Open Journal of Political Science
2013. Vol.3, No.2, 59-68
Published Online April 2013 in SciRes (http://www.scirp.org/journal/ojps) http://dx.doi.org/10.4236/ojps.2013.32009
Electing an All-Party, Proportional, Power-Sharing Coalition,
a Government of National Unity
Peter Emerson
The de Borda Institute, Belfast, Northern Ireland
Received January 23rd, 2013; revised February 27th, 2013; accepted March 9th, 2013
Copyright © 2013 Peter Emerson. This is an open access article distributed under the Creative Commons Attri-
bution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
There are many instances when a group of people might want to choose a committee, a fixed number of
individuals to undertake a particular collective function. At their AGM or annual conference, residents in
a community group, shareholders of a limited company, members of a trades union, and those of a politi-
cal party, may all want to elect an executive: one person to be chair, another secretary, a third treasurer,
etc. All these posts require different talents and all the individual office bearers undertake necessary but
separate functions for the successful operation of that committee. In like manner, a parliament may
choose to elect a government of national unity (GNU). The only voting procedure so far devised by which
a given electorate—those concerned at an AGM or members of parliament (MPs)—may elect, not only
those whom they wish to be in cabinet, but also the ministerial posts in which each of those chosen will
then serve, is the matrix vote. This paper describes 1) an experiment held at the Political Studies Associa-
tion of Ireland (PSAI), undergraduate conference in Dublin on 23rd June 2012 in which participants, role
playing as members of the Irish parliament, elected a GNU; and 2) the matrix vote methodology, such that
others may also employ this voting system. An obvious instance would be for the election of an all-party
power-sharing executive in a post-conflict zone.
Keywords: Power-Sharing; Consensus; Modified Borda Count (MBC); All-Party Coalition
Introduction
“Democracy is for everybody, not just 50 per cent
and a bit.”
The matrix vote1 is a means by which any electorate may
choose a fixed number of individuals, each of whom is to un-
dertake a specific function, while all of whom are to co-operate
for a common purpose. The methodology could be used, for
example, for the AGM elections of executive committees by
community groups, limited companies and trades unions. It
could also be used for the election of:
1) an executive committee at the annual conference of a po-
litical party2;
2) a majority coalition government by the parliamentary
members of the parties involved (currently, in Ireland, Fine
Gael (FG) and Labour);
3) the chairpersons of select committees in parliament and
their equivalents in local councils;
4) governments of national unity, (GNUs), especially in plu-
ral societies like Belgium and/or post-conflict zones such as
Afghanistan and Zimbabwe.
The peace process in many such zones often involves a form
of power-sharing. In these jurisdictions, general elections are
often held under a system of PR, in order to ensure that all the
erstwhile opponents are then represented in parliament. Fair-
ness in the democratic process is, thus far, achieved, for all the
successful candidates have an equal status: they are all MPs.
The problem comes when forming the government, for every
cabinet minister will have a different status: one will be the
prime minister, another the minister of finance, while yet an-
other could be in what is considered to be a relatively unimpor-
tant department such as that of culture and sport. The question,
then, is how to elect a GNU, an all-party coalition cabinet such
that, in the election:
1) Every MP is eligible to aspire to office;
2) Every MP is able to cast their preferences, and on an equal
basis;
While in the outcome:
3) Individually, each minister is appointed to that department
for which, in the consensus of parliament, he/she is most suited;
and
4) Collectively, the chosen ministers represent the entire par-
liament in fair proportion to their party strengths.
The methodology by which an electorate may elect such a
team is the matrix vote. This paper will consider that which is
potentially its most important function, namely, to facilitate the
election by a parliament of a GNU; accordingly, all relevant
references will apply to Dáil Éireann (the Irish Parliament).
1A full description of this methodology is in (Emerson, 2007: p. 61 et seq.).
See also (Emerson, 2011: pp. 21-30).
2The matrix vote has often been used for this purpose by the Northern
Ireland Green Party (NIGP).
