FINDING CONSENSUS
Submission from the de Borda institute
www.deborda.org
ABSTRACT
A debate on an emotive topic like abortion should not be reduced to only two options. A multioption debate would be more likely to happen if the ballot paper by which such a discussion was to
be resolved were itself to be multi-optional. Accordingly, after just a little background, this
submission will offer a critique of majority voting, if only to show it to be unreliable. It will then
outline a more inclusive voting procedure by which discussions in the Citizens’ Assembly itself, or
in the Dáil, or indeed in any future referendum, could not only ensure that the outcome was an
accurate reflection of the given electorate’s collective will, but also facilitate a more inclusive and
more nuanced debate prior to that vote.
A SHORT BACKGROUND
Before the 2002 referendum, the government suggested that there were seven options on the table.1
The de Borda Institute response proposed a four-option referendum,2 but this was dismissed at a
public hearing.3 The referendum itself, then, was binary; it took place on 7.3 2002, but the motion
was defeated by 50.4% to 49.6%, namely, by some who thought it too illiberal combining with
others of an opposite persuasion. “The people have spoken,” said the then Taoiseach, Bertie Ahern.
“So what did they say?” we asked in a letter to The Irish Times.4
MAJORITY VOTING
The simple or weighted two-option ballot dates back to the city states of Ancient Greece and the
Imperial Court of the Former Han Dynasty in China. It is, then, the oldest measure of collective
opinion ever invented. It is also the most inaccurate.
Indeed, one cannot identify the popular will in this way, not least because the outcome of such a
process has to be identified earlier if it is to be already on the ballot paper. Little wonder, then, that
this voting procedure has been used not only by a large number of dictators, (Emerson 2012: 143) –
one of whom was Irish, Bernardo O’Higgins in Chile in 1818, the first ever to get 100%
‘democratic’ support – but also by many other, rather more democratic leaders: they dictate the
question and, in most instances, the question is the answer.5
Furthermore, a binary vote cannot measure the given electorate’s degree of consensus because –
with so many ‘for’ and so many ‘against’ – it measures the very opposite, the degree of dissent.
1
Undated, Green Paper on Abortion, The Stationery Office, Dublin, p 107, para 7.16.
2
10.12.1999, An Outline Submission on the Abortion Question to the All-Party Oireachtas
Committee on the Constitution, The de Borda Institute, Belfast.
3
17.5 2000, Public Hearings on Abortion, Joint Committee on the Constitution, Dublin.
4
Op. cit., 8.3.2002.
5
The only dictator to fail in this regard was Augusto Pinochet who, in 1988, lost his third
referendum. Robert Mugabe also lost a poll in 2000, but he had taken the precaution of declaring it
to be non-binding. Rather more democratic losers occur more frequently, a recent example being
David Cameron who also succeeded twice but who also lost his third referendum, the 2016 brexit
poll.
In a participatory democracy, in contrast, no one individual would have a monopoly on the choice
of options. Rather, the people or their elected representatives would be allowed, not only to vote in
any final decision-making procedure, but also to join in the debate which first determined which
and how many options were to be involved. More of this anon; first, however, this paper looks at
two instances where binary and/or other forms of single-preference voting would be inadequate in a
discussion on such an emotive and complex topic like abortion: firstly, in any debate on a related
policy option; and secondly, in any multi-option ballot.
A MULTI-OPTION DEBATE
Many debates are conducted in a dichotomous manner, but such a procedure can sometimes be
inaccurate. Consider a debate on a motion with two possible amendments. Let:
option A be the motion, unamended;
option B be the motion amended; and
option C is the status quo ante.
If just three people use majority voting, and if these three have the following sets of preferences:
A-B-C,
B-C-A and
C-A-B
Then a majority prefers A to B, another majority prefers B to C and a third majority prefers C to A.
This phenomenon is known as the paradox of voting, first identified by Le Marquis de Condorcet, a
contemporary of Jean-Charles de Borda of whom, more in a moment. The paradox suggests that
any use of binary decision-making in a multi-option setting may be erroneous.
A MULTI-OPTION BALLOT
So what might happen in a multi-option poll? If and when there are only two options on the table,
majority voting could be appropriate; in a plural society and a pluralist democracy, however, such
occasions should be rare.
When there are more than two options under discussion, quite a few voting methodologies are
available. They include:


plurality voting, which is like the UK’s electoral system, first-past-the-post, but it is also
used in the Danish parliament; the voters chooses just one option, and the winning option is
the one with a majority, or maybe just the largest minority, of the votes.


two-round voting, TRS, is used in French presidential elections and in some referendums as
in Finland and New Zealand; if no one option has a majority in the first round plurality vote,
a second round majority vote is taken between the two leading options from the first.


the alternative vote, AV,6 is like Ireland’s single transferable vote, STV, when electing only
one representative; it is a series of plurality votes, eliminating the least popular option after
each round and transferring its votes in accordance with the relevant voters’ 2nd and
subsequent preferences until an option gets 50% of the vote (or wins by default).


