About us

The de Borda Institute

aims to promote the use of inclusive, multi-optional and preferential voting procedures, both in parliaments/congresses and in referendums, on all contentious questions of social choice.

This applies specifically to decision-making, be it for the electorate in regional/national polls, for their elected representatives in councils and parliaments, for members of a local community group, a company board, a co-operative, and so on.  But we also cover elections.

               * * * * *

The Institute is named after Jean-Charles de Borda, and hence the well-known voting procedure, the Borda Count BC; but Jean-Charles actually invented what is now called the Modified Borda Count, MBC - the difference is subtle:

In a vote on n options, the voter may cast m preferences; and, of course, m < n.

In a BC, points are awarded to (1st, 2nd ... last) preferences cast according to the rule (n, n-1 ... 1) {or (n-1, n-2 ... 0)} whereas,

in an MBC, points are awarded to (1st, 2nd ... lastpreferences cast according to the rule (m, m-1 ... 1).

The difference can be huge, especially when the topic is controversial: the BC benefits those who cast only a 1st preference; the MBC encourages the consensual, those who submit not only a 1st preference but also their 2nd (and subsequent) compromise option(s) And if (nearly) every voter states their compromise option(s), an MBC can identify the collective compromise.

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DECISION-MAKER
Inclusive voting app 

https://debordavote.com

THE APP TO BEAT ALL APPS, APPSOLUTELY!

(The latest in a long-line of electronic voting for decision-making; our first was in 1991.)

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FINANCES

The Institute was estabished in 1997 with a cash grant of £3,000 from the Joseph Rowntree Charitabe Trust, and has received the occasional sum from Northern Ireland's Community Relations Council and others.  Today it relies on voluntary donations and the voluntary work of its board, while most running expenses are paid by the director. 

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A BLOG 

"De Borda abroad." From Belfast to Beijing and beyond... and back. Starting in Vienna with the Sept 2017 TEDx talk, I give lectures in Belgrade, Sarajevo, Istanbul, Tbilisi, Yerevan, Tehran, Beijing, Tianjin, Xuzhou, Hong Kong and Taiwan... but not in Pyongyang. Then back via Mongolia (where I had been an election observer in June 2017) and Moscow (where I'd worked in the '80s).

I have my little fold-up Brompton with me - surely the best way of exploring any new city! So I prefer to go by train, boat or bus, and then cycle wherever in each new venue; and all with just one plastic water bottle... or that was the intention!

The story is here.

In Sept 2019, I set off again, to promote the book of the journey.  After the ninth book launch in Taipei University, I went to stay with friends in a little village in Gansu for the Chinese New Year.  The rat.  Then came the virus, lockdown... and I was stuck.

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The Hospital for Incurable Protestants

The Mémoire of a Collapsed Catholic

 This is the story of a pacifist in a conflict zone, in Northern Ireland and the Balkans.  Only in e-format, but only £5.15.  Available from Amazon.

 

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The director alongside the statue of Jean-Charles de Borda, capitaine et savant, in l’École Navale in Brest, 24.9.2010. Photo by Gwenaelle Bichelot. 

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WELCOME

Welcome to the home page of the de Borda Institute, a Northern Ireland-based international organisation (an NGO) which aims to promote the use of inclusive voting procedures on all contentious questions of social choice. For more information use the menu options above or feel free to contact the organisation's headquarters. If you want to check the meaning of any of the terms used, then by all means have a look at this glossary.

As shown in these attachments, there are many voting procedures for use in decision-making and even more electoral systems.  This is because, in decision-making, there is usually only one outcome - a singe decision or a shopping ist, a prioritisation; but with some electoral systems, and definitely in any proportional ones, there can be several winners.  Sometimes, for any one voters' profile - that is, the set of all their preferences - the outcome of any count may well depend on the voting procedure used.  In this very simple example of a few voters voting on just four options, and in these two hypothetical examples on five, (word document) or (Power-point) in which a few cast their preferences on five options, the profiles are analysed according to different methodologies, and the winner could be any one of all the options.  Yet all of these methodologies are called democratic!  Extraordinary!