The said methodology enables every Teachta Dála, TD,
(member of the Dáil) to choose, not only those whom they wish
to be in cabinet, but also the particular ministry in which they

P. EMERSON
wish each of their nominees to serve. The matrix vote is PR, so
the outcome is (almost) bound to be a proportional, all-party,
power-sharing coalition3. It should also be noted that the meth-
odology is “ethno-colour blind” and, as such, is ideally suited
for use in plural societies, especially in post-conflict jurisdic-
tions.
An Experiment
Earlier experiments have examined the viability of the matrix
vote when those concerned have voted as party blocks4. This
latest exercise was designed to test whether or not the method-
ology is robust, that is, to see how it might work even when
individual voters (TDs) act independently of each other.
The Candidates
For the purposes of this experiment, a short list of only 26
TDs was produced, as shown in the annex to this paper; but a
similar process would be expected to take place in real life, as
each party chose its principal candidates. The 26, some of the
more well known TDs, consisted of 12 Fine Gael (FG), 6 La-
bour, 3 Fianna Fáil (FF), 2 Sinn Féin (SF) and 3 “independents”;
and the number of 26 was chosen as the best small whole num-
ber to represent the relative party strengths in due proportion.
The Dáil is not, as yet, gender balanced, so nor was this short
list; the balance in the latter, however, was strengthened.
The Electorate
The participants in the experiment were not representative of
any national electorate, neither of the Dáil nor of the Irish
population as a whole. There again, the purpose of the experi-
ment was only to demonstrate that it is possible to identify a
complex collective will, even from a group of disparate indi-
viduals. Accordingly, each person present was asked to con-
sider themselves to be an un-named, unidentified and unaffili-
ated member of the current Dáil.
The Ballot Paper
It was assumed that parliament had already decided to elect a
government of ten ministers, the specific departments being as
listed on the ballot paper, as in Table 1.
The voter (the first one is male), enters the names of those
whom he wishes to serve in government in “The Cabinet” col-
umn (shown in Table 1 in tint); his list of names is his choice
of cabinet and even if he casts only a 1st preference, the vote is
already deemed to be valid. In addition, for all of his nominees,
he may choose the portfolio in which he wants each to serve;
this he does by marking the relevant box in the matrix with a
letter A. Thus a full ballot will consist of ten different names in
the light-tinted “Cabinet” column, and then, in the matrix of the
ballot, ten As, one in each column and one in each row. An
example is shown in Table 2, with the As in a darker tint.
In case a candidate elected to the cabinet could not be allo-
cated to the department chosen by the particular voter—this
would happen if another candidate had received a higher sum
for, and was thus already appointed to, that ministry—the voter,
(this one is female,) is also entitled to give any or all of her
nominees a B and, if desired, a C as well. An example is shown
in Table 3.
The Voters’ Profile
The total number of votes was 16. All of them were valid.
All of the voters cast preferences for a full slate of 10 different
names from the given short list. Most of the voters cast a num-
ber of As, though not all cast a full slate of 10 As, and, with just
one exception, every A cast was also valid (i.e., there was only
one instance of two As in one row or one column). Four voters
also cast some Bs and Cs.
The Count
A matrix vote works on the basis of two counts: the first is to
identify the ten most popular individuals—these then make up
the cabinet; and the second is to allocate each of these ten to a
particular ministerial department. Both counts are conducted on
just the one ballot, the one set of cast preferences. The former is
held according to the rules of a quota Borda system (QBS)
election5 (Emerson, 2007: p. 39 et seq.); and the latter, as per
the rules of a modified Borda count (MBC)6 (Ibid: 15 et seq.).
The QBS Count, in Theory
As its name implies, success in a QBS election is based upon
either a quota of high preferences and/or an MBC total7. The
count proceeds in stages on the basis of the following three sets
of data: the 1st preference totals for single candidates, the 1st/
2nd preference totals for pairs of candidates8, and the MBC
totals. Throughout the count, the procedure goes to a subsequent
only if there are seats still to be filled.
Stage 1. candidates with a quota of 1st preferences get
elected;
Stage 2. if a pair of candidates gets two quotas of 1st/2nd
references, both candidates in the pair are elected. p
5In political circles and in any cross-community organisations, the recom-
mended methodology is the QBS matrix vote, so the first count is under the
rules of QBS, the second under those of MBC (see footnote 6). In those
organisations where internal ethno-religious or even gender tensions are not
so keenly felt, the simpler MBC matrix vote may be used, in which case
both counts are conducted under MBC rules.
