Voting systems may be used in decision-making
and/or in elections. In decision-making, the outcome is usually
a single decision, or a single complex (as in a budget). In
elections, the outcome may consist of one person (as in most
presidential elections, and as in a general election in a
single-seat constituency) or it may consist of many persons
(as in a PR election, in a multi-member constituency). There
are, in fact, over 300 different voting systems. You can look
at first preferences only to see which is the 'most popular'.
You can look at the last preferences only to see which is
the 'least unpopular'. You can do all sorts of things. Suffice
to say, here, that some of these counting procedures are in
accurate and others are rather better. (For a comparison of
the most common decision-making processes and electoral systems,
see this Institute's Beyond the Tyranny of the majority.)
Most elections of more than one person relate
to individuals of equal status. In a local election, the electorate
votes for their local councillors. In a general election,
they vote for their members of parliament. Whether or not
any of them then go on to become Mayor or Prime Minister is
another matter.
In this respect, the matrix vote is unique.
It involves the election of persons of different status. It
is designed for councils and parliaments, whenever they wish
to elect a power-sharing executive; in which case, of course,
they will want to choose a minister of justice, a chancellor
of the exchequer, a prime minister, a minister of foreign
affairs and so on… all posts of varying status. Accordingly,
the ballot paper takes on a tabular format, and the individual
voter (councillor or MP) may choose, in his/her order of preference,
not only those whom they wish to be in government, but also
the specific ministerial posts in which they wish each to
serve. This electoral system may also be used by any organisation
when electing its executive committee of a chairperson, a
secretary, a treasurer, and so forth. More of all that below.
The three voting procedures which this Institute
seeks to promote are as follows:
In decision-making:Modified Borda
Count
In elections: Quota Borda System
And in power-sharing: Matrix Count
What is a modified Borda count
(or Borda preferendum)?
The modified Borda count (MBC) is a preference
voting procedure by which is identified that option which
gains the highest average preference score. It may also be
regarded as a points system, in which the winner is the outcome
with the most points. The procedure involves three stages:
the debate, the vote and the analysis of that vote.
Prior to the debate, all concerned may propose
any relevant option, as long as it conforms with some agreed
norm like the United Nations Charter of Human Rights; a summary
of these options may be put on display, preferably on a computer
screen. During the debate, any participant may propose either
amendments or new options, and the list on display will be
up-dated accordingly. Finally, at the close of the debate,
the chair will ask each group to confirm the list includes
its particular aspiration, either verbatim or in composite.
This list then becomes the MBC ballot paper.
In the vote, participants are asked to express
their preferences on the various options listed, giving (in
a 5-option ballot) a 1st preference to their most preferred
option, a 2nd preference to their next favourite, a 3rd preference
to their third choice, and so on, as they wish. In the count,
if the voter has completed his/her ballot, a 1st preference
gets 5 points, a 2nd preference gets 4 points, a 3rd preference
gets 3 points, and so on.
The basic rule, then, is this: in an n-option
MBC, the voter who lists all n preferences thus exercises
n, n-1 … 2, 1 points. If, however, a voter wishes to
submit only a partial vote, voting for only m options, then
of course he/she may; in this instance, however, he/she exercises
only m, m-1 … 2, 1 points.
Thus he who votes for only one option gives only 1 point to
his favourite option. She who votes for two options gives
2 points to her favourite option and 1 point to her second
favourite. He who votes for three options gives 3 points to
his favourite option, and 2 points and 1 point to his subsequent
preferences. And so on. While she who votes for all 5 options
gives 5 points to her favourite option, and 4, 3, 2 points
and 1 point to her other preferences respectively.
The MBC thus encourages everyone to express,
not only their favourite option, but also those options on
which they are prepared to compromise. And when every voter
expresses his/her compromise position, it is possible to find
the common consensus or the collective best compromise, i.e.,
the option with the most points or the highest average preference.
In theory, in a 5-option ballot on options
A, B, C, D and E, if everyone gives their 1st preference
to option D, say, then D will get an average preference score
of 1. If at the same time, everyone gives option A their last,
their 5th preference, then A will get an average preference
score of 5. And if everyone gives option B a 3rd preference,
or if some give it a 2nd preference while an equal number
give it a 4th, then option B will get an average preference
score of 3, the mean. Now again in theory, the chances of
every option finishing up with the exact mean score are just
about zilch. The MBC will always give a result! Something
will invariably be seen as more popular than the mean, and
others, obviously, less popular.