« 2023-8 CHINA (And 2024-09.) | Main | 2023-6 Ukraine, letter in Irish News »
Monday
Mar132023

2023-7 Peace, Preferendums and the GFA

 

PEACE, PREFERENDUMS, and the Belfast Agreement.

 

“Simple majority decisions… cannot be fair in a democratic sense

because the imposition of binary alternatives is itself unfair.”

William Riker, p 68.

 

" I have noticed an inclination for [western] people to

think in terms of 'black' and 'white' and 'either, or'.

They [tend] to lose sight of the grey areas which

inevitably exist between two points of view."

The Dalai Lama, p 218.

 

PREFACE

 

“All the wars in the former Yugoslavia started with a referendum,” (Oslobodjenje, Sarajevo’s newspaper, 7.2.1999).

The same now applies to Ukraine.

 

COMPROMISE

To resolve NI’s constitutional status, we need compromise.  A consensus may still be a few generations away, so for the moment, a compromise will do.  But a compromise cannot be identified in a binary ballot.  As often as not, dichotomies don’t help at all: “Are you Protestant or Catholic?  Serb or Croat?  Hutu or Tutsi?  Sunni or Shi’a?  Arab or Jew?  Russian or Ukrainian?  (Left-wing or right-?)”

Admittedly, the Belfast Agreement allows the individual to compromise, and NI citizens may choose to be either British or Irish… or both!  Good.  Collectively, however, the Good Friday Accord says our identity is to be settled in a binary ballot, either/or: NI is to be either in the UK (as currently defined, though Scotland may change things a little) or in a united Ireland (as yet undefined).  NI is not allowed to be in both; such options are not even on the table.  And that’s not good.

So maybe it would be better to let the debate consider other options – joint sovereignty, a W-I-S-E (Wales-Ireland-Scotland-England) federation, whatever – to allow for, or even rejoice in, a degree of pluralism, to allow for a compromise.  But that can best be effected if there are more than two options on any future ballot paper.

Accordingly, this text first looks at some of the world’s binary ballots, many of which were bad; next at a few multi-option referendums, some of which were pretty good; and then at a proposal for NI.

CONTENTS

Preface                                                                        3

Glossary                                                                      5

Abbreviations                                                               6

Introduction                                                                 7

            Majoritarianism                                                7

Self-determination                                                       8

Multi-option Referendums                                           10

A Proposal                                                                 10

Ratification                                                                15

Postscript                                                                  15

LIST OF TABLES

Table I             False-flag Referendums                      9

Table II           A Preferential Ballot                           12

Table III          Single-peaked Preferences                 14

 

GLOSSARY 

It is extraordinary but, while many people often discuss lots of electoral systems, very few politicians or professors debate decision-making voting procedures.[1]  Yet there are several:

 

Dichotomies

+          majority voting, on singletons: “option X, yes or no?”

                                        or pairings: “option X or option Y?”

 

Multi-option Voting

+          plurality voting: a single-preference choice of more than two options; the winner may have a majority, or maybe only the largest minority. 

+          two-round system TRS: a plurality vote, followed if need be, i.e., if no one option gets a majority, by a majority vote between the two ‘leading’ options.

+          alternative vote AV: voters cast preferences.  It is a plurality vote but, if no one option gains a majority of 1st preferences, the smallest option is eliminated and its votes are transferred to its second preference option(s); the process is repeated until one option does gain a majority.

+          approval voting is non-preferential; voters ‘approve’ or one or more options, and the winner is the option with the most ‘approvals’.

+          serial voting: a series of majority votes, usually on amendments arranged in order, cheap to expensive, or whatever.

+          Borda count BC: in an n-option ballot, voters cast up to n preferences; these are turned into points – a 1st gets n points, a 2nd gets n-1, a 3rd gets n-2, etc. – and the option with the most points is the winner.

+          modified BC, MBC, which is the original formula: voters cast m preferences, so m < n, and points are awarded, m, m-1… etc.[2]

+          Condorcet: the voters cast their preferences; options are compared in pairings, and the option which wins the most pairings is the winner.

