due to the Droop quota.  This variant is one more negative design
feature imposed on Droop Preference Voting.  Meek is not necessary.  Meek
is overkill.  Because the quota has already been lowered via Droop, there
is no need to lower it anymore.  The Droop quota became part of Preference
Voting many years ago in order to benefit the political parties at the
expense of the independent candidates.  Meek merely continues this benefit
to the political parties.

Droop Preference Voting is able to elect the members at quota or at least
very near quota, if so, then there is no need to lower the quota via Meek.
We already have what we want, that is, we have all the members elected with
the same number of votes.  There in no need to increasse the number of
excluded voters via Meek.

Meek's alleged reason for being is to adjust for exhausted ballots, but
almost all of the voids of the exhausted ballots end up outside of the
votes of the elected members, and outside voids do not influence the
election.  Meek will lower the proportionality of the election, meaning
less votes will elect the members.

For example, the 1995 Cambridge election elected seven of nine members by
the exact Droop quota.  Had the votes of the first runner-up been
transferred for the record, the remaining two members most likely would
also have been elected by the exact Droop quota.  If so, then no way are
the exhausted ballots having any influence on the election.  It follows
that there is no reason to adjust for exhausted ballots.  In other words,
if the members are all elected by the same number of votes, the Droop
quota, then what's the point of using Meek.  It would merely increase the
excluded voters and reduce the proportionality.

1995 Cambridge Council Election:         Droop Quota 1887
    Results    A ======================================|
   when down   B ======================================|
     to ten    C ======================================|
   Candidates  D ======================================|
     after     E ======================================|
    working    F ======================================|
  the math of  G ============================1837===== |  void =  50
  Preference   H ======================================|
    Voting     I === First Runner-Up =====1523=====    |  void = 364
               J ============================1864===== |  void =  23

As you should be able to see in the above real election, most of the voids
of exhausted ballots only lessens the votes of the first runner-up (364 vs
73).  There is no need to lower the quota so that the runner-up will have
the same votes as an elected member.  There is no need to take the
runner-up's void of 364 votes and divide them up among the elected members.
In this election, the Meek variant would lower the quota to 1844, a
difference of 43 votes.  A faction with five candidates and four at quota,
will receive an extra 172 votes to help their fifth candidate, that extra
help may be enough to elect the fifth candidate and gain majority control
of the council, inturn the number of excluded voters will be increased by

                               - end -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Units of Measurements:

Ratio of an igloo's
      circumference to its diameter:  Eskimo Pi

        2000 pounds of Chinese soup:  Won ton

         1 millionth of a mouthwash:  1 microscope

Time between slipping on a peel
          and smacking the pavement:  1bananosecond

Weight an evangelist
                   carries with God:  1 billigram

Time it takes to sail 220 yards at
           1 nautical mile per hour:  Knot-furlong

365.25 days of drinking low-calorie
     beer because it's less filling:  1 lite year

     16.5 feet in the Twilight Zone:  1 Rod Serling

          Half of a large intestine:  1 semicolon

                         1000 aches:  1 kilohurtz

           Basic unit of laryngitis:  1 hoarsepower

Shortest distance between two jokes:  A straight line.

              453.6 graham crackers:  1 pound cake

              1 million microphones:  1 megaphone

                 1 million bicycles:  2 megacycles

                           10 cards:  1 decacards

         1 kilogram of falling figs:  1 Fig Newton

1000 cubic centimeters of wet socks:  1 literhosen

              1 millionth of a fish:  1 microfiche

                    1 trillion pins:  1 terrapin

                         10 rations:  1 decoration

                        100 rations:  1 C-ration

                        2 monograms:  1 diagram

                          8 nickels:  2 paradigms

3 statute miles of
intravenous surgical tubing at
           Yale University Hospital:  One I.V. League

                       100 Senators:  Not 1 decision

                  2000 mockingbirds:  Two kilomockingbirds

More information about the Election-Methods mailing list