2026-02 AERC, full talk (see 2026-01)

Thank you very much for today’s invitation to the de Borda Institute, and, as my presentation will make clear, my thanks must also go to the late Professor Elizabeth Meehan of Queen’s University, the late Dr. John Robb of the New Ireland Group and Andy Pollak, formerly of the Centre for Cross Border Studies.  I will of course mention my first submission, hereinafter called the reference, but today confine myself almost entirely to decision-making.

DEFINITIONS 

May I start with a few definitions?

            a)         In a vote on n options, a ballot of n preferences is a full ballot; a ballot of m preferences, where m < n, is a partial ballot.

b)         The modified Borda count MBC or Borda preferendum, which dates from 1770, is a points procedure.  Its multi-optional, preferential ballots are mainly for decision-making: a voter’s 1^st preference gets m points, their 2^nd preference gets (m-1), and so on.  The winning option is the one with the most points.

If adopted, in what is usually a five or six-option ballot (as could often be expected in the Assembly), this methodology would encourage all MLAs to state, not only their 1^st preference, their favourite option, but also their compromise option(s).  And, at best – i.e., if everyone does cast a full ballot – the MBC can identify the option with the highest average preference; the vote is inclusive, literally!  It is non-majoritarian, egalitarian, and ideal for any power-sharing structure.  It requires no designations.  It disallows any vetoes.

            c)         As stated, if every voter casts a full ballot, the winning option will be the one with the highest average preference.  If one or more voters cast a partial ballot, however, another measure is required: the consensus coefficient CC.  For option A, it is defined as:

                        CC_A      =                      option A’s MBC score           

                                                   the maximum possible MBC score

In a five-option ballot, it varies from a CC_MAX of 1.00 to a CC_MIN of 0.20.

d)         The quota Borda system, QBS, is a PR electoral system, very like PR-STV – 1, 2, 3 and all that.  (FPTP prevents the voters from casting any preferences); PR-STV allows them to cast their preferences; in contrast, QBS, which is based on the MBC, actually encourages them to do so.

e)         As noted in my first submission, the QBS matrix vote is a PR, two-dimensional ballot in which every MLA may nominate, in order of preference, not only those whom he/she wishes to be on the executive (on one axis) but also the ministry in which they wish each nominee to serve (on the other axis).  A QBS count identifies the ten (or twelve) most popular MLAs, and then, having turned the preferences into points (as in an MBC), allocates each, in sequence, to the ministry for which they have the most points.  (It was used in 1986 in the New Ireland Group’s People’s Convention with Dr. Robb; in Queen’s in 1998 with Prof. Meehan; and as noted in the reference, in a public meeting in Dublin with a computerised count, hosted by The Irish Times in 2016.  More recently, it was key to an on-line exercise in the Centre of Conflict Resolution in Munich, in 2021.

* * * * *

OBSERVATIONS

1          Majority voting is the world’s most primitive voting procedure.  It is used almost everywhere, from the UN Security Council, via nearly every national parliament or congress, and it’s even in the constitution of North Korea, (Article 97).  One notable exception is the UNFCCC’s COP talks, the most recent of which, COP30, was in Brazil, (and by the way, I attended 2024’s COP29 in Baku).

2          Needless to say, one cannot get the consensus of up to 200 countries in a majority vote.  (For reasons unknown, however, the UN has yet to consider multi-option voting.) 

3          Voting and power-sharing relate firstly to the election of representatives and officers, and secondly to decision-making, both in the Assembly and in referendums.  What with PR and so on, there are over 300 electoral systems to choose from and they vary enormously; in contrast, there are just a dozen or so decision-making systems.

4          Yet many politicians and umpteen political scientists - some of whom have made presentations to this committee - seldom consider the suitability of multi-option decision-making.  They tend to debate only a few variations of binary voting like consociationalism, which dates from 1603 and was used, rather ineffectively, in Czechoslovakia from 1968.

5          As noted in some of your earlier evidence sessions, power-sharing is relevant to other jurisdictions, like the two-part divided society of Belgium, and other conflict zones, like the three-part country of Bosnia.  