 

ABBREVIATIONS

                                                              As used in

                                                   decisions           elections

 

AV*     alternative vote                                         Australia

BC       Borda count                                              Slovenia

EUMM EU Monitoring Mission in Georgia

(first deployed in Sept. 2008)

FPTP    first-past-the-post                                     India, UK

    =     plurality voting                  Denmark

MBC    modified Borda count

PR       proportional representation

PR-STV                                                                Ireland, Malta

RCV*   ranked choice voting                                  some US states

            serial voting‡                    Sweden

STV*    single transferable vote

TRS      two-round system             Norway†           France

                                                   NZ

UCL     University College London

WWI    World War I

 

*          all names for the same methodology;

‡          a serial vote identifies the Condorcet winner (if there is one);

†          used in parliament, but only once;

¶            used in some of their referendums. 

INTRODUCTION

Majoritarianism

Binary voting was used by Hitler in his referendums – to become the führer, for example, by 98.1% on a 98.9% turnout – and also in the Bundestag where, in 1933, he manipulated the Enabling Act to ensure he won the necessary 2/3rds majority.

Lenin also used binary voting.  In 1903, the Russian Social Democratic Workers’ Party met, voted and split.  Lenin gained (not a majority, just) the largest minority, 19 votes to 17, with 3 abstentions; but he pretended it was a majority bolshinstvo, and called himself a Bolshevik, while the 17, the second minority menshinstvo, became the Mensheviks.

Napoléon started it.  He wanted to control only everything, so he threw out the preferential points system adopted by l’Académie des Sciences, reverted to majority voting and, in his third referendum in 1804, he became the emperor: 99.7% in a turnout of 43.3%.  Today, the entire world uses binary voting, from the UN Security Council downwards: it’s even in the Constitution of North Korea, (Article 97).

Some have suggested better methodologies.  In the year 105, Pliny the Younger pointed out the following: whenever a debate is multi-optional,{which in a pluralist democracy, should (nearly) always be the case}, if there’s no majority in favour of any one option, then, of course, there’s a majority against every option.  (As in Brexit.)

The first government to actually use a multi-option vote was Chinese; there again, in those days, they invented pretty well everything.  They had first used binary voting in the first Century BCE – the Greeks were earlier still – and then, on the question of war with Mongolia, the Jīn Dynasty used plurality voting in 1197.  (Emerson 2022: 68.)

Self-determination

In WWI, President Wilson’s ‘right of self-determination’ could enable a society to resolve its external problem of colonialism; it was not meant to facilitate solutions to internal questions of secessionism. 

Northern Ireland, roughly 60% Protestant and 40% Catholic, had a border poll in 1973.  So the turnout was 59%, as ‘all’ the Protestants voted ‘yes’ because they knew they’d win.  The Catholics abstained.  The result, 98.9% in favour, told everyone… what they already knew.  1988 saw the first clashes between (Moslem) Azeris and (Christian) Armenians in Nagorno-Karabakh.  The headline in a Moscow newspaper the next morning was, “This is our Northern Ireland.”[3]

Wanting to opt out of Yugoslavia, Croatia planned a referendum, in 1991.  The Krajina[4] wanted to opt out of opting out, so they had a referendum as well, one week earlier.  On a 95% turnout, 99% of the Serbs said ‘yes’; next, 93% of 84% of Croats said the opposite ‘yes’; the result was war.  Similarly, Kosovo had a referendum in the same year.  The population was 90% Albanian, so the turnout was 87%; and 99% voted for ‘independence’.  But ‘unity with Albania’ or ‘a Greater Albania’… would also have won a majority.   

Likewise again, in the Caucasus, Georgia opted out of the USSR, so South Ossetia opted out of Georgia, so Akhalgori[5] opted out of opting out and… more referendums, more suffering, more violence.  A summary of it all is shown in Table I. 