6In an MBC, if there are n options/candidates, the voter may cast m prefer-
ences, where 1 ≤ m ≤ n. Points are awarded as per the rule (m, m − 1 … 1).
Thus he who casts only one preference gives his favourite 1 point; she who
casts two preferences gives her favourite 2 points (and her second choice 1
point); and so on. The voter is thus incentivised—but not forced—to cast a
full ballot. Evidence suggests that the BC, as originally envisaged by
Jean-Charles de Borda, was in fact an MBC (Saari, 2008: p. 197; Emerson,
2013: pp. 353-358).
7A candidate’s MBC total is the addition of all his/her sums plus any unal-
located points, i.e., those points where the voter has cast a preference for
this particular candidate but has not cast an A for a ministerial post for this
nominee.
8If x people give Jean a 1st preference and Joan a 2nd preference; if y people
give Joan a 1st preference and Jean a 2nd preference; and if x + y >2 quotas
then the Jean
/
Joan
p
air is said to have two
q
uotas
(
E
m
erson
,
2007:
p
. 41
)
.
3The matrix vote is based on the quota Borda system (QBS), which like
p
roportional representation—single transferable vote (PR-STV), is
pr
oportional according to the wishes of the voters. That is to say, if a
quota of individuals decides to vote for all women or all anti-nuke
candidates, then one such candidate is bound to be elected. In other
p
roportional systems, PR-list, proportionality is based on party labels
only.
4In 2009 under the last Dáil, the de Borda Institute ran an experiment in
which participants acted as if they were members of the relevant political
parties: FF, FG, GP, Lab, Progressive Democrats and SF (Emerson, 2011:
pp. 21-30).
60

P. EMERSON
Table 1.
A matrix vote ballot paper
The Portfolios
The Cabinet
Names of Candidates
in Order of
Preference:
Taoiseach (PM)
Department of
Finance
Department For-
eign Affairs and
Trade
Department Of Education A nd
Skills
Department of
Jobs, Entep rise and
Innovation
Department of
Defence
Department of
Justice and Equal-
ity
Department of
Health
Department of
Environment,
Community an
Local Govt
Department of
Arts, Heritage and
the Gaetac ht
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
Table 2.
A full ballot—an example
The Portfolios
The
Cabinet
Names of
Candidates in
Order of
Preference:
Taoiseach (PM)
Department of Fi nan ce
Department Foreign Affairs and Trade
Department Of Education And S kills
Department of Jobs, Enterprise
and Innovatio n
Department of Def en ce
Department of Justice and Equality
Department of He alt h
Department of Environment, Community
and Local Govt
Department of A rts, Heritage and
theGaetacht
1st Jean A
2nd Jim A
3rd Jane A
4th Joe A
5th Joan A
6th Jan A
7th James A
8th John A
9th Jo A
10th Jill A

P. EMERSON
Table 3.
A full ballot—another example
The Portfolios
The Cabinet
Names of Candidates
in
Order of Preference:
Taoiseach (PM)
Department of
Finance
Department For-
eign Affairs and
Trade
Department Of Education A nd
Skills
Department of
Jobs, Enterprise
and Innovatio n
Department of
Defence
Department of
Justice and Equal-
ity
Department of
Health
Department of
Environment,
Community and
Local Govt
Department of
Arts, Heritage and
the Gaeltacht
1st Jean C B A
2nd Jim A C B
3rd Jane A C B
4th Joe A
5th Joan A B C
6th Jan B A C
7th James A B C
8th John B A
9th Jo A
10th Jill A
Elected candidates are not counted in any further calculations.
Stage 3. if a pair of candidates gets a single quota of 1st/2nd
preferences, the more popular, i.e., the one with the Higher
MBC total, is elected;
Stage 4. candidates are chosen on the basis of their MBC totals.
There are no transfers and no eliminations in QBS; further-
more, all preferences cast are taken into account9.
The QBS Count, in Practice
The valid vote was 16. The number of persons to be elected
was 10. Therefore the quota was 2.