6          The GFA proposal for a referendum is, of course, outside your remit.  May I nevertheless note that, while its authors firmly supported the notion that voters should be enabled to cast their preferences in any NI elections - and quite right too! - they did not think that the voters should enjoy a similar degree of pluralism in any future referendum.  Strange it is indeed that a peace agreement should initiate a binary ballot, a stark ‘option X or option Y’ vote, without the existence of even one peace or compromise option.

CONCLUSIONS

I would like to suggest the that power-sharing can best be effected if:

            a)         there are no designations, and no vetoes;

            b)         all posts are shared; so there should indeed be ten ministers and two ‘joint first ministers’ - or just twelve - but there could also be two ‘joint speakers’;

            c)         all posts are elected and shared, ideally at least two at a time, under PR: the ten (or all twelve) ministers in a QBS matrix vote, others in a straight QBS ballot, with success dependent on a minimum CC threshold.  

            d)         decisions, especially those on contentious topics, should be multi-optional and, ideally, preferential.      

* * * * *

PRESENTATION

Today, I wish to concentrate on decision-making, on the weaknesses of majority voting, and on the huge potential of preferential voting.

A          MAJORITY VOTING

1          Binary voting can be used in elections – “Candidate X, yes or no?” – but the only country to do so regularly is North Korea.  As mentioned, it is often used in decision-making, either in singletons – “Option X, yes or no?” – or in pairings – “Option X or option Y?”

2          Now we have probably all had the experience of trying to get a bunch of kids to come to a collective agreement: “ok children, what shall we have for lunch? – parsnips, turnips, swedes or sprouts?” – and if that’s all there is in the fridge, there may well be a majority against everything!  (Such was the case in Brexit.)  So what’s for afters? – ice-cream, jelly, trifle or chocolate cake? – and there may now be majorities in favour of everything!  In any multi-option setting, binary voting is at least inappropriate.

3          A binary vote on just one option cannot identify the collective opinion, not least because those voting ‘against’ are not even stating their (positive) opinion.  Brexit was just such a vote: “In the EU, yes or no?”  In contrast, a binary vote on a pairing – “Option X or option Y?” – is ok, but only if the pair are a duality.  The question – “Shall we friends have a bottle of red or white for dinner?” – is fine; it is a duality.  A dichotomy which would not have been fine, but could have been used in 2016 – “The UK in the EU or the Customs Union?” – is not a duality, for we could also have been in the EEA or WTO.  The UK’s relationship with the EU was a multi-option question, (as was noted in a de Borda Institute press release four months before Brexit); it deserved a multi-option ballot.

4          To show how inappropriate binary voting is in a multi-option scenario, consider another example, similar to that used in the reference: a committee of a dozen members is debating three options – A, B and C– 5 want A; 4 want B, 2 want C and 1 is the impartial, non-voting chair.  So there are majorities of 6, 7 and 9 respectively against all three options.  Maybe we should consider their preferences.

5          Let us assume the 5 have 1^st-2^nd-3^rd preferences A-B-C, the 4 opt for B-C-A and the 2 for C-A-B.  In this case, A is more popular than B by 7:4, B is more popular than C by 9:2, and C is more popular than A by 6:5, so

A > B

B > C

and

C > A

which means 

A > B > C > A > B…

and it goes round and round in circles, forever: Le Marquis de Condorcet’s famous ‘paradox of binary voting’.  This means that, by resolving a three-option conundrum with binary voting, i.e., with two ballots, the chair of any meeting can get whatever outcome she wants.

(A v B) v C        =          C

(B v C) v A        =          A

and

(A v C) v B        =          B.

6          To take another very simple example, a dispute on the colour of the front door could be reduced to three options, as follows.  “Let the door be painted Amber, option A.”  “Delete ‘Amber’ and insert ‘Blue’ option B.”  “Delete ‘Amber’ and insert ‘Claret’ option C.”  But maybe the chair wants the door to be Damson, option D.

If the 5 have preferences                         A-B-C-D

the 4 prefer                                            B-C-D-A

and the couple                                        C-D-A-B

then D is not very popular at all!  Furthermore, everyone prefers C to D.  The chair can nevertheless lay down the following order of voting:

                       {(B v C)            v          A}        v          D

gives

                          { B                 v          A}        v          D

which gives

                                                            A          v          D

for a result of

                                                                                    D.

