[EM] 01/27/02 - Re: PR/STV Hybrid for multi-winner?

Donald Davison donald at mich.com
Sun Jan 27 02:38:26 PST 2002

01/27/02 - Re: PR/STV Hybrid for multi-winner?

Adam Tarr, you wrote: "Proportional Representation (PR) has the obvious
advantage of matching the expressed voter preference as closely as possible
in a multi-winner election.
The problem with PR, in my opinion, is that it limits the voter preference
to a single party (and a single order within that party) and as such gives
too much power to the party leadership."

Proportional Representation (PR) is not an election method in itself, it is
a category of methods that give better proportionality than

What you are talking about above is called `Closed Party List'.  While it
is a PR method it is only one of a number of PR methods.

You also wrote:  "In order for a party to be an option for the ballot, it
must provide a list of candidates equal to the number of seats available."

Donald:  You are being too harsh.  Parties should be free to field as many
candidates as they care to put on the ballot.  No party would expect to
elect all the seats.

Adam: Any thoughts?  Has this sort of method been proposed before? -Adam

Donald:  Yes, it has been proposed before to allow people to vote for
candidates and/or parties in any mix.

Regards, Donald Davison

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 Multi-Seat Election Methods: by Donald E Davison
 For Elections Conducted in a Single-Area
 Study Material for Political Change - Revised 11/01/00

The Ladder of Methods for the Election of Lawmakers: We should move up this
ladder anytime we have a chance to do so, but we should always think about
reaching for one of the best methods near the top.

                           Pure STV
                      Preference Voting(STV)
                           Bottoms Up
                   Single Non-Transferable Vote
                        Cumulative Voting
                         Limited Voting

I determined my order of these methods based mainly on factors that I felt
were more democratic. While I favor voting directly for candidates, I also
favor the method that will elect members close to the proportionality of
the parties. This is why Closed-Party-List is more than half way up the
   I favor the methods that result in the lowest number of wasted votes,
which are votes that did not end up on one of the winning candidates
because of the design of the election method. Exhausted votes are votes
that did not end up on one of the winning candidates because the voter did
not make enough choices. There may be a valid reason the voter did not make
enough choices, like maybe he felt the rest of the choices were equally
bad, but there is no valid reason for a design feature, that waste votes,
to be acceptable.
   I favor the methods that have an open door so that all votes can help
some candidate win. But simplicity and elector acceptance are other factors
to be considered.
     I see the next election reform is for us to move up the ladder of
election methods. Most elections in this country for lawmaking bodies use
either the Single-Seat District Purality method or the At-Large Purality
method. We should try to move away from these to better methods. What
follows is a summary of each of the election methods that appear on this
ladder, from the bottom up.

At-Large Plurality
     At-Large Plurality is when we use the entire election area as one
single at-large district in which all candidates will run together. Each
voter has as many votes as there are seats to be filled. The voter can vote
for as many candidates as there are seats - each selection receives a vote
and all votes have equal value. The candidates with the most votes are the
winners. The At-Large Plurality method of electing lawmakers is very common
in the election of city councils and school boards. If ten council persons
are to be elected each voter would have ten votes to cast. The ten highest
candidates would be the winners.
    The method allows fifty percent plus one of the voters the power to
elect the entire city council. It is also possibile that the entire council
could be elected by less than fifty percent of the votes which would result
in wasted votes of more than fifty percent.
     In this method the people are able to give some proportional
representation. The method is not proportional, but the people do add some
proportionality to the results. It appears that when people have a number
of votes they are willing to use some votes for other genders or other
races or other anything else. But it must be remembered that this is not
carved in stone. The simple majority always has the power to elect the
entire membership of a council. I rate this method higher than the mold of
single-seat and single-slot districts, which if once broken, it will be
easier for us to move further up this ladder once we are on this ladder in
which all methods use the same entire election area as one at-large
     A twenty percent bloc will not be able to elect one seat out of five.