Stage 1. Joan Burton came first with 7 in number 1st prefer-
ences. Enda Kenny and Micheál Martin came joint second, so,
based on their MBC totals, the former came second and the
latter third;
Stages 2-3. there were no pairs with 2 quotas, and no pairs
with 1 quota10;
Stage 4. the remaining seats were awarded on the basis of the
MBC totals.
The results of the QBS count, the ten persons chosen to form
the cabinet, are shown in Table 4.
The MBC Count, in Theory
Once the ten most popular candidates have been thus identified,
the second count takes place, and this is based on the MBC
sums, i.e., the number of A points each candidate has received
for any one specific department. These sums are then consid-
ered, in descending order, allocating in turn each of the ten
cabinet members to a specific ministry. If at any time there is a
draw between two sums, consideration is given first to the more
popular candidate, as measured in the QBS election; and if
there is still a draw, priority is given to that ministerial post for
which the MBC total was the greater. This last item of data is
shown in the bottom row of Table 5 only. It gives an indication
of the degree of importance to which the electorate regard each
department. The discrepancy between the two overall totals—
873 and 555, in the bottom right hand corner—is because of the
318 points which were cast by the voters for unsuccessful can-
didates.
The MBC Count, in Practice
The matrix is as shown in Table 5, and successful candidates
are now appointed to the various ministries in accordance with
the sums received. The highest of all, 55—shown in Table 5 in
blue—means (Joan) Burton gets Finance. The next highest is
40, also in blue, so Quinn takes on Education. Then comes 33—
(Richard) Bruton for Finance, but this post is already allocated;
the 33 total of A points is thus redundant, so Bruton’s votes are
examined to see if any of these are transferred into B points …
and sure enough, 9B points support his candidacy for Health.
Redundant sums are shown in yellow, and transferred sums are
in green, as in Table 6.
The next highest sum is 30 for Burton for Taoiseach (Prime
Minister), but she is already in Finance, so this 30 also becomes
redundant, with no transfers required as the individual con-
cerned has already been appointed. Next comes the sum of 25,
of which there are two, but it is an uncontested tie because one
sum of 25 gives Gilmore Foreign Affairs and the other 25 allo-
cates Higgins to the Jobs department. The next sum, 23, is
again Gilmore’s, so this is also redundant, with no transfers
required. Then comes 21, for Mary L. McDonald to get De-
fence.
9For a comparison of PR-STV and QBS, see (Emerson, 2010: pp. 197-209).
10Pairs of candidates are more likely to occur when participants are acting
in blocs.
The count continues, and the next highest sum is 20, as
shown in Table 7. In this instance both Kenny and Martin are
62

P. EMERSON
Table 4.
The QBS results.
The Cabinet
Names of Elected
Candidates
Party 1st Preference Totals1st/2nd Preference
Totals QBS Results MBC Totals
Joan Burton FG 7 - 1st 108
Enda Kenny FG 2 - 2nd 48
Micheál Martin FF 2 - 3rd 26
Pat Rabbitte Lab 1 - 4th 67
Eamon Gilmore Lab 1 - 5th = 65
Ruairí Qui nn Lab - - 5th = 65
Kathy Lynch Lab - - 7th 52
Mary L. McDonald SF 1 - 8th = 43
Joe Higgins Ind - - 8th = 43
Richard Bruton FG 1 - 10th 38
Table 5.
The first MBC matrix
The Portfolios
The Cabinet
QBS
Count Names of Elected Candidates
Taoiseach (PM)
Department of Finance
Department Foreign Af-
fairs and Trade
Department Of Education
And Skills
Department of Jobs, En-
terprise and Innovation
Department of Defence
Department of Justice and
Equality
Department of Health
Department of Environ-
ment, Community and
Local Govt
Department of Arts, Heri-
tage and the Gaeltacht
Unallocated As
MBC totals
1st Joan Burton 30 55 13 9 1 108
2nd Enda Kenny 20 6 8 11 3 48
3rd Micheál Martin 20 6 26
4th Pat Rabbitte 10 8 15 13 10 4 3 4 67
5th = Eamon Gilmore 23 25 3 8 4 2 65
5th = Ruairí Quinn 7 40 7 4 7 65
7th Kathy Lynch 9 7 13 8 1 11 2 1 52
8th = Mary L McDonald 10 7 21 3 2 43
8th = Joe Higgins 1 25 3 9 3 2 43
10th Richard Bruton 33 4 1 38
555
Total numbers of points cast: 133 132 99 84 79 72 88 73 51 54 8 873
rivals for the post of Taoiseach, so this tie is definitely con-
tested. It is however easily solved: Kenny is the QBS more
popular cabinet member, so he gets this post. Martin’s A points
are therefore transferred as per his B points, and so to Table 8.