7          In a nutshell, majority voting is manipulable and should rarely be used in politics, especially on any topic which is controversial.  

B          PREFERENTIAL VOTING

1          In any dispute, let every option be on the table – in the above example, A, B, C (and maybe also D). Let every option be debated in turn and, if suggestions are made, the said option may be changed or even composited, but only if the original proposer(s) agree.  Then, when all is said but nothing yet done, the chair may ask everyone for their preferences which were, I repeat: 

5 A-B-C-D, 4 B-C-D-A and 2 C-D-A-B.

2          In an MBC with full ballots, a 1^st preference gets 4 points, a 2^nd gets 3, and so on. So:

A gets              5 x 4    +          4 x 1    +          2 x 2    =          20 +   4 +  4      =          28

B                      5 x 3    +          4 x 4    +          2 x 1    =          15 + 16 +  2     =          33

C                      5 x 2    +          4 x 3    +          2 x 4    =          10 + 12 +  8     =          30

D                     5 x 1    +          4 x 2    +          2 x 3    =            5 +    8 +  6     =          19 

As suspected, D is definitely the most unpopular option!  And, on a score of 33, the undisputed winner is option B.

* * * * *

3          As can be seen, the above methodology, the MBC, is a points system.  In let us say a five-option debate, with 90 MLAs voting, the

-       maximum average preference score        =      all 1^sts      =          90 x 5  =  450 points;

-       minimum              ”                                  =      all 5^ths      =          90 x 1  =    90 

-       mean                     ”                                  =          3^rds      =          90 x 3  =  270 

and a mean score, of course, might be a mixture of 2^nd and 4^th preferences, or whatever.

4          The chances of all five options getting the mean are probably zero; something(s) will undoubtedly be above the mean, some below.  If the winning option gets < 300 points, say, that should be regarded as inadequate; if it gains > 300, it could be termed the best possible compromise; if > 350, a consensus; and if > 400, a collective wisdom.  (These figures are arbitrary, and may be adjusted as all concerned become more accustomed to the practice of sharing power in general, and sharing decision-making in particular.)

5          Depending on the make-up of the Assembly – currently at 27 SF, 25 DUP, 17 Alliance, UUP 9, SDLP 8, PBP 1 and TUV 1) – and with, therefore, 37 ‘unionist’, 35 ‘nationalist’ and 18 ‘other’ – the following CCs give an indication of the levels of support needed for a given CC.

Scenario	Unionist 37 DUP + UUP + TUV	Nationalist 35 SF + SDLP	Other 18 Alliance + PBP	Points total	CC
a	Abstain	5th preference	3rd preference	89	0.20
b	5th preference	Abstain	3rd preference	91	0.20
c	5th preference	5th preference	3rd preference	126	0.28
d	Abstain	1st preference	3rd preference	229	0.51
e	1st preference	Abstain	3rd preference	239	0.53
f	5th preference	1st preference	3rd preference	266	0.59
g	3rd preference	3rd preference	3rd preference	270	0.60
h	1st preference	5th preference	3rd preference	274	0.61
e	1st preference	3rd preference	3rd preference	344	0.76

6          The worst-case scenarios are as follows.

Scenario	Unionist 37 DUP + UUP + TUV	Nationalist 35 SF + SDLP	Other 18 Alliance + PBP	Points total	CC
a	1st preference	Abstain	Abstain	185	0.41
b	Abstain	1st preference	Abstain	175	0.39
c	Abstain	Abstain	1st preference	90	0.20

From this we can conclude that a CC of 0.42 or more indicates some cross-community support, and for any given break-down of the assembly by assumed designations, minimum CC scores can easily be calculated.  

I must emphasise again, therefore, that cross-community support can be measured without any designations.  

C          CONCLUSIONS

1          It has long been assumed that the very use of designations helps to perpetuate the very sectarianism they were supposed to overcome.  In like manner, devices such as vetoes and special concerns tend to hinder the functions of the Assembly rather than promote consensus.  

2          It is strongly contended, however, that if the above MBC voting procedure were to be adopted, cooperation would be more readily effected.  Furthermore, it could relatively easily be adopted in other divided societies, like those in the Balkans and Caucasus, which are far more complex of course.

Thank you.  Go raith mile maith agaibh.