Referendums in the United Kingdom - Constitution Committee Contents

Memorandum by the de Borda Institute and the New Economics Foundation


  As it were by definition, in a plural democracy, there are bound to be more than two possible options on most contentious subjects. Accordingly, any decision-making procedure should also be multi-optional.

  If the decision-making process is to facilitate the correct identification of the collective will, the voting procedure must be one by which the voter can express his/her individual will with a certain degree of accuracy. Any single-preference voting procedure is therefore insufficient; instead, the procedure should be multi-optional; and in the count, all preferences cast should be taken into consideration.[2]

  Accordingly, it is suggested that, as and when appropriate, referendums should be multi-optional and preferential. (Such referendums are sometimes known as "preferendums".) Furthermore, the democratic process should enable the electorate, not only to vote in the ballot, but also to participate in the choice of questions. In debating electoral reform, for example, everyone should be able to submit their proposals to an independent commission or enquiry, and then to vote on the resulting short list of, let us say, about five options.

  If the voting procedure is the Modified Borda Count, MBC, individuals will be encouraged to cast preferences for all the options listed. Not only, then, can they cast their 1st preference for their favourite option; they may also state their compromise option(s); and in casting a last preference, they will acknowledge the legality of that option and the aspiration of its supporters. In a word, in consensus voting, no one votes "no" against anyone or anything; instead, everyone votes (with varying degrees of enthusiasm) in favour.

  And just as majority voting can divide societies or exacerbate existing divisions therein,[3] so, in contrast, an MBC can be the very catalyst of consensus.


  The Constitution Committee's Call for Evidence, Referendums in the UK's Constitutional Experience, dated 20 Nov. 2009.

AMSadditional member system AValternative vote
AV+AV plus a form of PR-list BCBorda count
FPPfirst-past-the-post IOCInternational Olympic Committee
IRVinstant run-offMBC modified Borda count
MMPmulti-member proportional STVsingle transferable vote
TRStwo round system WTOWorld Trade Organisation


  1.0  The following submission concentrates on two aspects of para 8 of the reference: the wording of the referendum; and the appropriateness of multi-option questions.

The wording of the question

  2.0  Some referendum questions are dichotomous. Even in these circumstances, however, the choice of question can be crucial. In the French 2002 referendum on the EU constitution, the question was "oui ou non". Those who supported M. Giscard d'Estaing's new proposals voted "oui"; and those opposed "non". But a number of others also voted "non": those who did not like the EU in general, and/or McDonalds, globalisation, Jacques Chirac, the prospect of Turkish accession, or "je ne sais quoi". At the very least, the question should have been set in a positive format: "should the EU constitution be 'comme ci ou comme ça'?"

  2.1  To identify the collective will, one first has to identify all the individual wills. This cannot be done if some voters are saying only "no", identifying only what they don't want. Such negative voting has hindered many political processes: in Northern Ireland (as in Dr. Paisley's "Ulster says no" campaign following the 1985 Anglo-Irish Agreement); in Bosnia (when Radovan Karadžic used three referendums in Republika Srpska in 1991-92 to veto every peace initiative); in Gibraltar (2003); and in Cyprus (2004). A referendum, therefore, should always offer a choice of positive alternatives, as in a constructive vote of no confidence in the German Bundestag.

The appropriateness of multi-option questions

  3.0  If, for instance, the UK were to choose a new electoral system,[4] there could be a multi-optional referendum, as there was in New Zealand in 1992.[5] And some UK referendums could have been multi-optional: the SNP had hoped the 1997 Scottish referendum would include an independence option and be three-optional, while Plaid Cymru had requested a four-option ballot in Wales[6] (Wigley, 1996).

  3.1  If a two-option question is posed when the debate is in fact multi-optional, the outcome may well be inaccurate. In the Welsh referendum, for example, the outcome was "devolution" 50.3% and "status quo" 49.7%. If a third option, "independence", had been included; and if but 1% of the devolution supporters had voted in favour of independence, the winner of a plurality vote would have been the "status quo" option.[7]

  3.2  A theoretical comparison can be made with the IOC's decision on London for the 2012 Olympics. Given the five options—London, Madrid, Moscow, New York and Paris—a majority vote could have been held—"Madrid, yes-or-no?" say, or maybe "Moscow or Paris?"—but the outcome might have been meaningless.[8] Similarly, returning to the theme of electoral reform, any Jenkins type ballot between FPP and AV+ could be a totally inaccurate measure of the collective will; and the best way to ensure an accurate outcome is to use a more accurate, multi-optional measure.

  3.3  In 1948 in Newfoundland, it was proposed that the people should decide their constitutional status on a choice of "Commission Government" or "Responsible Government". Some wanted a third option, "Confederation with Canada", and after demonstrations on the streets of Halifax, this was duly added… and it won (Emerson, 2002, p 120).

  3.4  In the wake of this precedent, there can be no legal/constitutional obstacle to the holding of a multi-option ballot in the UK. There may, therefore, be considerable interest in the latest White Paper from the Scottish Government.


  4.0  If there are only two options on the ballot paper, then, no matter which voting procedure is used, the outcome will be the same as that which would be given by a majority vote, which may be the preferred choice of the majority.[9] If there are more than two options, however, then there are a number of different ways in which the votes may be counted. They include the following:

  4.1  plurality vote: but the winner may have only the biggest minority.[10] In the voters' profile shown, A would win because five people think it is the best, yet seven think it is the worst.

Table I

PreferencesNo of Voters
54 3
1stAC B
2ndBB C
3rdCA A

  4.2  two-round voting:[11] In the above profile, C wins the second round by 7 to 5.