Next comes 15, Rabbitte for Foreign Affairs, but that is al-
ready allocated. His 13 for Education is also redundant, as is
Lynch’s which is for Education and Burton’s for Justice. Rab-
bitte’s 15 and 13 are examined for any B points, and he gets 6
for Justice; from her own A points, Lynch does not get any B
points; while Burton’s votes are not examined for B points
because she has already been appointed.
Then comes 11: Kenny’s is redundant, Lynch’s 11 appoints

P. EMERSON
Table 6.
The second MBC matrix
The Portfolios
The Cabinet
QBS
Count
Names of
Elected
Candidates
Taoiseach (PM)
Department of
Finance
Department Foreign Aff airs
and Trade
Department Of Education
And Skills
Department of Jobs, Enter-
prise and
Innovation
Department of Def en ce
Department of
Justice and Equality
Department of He alt h
Department of
Environmen t, Community
and Local Govt
Department of A rts, Herita ge
and the Gaeltach t
Unallocated As
1st Joan
Burton 30 55 13 9 1
2nd Enda
Kenny 20 6 8 11 3
3rd Mcheál
Martin 20 6
4th Pat
Rabbitte 10 8 15 13 10 4 3 4
5th = Eamon
Gilmore 23 25 3 8 4 2
5th = Ruairí
Quinn 7 40 7 4 7
7th Kthy Lynch 9 7 13 8 1 11 2 1
8th = Mary L.
McDonald 10 7 21 3 2
8th = Joe Higgins 1 25 3 9 3 2
10th Richard
Brton 33 4 9 1
Table 7.
The third MBC matrix
The Portfolios
The Cabinet
QBS
Count Names of Elected Candidates
Taoiseach (PM)
Department of Fi nan ce
Department Foreign Affairs and
Trade
Department Of Education An
Skills
Department of Jobs ,
Enterpris e a nd Innovation
Department of Def en ce
Department of Justice and
Equality
Department of He alt h
Department of En vir onm e nt,
Community and Local Govt Department of Arts, Heritage
and the Gaeltach t
Unallocated As
1st Joan Burton 30 55 13 9 1
2nd Enda Kenny 20 6 8 11 3
3rd Micheál Martin 20 10 6
4th Pat Rabbitte 10 8 15 13 10 4 3 4
5th = Eamon Gilmore 23 25 3 8 4 2
5th = Ruairí Quinn 7 40 7 4 7
7th Kathy Lynch 9 7 13 8 1 11 2 1
8th = Mary L. McDon-
ald 10 7 21 3 2
8th = Joe Higgins 1 25 3 9 3 2
10th Richard Bruton 33 4 9 1
64

P. EMERSON
Table 8.
The fourth MBC matrix
The Portfolios
The Cabinet
QBS
Count
Names of
Elected
candidates
Taoiseach (PM)
Department of
Finance
Department Foreign
Affairs and Trade
Department Of Edu-
cation
And Skills
Department of Jobs ,
Enterpris e a nd In-
novation
Department of De-
fence
Department of
Justice and Equality
Department of Health
Department of
Environment,
Community and
Local Govt
Department of Arts,
Heritage
and the Gaeltach t
Unallocated As
1st Joan Burton 30 55 13 9 1
2nd Enda Kenny 20 6 8 11 3
3rd Micheál
Martin 20 10 10 6
4th Pat Rabbitte 10 8 15 13 10 4 6 3 4
5th = Eamon Gil-
more 23 25 3 8 4 2
5th = Ruairí Quinn 7 40 7 4 7
7th Kathy Lynch 9 7 13 8 1 11 2 1
8th = Mary L
McDonald 10 7 21 3 2
8th = Joe Higgins 1 25 3 9 3 2
10th Richard
Bruton 33 4 9 9 1
her to Health, which renders Bruton’s 9B points redundant, and
he gets 9C points instead for the Environment.