Limited Voting
     The Limited Voting method is similar to the At-Large Plurality method
except that the voters are allowed less votes than the number of seats to
be filled. The number of votes allowed will usually be a majority of the
     The use of an example will help us understand the probability of
candidates being elected from different size voting blocs. Suppose we have
three voting blocs, a sixty percent bloc and two twenty percent blocs.
There are five seats and a voter can vote for three candidates. We seek an
anwer to the question: Will Limited Voting allow each twenty percent of the
voters to elect one seat of five and give the voters Fair representation?

     The probability of each bloc electing one seat per twenty percent
depends on how the people of all blocs vote. Our sixty-bloc has a
probability of one hundred percent of voting in three candidates. All the
bloc needs to do is to run three candidates and if all members of the
sixty-bloc vote for all three then each candidate will receive sixty votes
per hundred cast in the election. And, the two twenty-blocs can elect one
seat each.
     But, the leader of the sixty-bloc may want to try for all five seats,
it is possible. He could run five candidates and the members of the bloc
would be instructed to vote according to the last digit of their house
number, as follows:

     Last Digit    Vote for these candidates:
          0              A B C
          1              B C D
          2              C D E
          3              D E A
          4              E A B
          5              A B C
          6              B C D
          7              C D E
          8              D E A
          9              E A B

     This will result in each of his five candidates receiving about
thirty-five votes per hundred, which is more than the 20 votes/100 a twenty
percent bloc could muster.
     So you see, the probability of a twenty percent bloc electing one
candidate has now changed due to a different voting plan by the sixty-bloc.

     Of course, if the two twenty-blocs put their heads and votes together
they could come up with three candidates with forty votes per hundred each.
They, the two twenty-blocs, would have to agree on three candidates and
then instruct their combined supporters to vote for the three, but it could
result in electing three seats between them.

     If it looks like this is going to happen, the sixty-bloc would need to
go to `Plan B' which is to drop one of their five candidates and instruct
supporters to vote for the remaining four, as follows:

     Last Digit    Vote for these candidates:
          0              A B C
          1              D A B
          2              C D A
          3              B C D
          4              A B C
          5              D A B
          6              C D A
          7              B C D
          8              A B C
          9              D A B

     This voting will yield:
 48 votes/100 for candidates A and B
 42 votes/100 for candidates C and D

     With this turn of events, the two twenty-blocs will be able to elect
only one seat between them.
     Limited Voting is only a slight improvement over Plurality(FPTP). It
will not always yield Fair Representation. With Limited Voting, each twenty
percent of the voters may not always be able to elect one of five seats.

Cumulative Voting
     The Cumulative Voting method rules give the voter the same number of
votes as there are seats to be elected but the voter is allowed to use his
votes anyway he would like to use them. If there are ten seats, the voter
can put all ten on one candidate - or two votes on each of five - or one on
each of ten - or five on one, three on another, and two on a third - you
see the picture.
     I rate Cumulative Voting above Limited Voting because Cumulative
Voting will always allow a twenty percent bloc the ability to elect one of
five seats, but cumulative voting has too many votes. The more votes per
person the more uninformed choices will be made.<BR>
     If I had only two options, cumulative or status quo, I would go with
cumulative voting, it is an improvement. This cumulative rule does increase
voter representation and does increase proportional representation.
Cumulative Voting is a step in the right direction but it only goes about
half way. This step is not big enough to give everyone their just
representation in every election. Cumulative Voting is better than At-Large
Plurality or Limited Voting but we should think about moving further up the

Single Non-Transferable Vote(SNTV)
     I rate SNTV above Cumulative Voting because SNTV has only one vote.
     SNTV is a multi-seat election method that is better than most methods
being used today and it is also the simplest of proposed reform methods -
simple is good. There are better methods above it on the ladder of methods,
but this method makes most of the improvement over Plurality, that is made
by any of the better methods.
     It is a method that is very easy to work. Each voter only has one
vote. After the election the votes are counted and the top candidates are
the winners - as simple as that and yet the results are within the top
twenty percent rating of Full Representation, very close to the results we
get from Bottoms Up or Preference Voting, two methods that are better than
SNTV but not by much more.
     The single vote for one candidate gives us the greatest improvement,
greater than what we get from the vote transferring features of Bottoms Up
or Preference Voting.
    A twenty percent bloc will always be able to elect one of five seats.