finally, there is a points system, the modified Borda count, MBC, (see below); basically, in
a four-option poll, a 1st preference gets 4 points, a 2nd gets 3, and so on; and the option with
the most points wins.
Consider then an electorate of fourteen persons with preferences on the four options – A, B, C and
D – as shown in Table I.
6
AV
is known as IRV, instant run-off voting, in the US and PV, preferential voting, in Australia.
A VOTER’S PROFILE
TABLE I
Preferences
14 voters and their
preferences
5
2
3
4
1st
A
B
C
D
2nd
B
C
B
B
3rd
C
D
D
C
4th
D
A
A
A
A cursory glance would suggest that opinions on option A, with five 1st preferences but nine 4th
preferences (shown in dark tint), are very polarised; that D (in light tint) is rather less divisive; that
C (in reverse) is a little more acceptable; but that B, the 1st preference of only two but the 2nd of
everyone else, best represents the collective will. Consider, however, what happens when the above
voters’ profile is analysed by the four methodologies mentioned above: plurality voting, TRS, AV
and the MBC.
In a plurality vote, only the 1st preferences are taken into account, so the results are A 5, B 2, C 3
and D 4; so the winner is A.
In TRS, A and D go into the second round in which case (assuming the voters’ preferences remain
unchanged) the outcome is A 5 D 9, so D is the victor.
In AV, the first one to be eliminated is option B, and its two votes go to C, so the score is now A 5,
C 5 and D 4. D’s votes go (not to B, which is no longer in contention but) to C, so the scores are
now A 5 and C 9. So C comes out on top.
Lastly, in a BC or MBC, (of which more in a moment), preferences are turned into points – and the
results are A 29, B 44, C 36 and D 31; so the most popular option is deemed to be B.
The conclusion is stark: the democratic outcome could be A, or B, or C, or D; in this particular
example, it all depends on which voting procedure is used. It means that, while some counting
methodologies are accurate, others can be at best capricious, at worst hopelessly inaccurate. In any
multi-option vote or referendum on abortion, no matter what the forum or who the electorate, it is
vital that the chosen methodology be robust and accurate: the MBC fills that criterion.
Of these four methodologies, then, only AV and the MBC are preferential and therefore inclusive.
And of these two, only the MBC takes all preferences cast by all voters into account, so it is the more
accurate; this is especially the case if all the voters have submitted full ballots, but this is highly
likely because the MBC not only allows the voter to cross the gender, party and even ethno-religious
divides, the mathematics of the count actually encourages them so to do. In a nutshell, the MBC, is
“the soundest method of identifying the [option which] is most generally popular with the
electorate, or at least the most acceptable.” (Dummett 1997: 71.) Furthermore, at least in this
example, it is accurate, i.e., it gives the correct answer, option B, the one suspected to be the
winner.
A MORE INCLUSIVE PROCEDURE
In theory, to best identify the collective will, it is first necessary to know most if not all the
individual wills. In other words, voters should be enabled to vote positively, to state what it is they
like and in what order of preference. (If some people only state what they do not want by being
negative – voting ‘no’ or ‘out’ or, as in the brexit ballot, ‘leave’ – the identification of the vox
populi will be difficult if not impossible.)
When New Zealand debated its electoral system in 1992, an independent commission was
established, and it drew up a referendum of five options. So (nearly) every voter could be positive.
As a consequence, its citizens now enjoy a form of PR.
A similar process should be initiated for any debate on abortion. In the Citizens’ Assembly itself, a
team of ‘consensors’ could facilitate proceedings, while for the public at large, an independent
enquiry could be established to receive proposals from all concerned – politicians, pressure groups
and the public. The consensors or commissioners should then draw up a balanced (short) list of
four to six options, so to embrace the spectrum of opinions expressed during the discussions.
Let us assume they choose a ballot of four options. In the vote itself, the voters – members of the
Citizens’ Assembly, Deputies in the Dáil or the general electorate – will be allowed to cast their
preferences on one, some or all of the options. He who casts just one preference (and says nothing
about the other options) gives his favourite 1 point (and zero to the others). She who casts two
preferences gives her favourite 2 points (and her second choice 1 point). And so on. So he who
casts all four preferences gives his favourite 4 points, (his second choice 3, etc.).
Prior to the vote, the protagonist will know that success will go to the option with the most points.
Accordingly, she will need lots of 1st preferences, which she will get from her own supporters
anyway, but she will want all of those 1st preferences to be worth 4 points; so she will encourage all
concerned to cast a full ballot. She will also need some 2nd and/or 3rd preferences, so it will be
worth her while to talk with those with whom she is not in total agreement. More importantly,
however, she will not want any 4th preferences. It will therefore be in her best interests to meet
those who, in any binary contest, would have been regarded as her opponents.