We move on to the next highest matrix sum, which is 10. Mar-
tin’s sum of 10B points for Foreign Affairs is redundant, so he
gets 10C points for Jobs. But this too is redundant. Rabbitte’s
two 10 s are also redundant, but he gains no more B points.
McDonald’s 10 is redundant as well, as are Burton’s 9, Lynch’s
9 and Higgins’ 9.
Almost done: Table 9. Bruton’s 9 for Environment now
comes into play. We move on to 8: Kenny’s, Gilmore’s and
Lynch’s 8s are all redundant, as is Rabbitte’s, but only Rab-
bitte’s 8 is eligible for a transfer of B points, he being the only
one of these four individuals not yet appointed. When it comes
to 7, Quinn has three of them, while Lynch and McDonald both
have one; but all of these 7 s are redundant. Thus it is the sum
of 6 which sees the final two appointments: Martin to Arts and
Rabbitte to Justice.
The final result, therefore, as shown in Table 10, is an
all-party coalition of 1 FF, 3 FG, 1 Ind, 4 Lab and 1 SF.
An Analysis
As noted above, the electorate was not in any way represen-
tative. And while the voters were able to talk to each other,
most proceeded to act independently: indeed, not one ballot
resembled another, not even in their 1st and 2nd preferences, let
alone in all ten.
In such a matrix vote, a voter may choose any one of 26 can-
didates for her 1st preference; any one of 25 for her 2nd; any
one of 24 for her 3rd, and so on. In other words, there are
26!/16! > 19 × 1012 different ways of voting. In theory, then, in
an un-whipped Dáil, the chances of any one ballot being even
similar to another would be slim.
Now the more choices the individual TDs have, the more dif-
ficult it is for any party leader or whip to control his/her par-
liamentary party. Accordingly, the matrix vote is ideally suited
to a free vote.
Granted, the electorate in this experiment—16 persons—was
small. Nevertheless, the above evidence suggests that this sys-
tem is capable of application, no matter how many members are
in the parliament, no matter how (small or) large the number of
ministers to be appointed to cabinet.
The Psychology of the Matrix Vote
In any matrix vote election for a GNU cabinet of ten minis-
ters, in a parliament of, let us say, four parties—W, X, Y and Z,
with 40, 30, 20 and 10 per cent of the seats—each party could
expect to win 4, 3, 2 and 1 seats respectively of such an execu-
tive. Any W party TD, therefore, could well want to cast four or
maybe five preferences for her own party colleagues, but would
be wise to cast any other preferences for those whom she con
siders to be the best from the other parties. Such a course of
action is to her advantage because, as suggested earlier (see
footnote 6), an MBC incentivises the voter to cast a full slate of
ten preferences.
Overall, then, the said TD will have more chance of getting
her favourite candidates elected if she casts all ten preferences;
and more chance of influencing the final outcome if she votes
on a cross-party basis. This is the foundation stone of the ma
trix vote, but it is also, surely, the core of any multi-party coali-
ion: that TDs talk with each other, and that they vote with each t

P. EMERSON
Table 9.
The penultimate MBC matrix
The Portfolios
The Cabinet
QBS
Count
Names of
Elected
Candidates
Taoiseach (PM)
Department of
Finance
Department
Foreign Affairs
and Trade
Department Of Education A nd
Skills
Department of
Jobs, Enter prise
and Innovatio n
Department of
Defence
Department of
Justice and
Equality
Department of
Health
Department of
Environment,
Community and
Local Govt
Department of
Arts, Heritage
and the
Gaeltacht
Unallocated As
1st Joan
Burton 30 55 13 9 1
2nd Enda
Kenny 20 6 8 11 3
3rd Micheál
Martin 20 10 10 6
4th Pat
Rabbitte 10 8 15 13 10 4 6 3 4
5th = Eamon
Gilmore 23 25 3 8 4 2
5th = Ruairí
Quinn 7 40 7 4 7
7th Kathy
Lynch 9 7 13 8 1 11 2 1
8th = Mary L.