Finally, in the analysis of the vote, if and
when the two most popular options are 'neck and neck', any
aspects of the second most popular option which are compatible
with the first will be incorporated into the final outcome.
If the outcome has a certain minimum average
preference from all participants, that outcome may then be
adopted. Indeed, to take the example of a 5-option ballot,
if the winning outcome gets an average preference score greater
than 1½, it may be said to represent the overwhelming
view. If the score is about 2, it can be called the common
consensus. While if it is of the order of 2½, it may
be described as the best possible compromise. If the winning
option gets a score below, say 2.7, then maybe the chair should
ask for the debate to be resumed, and the process is repeated
until the required level of consensus is indeed achieved.
What is the Quota Borda System
(QBS)?
QBS is an electoral system for use whenever
an electorate is electing more than one person. In a general
election, it should be used in multi-member constituencies
of about 6 seats, if need be with a regional/national top-up.
QBS consists of a quota element, added to
an MBC. In a 6-seater constituency, a quota is one seventh
of the valid vote, plus 1.
The count proceeds in stages:
Stage I: if any candidate
gains a quota of 1st preferences, he/she is deemed elected.
Stage II: if any pair of
candidates gains 2 quotas, both candidates are deemed elected.
Stage III: if any triplet
of candidates gains 3 quotas, all three candidates are deemed
elected.
Stage IV: if any triplet
of candidates gain 2 quotas, the 2 candidates with the highest
mbc scores are deemed elected.
Then if seats are still to be filled:
Stage V: if any pair of candidates
gains a quota, the candidate with the higher MBC score is
deemed elected.
Stage VI: if any triplet
of candidates gains the quota , the candidate with the highest
MBC score is deemed elected.
And finally, if seats still remain to be filled
Stage VII: those candidates
with the highest MBC scores are deemed elected.
What is the Matrix Vote?
As noted above, the matrix vote is used whenever
a certain body, a parliament or an assembly, wishes to elect
a smaller number of persons to an equal number of perhaps
very different posts, as is the case in an executive or a
cabinet
The matrix vote is also a quota points system
of voting, but while QBS is a linear ballot, the matrix vote
has a tabular format. In the example which follows, we will
assume that the parliament has decided to elect a government
of 6 ministers: a PM, a deputy, and four ministers.
All members of the parliament, except those
who opt out, will be eligible for election to any ministerial
post on the executive. In the election itself, all MPs state,
in order of preference, which person should serve in which
post.
Portfolio
Preferences
1st
2nd
3rd
4th
5th
6th
PM
Deputy PM
Minister of A
Minister of B
Minister of C
Minister of D
In the vote, each mp considers whom he/she
wishes to serve, and in what order of preference; then he/she
decides in which ministerial post each should serve; and finally,
he/she casts his vote, putting one name in each row, and one
in each column. A sample is shown below.
Portfolio
Preferences
1st
2nd
3rd
4th
5th
6th
PM
Freda
Deputy PM
Jill
Minister of A
Joe
Minister of B
Fred
Minister of C
Phil
Minister of D
Jo
The count proceeds as follows:
Stage I: all points awarded
for each candidate in each post are totalled, as in an MBC.
Stage II: the most popular
candidates according to a QBS count are deemed elected but
not yet appointed.
Stage III: a new matrix is
drawn up, with both elected candidates and ministerial posts
in order of popularity; again, this shows the individual person/post
sums.
Stage IV: candidates are
appointed in order of popularity according to the highest
individual candidate/post sums in the matrix.
The outcome, the collective consensus of all
concerned, will specify just exactly who are the most popular
candidates, which are the most popular posts, and who will
serve in which.
OurKingdom, the new economics foundation and the de Borda Institute recently gave interested parties from think tanks, research groups and campaigning organisations, and members of the general public, the opportunity to participate in an online trial of consensus decision making.
The de Borda Institute and nef (the new economics foundation) have received a grant from the Joseph Rowntree Charitable Trust to test the potential of consensus voting More...
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