As an example take a look at an election in which the first count shows the
results of all the single votes.

   Number One Vote Count from the 1995 council election in Cambridge Mass.
               A ==============================2264==============
               B ===========================2087===========
               C ==========================2041===========
               D =======================1780==========
               E ======================1728========
               F =====================1690========
               G ====================1608========
               H ================1391========
               I ============1239========
               J ===========1204========
               K =====564===
               L ====458==
               M ==284=
               N =166
               O 121
               P 92
               Q 55
               R 43
               S 38
            plus 10 Written-In equals 18863 Total votes
        - - - - - - - - - - - - - - - - - - - - - - - - - -
    Results    A ======================================|
   when down   B ======================================|
     to ten    C ======================================|
   Candidates  D ======================================|
     after     E ======================================|
    working    F ======================================|
  the math of  G ============================1837===== |
  Preference   H ======================================|
    Voting     I =========================1523=====    |
               J ============================1864===== |

     Notice that the top ten at the start are still in the race after the
candidates are reduced down to ten - that is how close the first count can
come to the final results. Also notice that ninety percent of the number
one vote count went to these same ten candidates. Cambridge only elects
nine, so candidate(I) was dropped on the next count - but top eight out of
nine is still very good.
     Robert Winters lives in Cambridge, Mass and is active in elections in
that city - which since 1943 has had a proportional representation method
of electing their city council. Robert Winters says: "One thing that every
PR-STV advocate should understand is that Number One votes are still almost
the whole game. Lower preferences generally only play a role in the
election of the last one or two seats, but those seats may hold the balance
of power".
     When the people have a good method like SNTV for electing a council
the people will show that they are not screw ups. The people picked the top
ten before the numbers were crunched by the math of Preference Voting and
they picked them all with a majority of a share - that is excellent voting
by the people. It is this one policy of voting for only one candidate that
allows these people to look good and it is the policies of your systems,
imposed on the public by the politicians, that makes your people look bad -
it is the systems that screw up - not the people.

Bottoms Up - SNTV plus the Run-off Feature
     If we were to take the above SNTV method and add a run-off feature, we
would have a better method - it goes by the name of Bottoms Up or Choice
Run-Off. We add the run-off feature by allowing the people to make a number
of choices when they vote. In the event their first choice is dropped their
vote is not dropped - their vote is salvaged and transferred to their next
choice. We keep dropping the new lowest candidate and transferring votes to
the next choices on the ballots until we end up with the number of
candidates that is equal to the number of seats we are going to fill. In
this method all the voters can have their vote end up on a winning
candidate and thus they will all be represented. This run-off feature will
make an additional improvement in voter representation to the improvement
already made by the SNTV method. Choice Run-Off can also be used for
working a single-seat election race. We would merely keep dropping the new
lowest candidate until only one remained.
     In the Cambridge election the last nine candidates were dropped in
order from candidate(S) on up - none of the low nine were able to collect
enough of the transferred votes during the run-off cycle in order to jump
ahead of another candidate nor to end up in the winners' circle. But
candidate J did receive enough run-off votes in order to jump ahead of
candidate(I) and go on to be the last winner. Having the run-off did change
the results of this election. This method, the SNTV Plus Run-off Feature,
would have elected the same candidates in the Cambridge election as were
elected. The One Vote part elected eight candidates and the run-off elected
number nine.

     A sixty percent bloc may have a very popular candidate and most
supporters of the bloc may insist on voting for him. If the voting on their
candidates becomes too much out of balance, then one of three seats will be
at risk. Suppose the sixty-bloc votes: 38A 20B 2C and the two twenty-blocs
vote: 18X 16Y 6Z.
     The sixty-bloc still needs to do something to balance up their votes
in these last three methods, like it needed to do with Limited Voting. But
this can turn the election into a chess board when any of these four
methods is used. It is understandable if a group tries to reach for more
seats - but if a group does not know exactly how strong it is and tries for
too many seats they may lose seats and end up below their just
representation. Each interest group must watch the moves of all other
groups and then act accordingly - but it should not be neccessry for the
electors to go through these gyrations - too much trouble plus something
could go wrong. Using house numbers is not dependable. There are methods
that will automatically do the balancing for the sixty-bloc or any bloc
larger than an equal share of the votes.
     If the election is a partisan election then Party List is one of those
methods that will balance out the votes of the sixty percent bloc so that
the bloc will elect three seats out of five and a twenty percent bloc will
always be able to elect one of five seats.