McDonald 10 7 21 3 2
8th = Joe Higgins 1 25 3 9 3 2
10th Richard
Bruton 33 4 9 9 1
Table 10.
The outcome, the final matrix
The Portfolios
The Cabinet
QBS
Count
Names of
Elected
Candidates Party
Taoiseach (PM)
Department of
Finance
Department For-
eign Affairs and
Trade
Department Of Education A nd
Skills
Department of
Jobs, Enterprise
and Innovatio n
Department of
Defence
Department of
Justice and
Equality
Department of
Health
Department of
Environment,
Community and
Local Govt
Department of
Arts, Heritage
and the Gaeltach t
MBC totals
1st Joan
Burton FG 55 108
2nd Enda
Kenny FG 20 48
3rd Micheál
Martin FF 6 26
4th Pat
Rabbitte Lab
6 67
5th = Eamon
Gilmore Lab 25 65
5th = Ruairí
Quinn Lab 40 65
7th Kathy
Lynch Lab 11 52
8th = Mary L.
McDonald SF 21 4
8th = Joe Higgins Ind
25 43
10th Richard
Bruton FG 9 38
66

P. EMERSON
other. The former interaction will be more likely if the struc-
tures for the latter are already in place. Indeed, this inclusive
methodology will probably encourage co-operation, just as the
procedures laid down in the Belfast Agreement led to “the de-
partmental allocations [being] agreed in advance” (Wilford,
2009: p. 186).
In the above experiment, because some voters made use of
their Bs and Cs, no one cabinet member was appointed to a
ministry by default, i.e., by being the last person left for the one
remaining department. The chances of such under the present
arrangements in the Belfast Agreement are actually quite high11,
and while a similar case is always possible with a matrix vote,
the prospects in a full Dáil of any one minister being appointed
to a ministry for which he/she has no support (a sum of zero)
are minimal. Indeed, experience suggests that the use of inclu-
sive voting procedures like the MBC and QBS can be the very
catalyst of consensus.
Conclusion
In 2008, at the beginning of the most recent financial crisis in
Ireland, there were many calls for a GNU. There was next to
nothing, however, on a methodology by which such a cabinet
could be (s)elected.
Many other countries have had similar calls: the UK had a
GNU during the slump and again in WWII; some Belgians
were asking for a GNU during their recent protracted paralysis
on government formation—it eventually took them 541 days;
Greece in its present fiscal difficulties has also heard such sug-
gestions, and so on. There have also been calls for power-
sharing and unity governance in many plural societies, espe-
cially those which have endured internal conflicts: Afghanistan,
Bosnia, Cyprus, Egypt, Honduras, Iraq, Kenya, Lebanon, Libya,
Northern Ireland and Zimbabwe, to name but a few. Those
which have decided to form a GNU have usually relied on a
purely verbal process, and often these discussions have been
problematic and protracted; Iraq, for example, took 249 days
(Emerson, 2012: p. 173).
Only one country has moved to a form of permanent all-party
governance without first suffering a crisis, namely, Switzerland,
where use is made of a mechanism called a magic formula12.
Other attempts at devising a mechanism by which a GNU
might be chosen have been seen in some conflict zones but, in
many instances, sectarianism has often, in effect, thus been
institutionalised. The arrangements of the Belfast Agreement,
for example, are one of a few reasons why it “remains grounded
in the very structures it aspires to transcend” (Taylor, 2009: p.
320); the Agreement uses both party labels and designations. In
similar fashion, Bosnia uses ethno-religious distinctions, while
Lebanon differentiates on the basis of confessional beliefs.
As noted in the introduction, however, the matrix vote, in
contrast, is “ethno-colour blind”. It is fair, it is proportional, and
it is suitable for any post-conflict society because it caters for
all in that society on a non-sectarian basis; furthermore, it will
cater for all in the future, when hopefully any ethno religious
tensions will be less prominent.
The matrix vote is the only voting procedure so far invented
by which an electorate—a parliament—may elect a fixed num-
ber of persons to form a team, a committee, a cabinet—a gov-
ernment—such that each elected member has a different status,
as chosen by that electorate. In essence, therefore, it is ideally
suited for any society which aspires to a more inclusive polity.