In summary, an MBC7 encourages the voters to cast a full ballot; in so doing, each in effect
acknowledges the validity of the options and the aspirations of the various supporters. Furthermore,
in so doing, each implies that they will accept whichever of these four options is identified as the
democratic will. It should be emphasised that the MBC does not force the voter to cast a full slate of
preferences and those who, for whatever reason, opt to submit a partial ballot of three, two or
maybe only one preference, may do exactly that.
In effect, then, those who abstain have no influence on the democratic process. Those who
participate partially have a partial influence. And those who participate fully have a full influence.
It should also be pointed out that the difference in value between a voter’s xth preference and his
(x+1)th preference is always 1 point, regardless of whether or not he has cast that (x+1)th preference.
He who submits a partial ballot of just one preference exercises just 1 point; she who submits a full
ballot of all four preferences exercises (4 + 3 + 2 + 1 =) 10 points, but the difference between his
(stated) 1st and (unstated) 2nd preferences is the same as the difference between her (stated) 1st and
(stated) 2nd preferences.
7
The BC/MBC is a preferential points system of voting which is primarily designed for use in
decision-making. In a ballot of n options, a voter may cast m preferences where
n ≥ m ≥ 1.
st nd
In a BC, points are awarded to (1 , 2 … penultimate, last) preferences cast as per the rule:
(n, n-1 … 2, 1),
which might incentivise the voter to vote for his/her 1st preference only.
In an MBC, points are awarded to (1st, 2nd … penultimate, last) preferences cast as follows:
(m, m-1 … 2, 1),
and this encourages greater participation.
The MBC rule is in fact what Jean-Charles de Borda proposed in 1784 although he did not
cater for the possibility of truncated ballots; (Saari 2008: 197).
CONCLUSION
The concept of points voting is quite old. It might have been suggested by Ramon Llull in 1299,
but the science is uncertain. There is no doubt at all, however, that such was proposed by Cardinal
Nicholas Cusanus in 1435, primarily to elect the Holy Roman Emperor. The next inventor was the
Frenchman Jean-Charles de Borda, and his BC was adopted in l’Académie des Sciences in 1784,
only to be thrown out in 1800 by one not best known for his democratic idealism, one Napoleon
Bonaparte. Next came the Rev. Charles Dodgson, who though unaware of the works of de Borda
(just as the latter did not know about the Cardinal), proposed a BC for elections in Oxford
University. Unfortunately, he did not write a book about these ideas, partly because he wrote Alice
in Wonderland instead; he was indeed Lewis Carroll.
The BC was also ‘invented’ in Denmark by one Hothar Hage in 1860, in Nauru where a special form
of the BC was introduced in 1971 as an electoral system by the Irishman, the late Desmond
Dowdall; and in Brazil when participatory budgeting was initiated to Porto Alegre in 1989. It was
also ‘invented’ in Northern Ireland by the author of this report who, like so many of his
predecessors, only learnt of their inventions retrospectively: a prototype of the MBC was used in a
cross-community consensus experiment in Belfast in 1986 – the People’s Convention run by the
New Ireland Group, NIG. Though still eight years before the cease-fire, participants included
Unionists and Republicans, everything from SF to the UUP, all except the DUP, but even some
beyond that spectrum like the UDA and Ulster Clubs; in all, they numbered over 200.
Since then, the de Borda Institute has used the MBC on numerous occasions and in many countries,
not least in conflict zones like Bosnia. In a nutshell, the methodology is tried and tested. It is
robust, inclusive, accurate and, most importantly perhaps, ethno-colour blind. It is used as an electoral system in Slovenia, when choosing representatives of their ethnic minorities, but the world’s
first instance of a BC in use in decision-making in the elected chamber was in Dublin, when the City
Council chose the name Rosie Hackett for the new bridge over the Liffey, (Baker, 2014: 1-6).
It should also be pointed out that while majority votes in meetings can be taken by hand,
preferential voting is more easily executed with a computer. This Institute first used electronic
voting in another cross community event in Belfast in 1991 – the NIG’s The Other Talks, where the
keynote speaker was the current President, Michael D Higgins. More recently, this Institute and
CiviQ have developed an app, Decision-Maker, so that those concerned – Councillors in Chamber
and/or Deputies in the Dáil, or even members of the Citizens’ Assembly – may identify their
collective will by their smart phones.
In summary, then, the MBC is ideally suited to a modern, pluralist democracy. This is most certainly
the case when the subject under discussion is as complex and contentious as that of abortion.
Peter Emerson
Belfast, 21.11.2016
References
2014, Dublin City Council’s Rosie Hackett Bridge: A Landmark in
Decision-Making, The de Borda Institute, Belfast.
http://www.deborda.org/storage/Report%20on%20Rosie%20Hackett%20decision-final2.pdf
Baker. J.,
Dummett, M.,
1997, Principles of Electoral Reform. Oxford University Press,
Oxford.
Emerson, P.,
2012, Defining Democracy, second edition. Springer, Heidelberg,
Dordrecht, London, New York.
Saari, D.,
2008, Disposing Dictators, Demystifying Voting Paradoxes.
Cambridge University Press, Cambridge.