In a Closed-Party-List election the political party will make up the
selection and order of persons to be awarded seats. This list may or may
not be made known before the election. Sometimes the list is not completed
by election time. Some people on the list may not even be candidates. This
is clearly undemocratic but this method will give very good proportionality
between parties and that is why I have placed it here on my ladder of
     This method is very simple, the voters merely vote for the party of
their choice. The number of seats that the party will receive will depend
upon how many votes the party receives in the election. The more votes a
party receives means the more seats the party will be assigned.
     This is a method that gives the voters proportional representation(PR)
- but only for one reason - for political parties. It does not give the
voters proportional representation for any other reason. While it is true
that political parties are the main reason we should have proportional
representation, there are other election methods that will give
proportional representation for any reason including the political parties.
With the method of Closed Party List the people must depend on their
political party for some proportional representation. This is wrong - the
people should have an election method that allows them to decide
proportional representation in the ballot box.
     In defense of Closed-Party-List, the people are free, or should be
free, to create small parties and these small parties will elect members in
proportion to the size of each small party. These small parties may only
have one or two candidates running. This is how the people can show support
for their choice of candidates.
     The mechanics of the Party List is the same as transferring surplus
votes and votes of dropped candidates to other candidates - but only to
candidates of the same party. I feel that people should vote for
candidates. We are still able to vote for a political party by voting for a
certain candidate of that party. When we vote for the candidates we are
able to have a say in the direction of our political parties. Party List is
far more acceptable if it is an Open-Party-List - a list made up by the
electors. I have placed Open-Party-List above Closed-Party-List on this
ladder of methods.

     Open Party List will give as good party proportionality as we can get
from Choice Voting but Open Party List is far more simple in operation.
     Open-Party-List is a party list created by the voters - constructed
from the candidates of the party that are running in the election - in
order of high votes first as produced by the voters in the election. Having
the list decided by the voters makes the party list more democratic than if
the list is made up by the party. While the transfer of surplus and
salvaged votes is not controlled by each voter, it can be argued that this
is not so important. The voter did get to vote for his most preferred
candidate. If there are votes to be transferred, these votes will go to the
same party of the voter's most preferred candidate.
     Another method, that will automatically do the balancing for the sixty
percent bloc, is Preference Voting, which will balance out the votes
according to the quota of twenty percent per seat of five. It does this by
transferring surplus votes over the quota to other candidates according to
the next choices on the ballots.

Preference Voting
     The next improvement is to go back to the Bottoms Up method and add
the transfer of surplus votes over a quota. A quota is the total votes in
an election divided by the number of seats to be filled. This is known as
the Hare Quota, there are other quotas. Some candidates may receive more
than a quota of votes on the first tally - these candidates have a surplus
of votes needed to be elected. People who voted for a candidate with a
surplus are entitled to elect more candidates than the one. Consider the
true report that one candidate received three quotas of votes. The voters
of this one candidate should be allowed to elect three candidates. Two
quotas of surplus votes should be transferred to help other candidates get
   When we add this improvement we get a method that is called Preference
Voting, which is a Hare type voting method. The term Preference Voting has
its greatest name recognition in the United States. Internationally the
term Single Transferable Vote(STV) has greater name recognition. Australia
uses the term Hare Clarke because Clarke spend many years promoting
fractional STV in that country. The Center for Voting and Democracy uses
the term Choice Voting. All these terms mean the same method except for
different design features. I consider some of the design features to be
undemocratic, unproportional, even corrupt. Therefore, I have coined the
term Pure STV to mean a Hare type voting method like the others but without
any negative design features.

                                   File 05 end

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