The chances that this methodology might find application, not
only in Dublin and Belfast, but in other jurisdictions too, are
therefore high
Acknowledgements
Thanks are due, first of all, to the Political Studies Associa-
tion of Ireland (PSAI) in general, but especially to Claire
McGing thereof, who so arranged the postgraduates’ confer-
ence as to facilitate the experiment and who was at all times
most accommodating. Secondly, I wish to acknowledge the
work of my colleague in the de Borda Institute, Phil Kearney,
who is one of four government appointees in the current senate
of National University of Ireland (NUI); he was the main driv-
ing force behind the first Dublin-based experiment in 2009, and
he was here again to assist in the count. I should also add that
others involved in 2009, including Professor John Baker of
UCD, have given their continued support and interest in this
voting methodology. Finally, I would like to thank the partici-
pants at the conference who all took part in the exercise with
such enthusiasm and good humour.
References
Emerson, P. (2007). Designing an all-inclusive democracy. Heidelberg:
Springer.
Emerson, P. (2010). Proportionality without transference: The merits of
the quota Borda system. Representation, 46, 20-31.
Emerson, P. (2011). The matrix vote: Electing an all-party coalition
cabinet. Voting Matters, 29, 197-209.
doi:10.1080/00344893.2010.485820
Emerson, P. (2012). Defining democracy. Heidelberg: Springer.
Emerson, P. (2013). The original Borda count and partial voting. Social
Choice and Welfare, 40, 353-358.
Saari, D. (2008). Disposing dictators, demystifying voting paradoxes.
Cambridge: Cambridge University Press.
doi:10.1017/CBO9780511754265
Taylor, R. (2009). The injustice of consociationalism. In R. Taylor
(Ed.), Consociational theory. Londen: Routledge.
Wilford, R. (2009). Consociational government. In R. Taylor (Ed.),
Consociational theory. Londen: Routledge.
11The bigger parties take it in turns to appoint the executive of ten ministers.
12In 1959, Switzerland initiated a collective presidency called the Swiss
Federal Council, and party nominees are appointed to this body based upon
a Zauberformel of 2:2:2:1 ratio among the four largest parties.

P. EMERSON
Annex 1 Short List of 26 TDS
Short List of Potential Ministers
FINE GAEL (12) FIANNA FÁIL (3) SINN FÉIN (2)
Richard Bruton Micheál Martin Gerry Adams
Simon Coveney Éamon Ó Cuiv Mary Lou McDonald
Lucinda Creighton Willie O’Dea
Jimmy Deenihan
Frances Fitzgerald “INDEPENDENTS” (3)
Phil Hogan LABOUR Joan Collins
Enda Kenny Joan Burton Joe Higgins
Nicky McFadden Eamon Gilmore Maureen O’Sullivan
Michael Noonan Brendan Howlin
James Reilly Kathleen Lynch
Alan Shatter Ruairí Quinn
Leo Varadkar Pat Rabbitte
Abbreviations
BC: Borda Count.
DUP: Democratic Unionist Party.
FF: Fianna Fáil.
FG: Fine Gael.
GP: Green Party.
GNU: Government of National Unity.
Ind: Independent.
Lab: Labour.
MBC: Modified Borda Count.
MLA: Member of Legislative Assembly (NI).
MP: (= TD) Member of Parliament.
NI: Northern Ireland.
NIGP: Northern Ireland GP.
NUI: National University of Ireland.
PR: Proportional representation.
PR-STV: PR—Single Transferable Vote.
PSAI: Political Studies Association of Ireland.
QBS: Quota Borda System.
SDLP: Social Democratic Labour Party.
SF: Sinn Féin.
STV: Single Transferable Vote.
TD: (= MP) Teachta Dála (Member of Dáil Éireann, the Irish
Parliament).
UUP: Ulster Unionist Party.
Definitions
All-party: the term “all-party” implies all the larger parties,
but it does not exclude any of the smaller parties or even any
independent TDs.
Sum: for the purposes of this article, a “sum” is the number
of points a candidate gets for any one specific ministerial de-
partment.
Total: while a total refers to all the points a candidate re-
ceives—i.e. a total is the addition of all his/her sums (plus per-
haps any un-allocated points—see footnote 7).
68