  4.3  approval voting: in a ballot of n-options, voters may "approve" of as many options as they wish. A voter may thus be tempted to cast only one "approval"… in which case, the procedure is little more than a plurality vote. In the above profile, if only 1st preferences are regarded as "approvals" the winner is A; whereas if both 1st and 2nd preferences are counted, the score is B-12, C-7, A-5, and B is the winner.

  4.4  alternative vote:[12] In the above profile, B, arguably the most popular option because it is the 1st or 2nd preference of everybody, loses the first stage, and its votes are transferred to C which then wins the second stage. And the 2nd preferences of nine voters remain uncounted (see footnote 1).

Table II

OptionFirst stage Second stage
A5 5
B3-3 0
C4+3 7

  5.0  In the following three systems, the voter may cast his/her preferences on all n-options:

  5.1  In a BC, the voter's {1st-2nd-3rd-… preferences} get {n, (n-1), (n-2)…} points. The voter may again be tempted to cast only one preference, whereupon this methodology also deteriorates into a plurality count.[13] In an MBC, however, the voter who casts only m preferences, where 1 m < n, exercises only {m, (m-1), (m-2)…} points.[14] So, unlike the BC, the MBC is mathematically neutral.[15]

  5.2  A Condorcet count: five voters prefer A to B, but seven prefer B to A, so A:B = 5:7; similarly, A:C = 5:7 and B:C = 8:4. Thus B wins two pairings, C one, and A zero, so the winner is B.

  5.3  Condorcet suffers from the paradox, if one exists; a BC/MBC is susceptible to the irrelevant alternative. Nevertheless, of the above and other systems, "There are two defensible procedures for aggregating votes: the Condorcet rule and the Borda rule," (Iain McLean and Neil Shepherd, 2004 -W11). Nothing, of course, is perfect—Arrow's impossibility theorem—but as shown below, some procedures are better than others. Furthermore, "The BC is a unique method… to minimise the likelihood that a small group can successfully manipulate the outcome," (Saari, 1995, p 14), and the MBC is even better.

Table III



  6.0  In an MBC, success depends upon, not only a large number of high preferences, but also a small number of low preferences. Thus the protagonist of any one option would be wise to talk to any erstwhile opponents, so to persuade them to cast, say, a 3rd preference rather than a 5th. And just as the threat of a majority vote may often antagonise,[16] so, in contrast, the prospect of an MBC vote may well help to create a more inclusive milieu.

Arrow, Kenneth1963, Social Choice and Individual Values, second edition, Yale.
de Borda, Jean-Charles1781, M
moire sur les
lections au scrutin
, Histoire de l'Acad
mie Royale des Sciences
, Paris.
Emerson, Peter2002, Defining Democracy, The de Borda Institute.
Emerson, Peter (Ed)2007, Designing an All-Inclusive Democracy, Springer.
IDEA1997, The International Handbook of Electoral System Design, IDEA.
Irish Governmentundated, Green Paper on Abortion.
Macartney, Allan1992, Asking the People, Unit for the Study of Government in Scotland, Edinburgh University.
McLean, Iain and Neil Shepherd2004, A program to implement the Borda and Condorcet rules…, Nuffield College Politics Working Paper (University of Oxford).
Saari, Donald G1995, Basic Geometry of Voting, Springer.
      "2008, Disposing Dictators, Demystifying Voting Paradoxes, Cambridge.
Scottish Government2009, A National Conversation—Your Scotland, Your Voice.
SNP1992, A Multi-option Referendum—Let the People Decide.
Wigley, Dafydd, MP1996, A Real Choice for Wales, Plaid Cymru.

20 December 2009

2   AV or STV are therefore inadequate.


3   "… all the wars in the former Yugoslavia started with a referendum," Oslobodjenje, 7.2.1999.


4   Having been asked to propose just one alternative, the Jenkins Commission suggested AV+ .


5   New Zealand's five-option TRS ballot was on the status quo, FPP, or AMS, AV, MMP or PR-STV, (Emerson, 2002, pp 119-20). Slovenia chose a new electoral system on the basis of three options, but they held three majority votes, one on each, and all three were lost. Ibid.


6   Both supported AV.


7   Maybe the most popular option was indeed "devolution". If a more accurate measure of social choice had been used, however, the conclusion would not have been in such doubt.


8   The IOC take a series of plurality votes, with the loser dropping out of the next round. All but the results of the last round are kept secret.


9   This assumes that everyone votes "sincerely" as opposed to "tactically". And even when the question is dichotomous-as was, "which side of the road shall we drive on?"-there may be more than two ways of answering. Sweden posed this question in a 1955 referendum, with three options: "left", "right" and "blank".


10   As an electoral system, it is called FPP; the "smallest largest minority" was in Papua New Guinea in 1992, when the winner got 6.3%, (IDEA, p 42).


11   A form of TRS is used in French presidential elections. In 2002, this led to the anomalous situation in which, supposedly, M. Le Pen was the second most popular candidate whereas in fact, and but for the split Left vote, M. Justin deserved that accolade, (Maurice Salles, in Emerson, 2007, pp 107-8).


12   Sometimes called STV or IRV, AV is used as in Australian elections.


13   The BC is used in Slovenia for the election of the representatives of its ethnic minorities. It is also used in Kiribati.


14   Some think that this is the original formula, as proposed by Jean-Charles de Borda in 1781 (Saari, 2008, p 197). Others are not so sure (Arrow, p 94).


15   In practice, as it were psychologically, the MBC actually encourages the voter to submit a full ballot (Emerson, 2007). Such is the evidence from a number of MBC votes.


16   "…prior to the 1983 and 1992 referenda, the debate became bitter and polarised," Irish Government, p 126.


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