Initially, fearing a break-up of the Federation, Russia did not like referendums, the prospect of many of its 60+ indigenous peoples all opting out of ‘Mother Russia’.  So they called it “matryoshka nationalism”, after their famous dolls.  (Reid, 2003: 136.)  But then Moscow saw how a plebiscite could be used to its advantage, so (while still opposing any referendum in Kosova), they supported the plebiscites in both Abkhazia and South Ossetia.

Table I                        False-flag Referendums

Year

MATRYOSHKI

The

Result

Large

small

infinitesimal

(1920

UK

Ireland

NI)[6]

Troubles

1973

UK

 

NI (Border poll)

?

1990s

USSR

Georgia

South Ossetia

War

 

 

 

Abkhazia

War

 

 

Azerbaijan

Nagorno-Karabakh

War

1990s

Yugoslavia

Croatia

Krajina

War

 

 

Bosnia

Republika Srpska

War

 

 

 

Herzeg-Bosna

War

 

 

Serbia

Kosova/o

War

1991

USSR

Ukraine

 

(see below)

1998

NI Belfast Agreement

Peace

2014

UK

Scotland

Orkneys + Shetland

Unresolved

2014

Ukraine

Crimea

 

War

 

 

Donetsk

Krasnoarmiisk

War

 

 

Luhansk[7]

 

War

2022

Ukraine

Donetsk[8]

 

War

 

The conclusion is stark: binary referendums are often no bloody good.  One obvious exception, perhaps, is the Belfast Agreement… but some might have preferred a peace settlement without binary referendums!

Multi-option Referendums

The first ever multi-option referendum was in 1894 in New Zealand.  The debate was on prohibition – an obvious case for a compromise – and sure enough, cheers all round, a compromise won.

The UK held a multi-option referendum in Newfoundland in 1948.  Initially, there were to have been just two options on the ballot paper, but after protests a third – ‘confederation with Canada’ – was added and, in a two-round vote, it won! 

NZ had yet another multi-option referendum in 1992, this time on their electoral system.  The status quo, first-past-the-post FPTP, had produced some horribly unfair results, (as is its want), and many wanted a more accurate electoral system.  An independent commission produced a short list of five options: the status quo of FPTP, the Irish single transferable vote PR-STV[9] and three others in the middle.  The people voted and chose a compromise – half PR and half FPTP – the German system.  So here’s our second conclusion: pluralism is possible.

A Proposal

Given that the unwritten British constitution relies on precedents, the above Newfoundland plebiscite would suggest, there is no legal reason why the British Government could not allow NI to have a multi-option vote, and definitely not if it is to be non-binding.  It might require a change to the Belfast Agreement of course, but the latter caters for that, (page 26, para 7).  Accordingly, with a view to giving the NI electorate a multi-option preferential ballot, a citizens’ assembly or some such could be tasked to draw up, let’s say, six options, so to represent the range of opinions in NI society.  The people could then be asked to cast (one, some or ideally) all their preferences on these six options, giving a 1 to their 1st preference, and maybe as well a 2 to their 2nd choice, a 3 to their 3rd… and so on, as they wish.

In the count:

+          she who casts only one preference (and says nothing about the other options) gets her favourite option just 1 point… (and the other options get nothing);

+          he who casts two preferences gets his favourite option 2 points (and his 2nd choice gets 1 point);

            and so on; so

+          she who casts all six preferences gets her favourite 6 points, (her 2nd choice 5, her 3rd option 4, etc.).

The difference is always 1 point.

Some people argue that he who casts only one preference should get 6 points for his favourite; but that would give his option a 6-point advantage over the other options.  The above rules, as first devised in 1770 by Jean-Charles de Borda, would be fairer.  In a ballot on n options, a voter may cast m preferences, so obviously,

n > m > 1

Then, in a 6-option ballot, M de Borda stated that points shall be awarded to (1st, 2nd … 6th) preferences cast, according to the rule

(m, m-1 … 1).

Unfortunately, someone changed this to

(n, n-1 … 1) or even (n-1, n-2 … 0)

The n rules favour the intransigent, as would a rule like (25, 18, 15, 12, 10, 8), from Formula 1 racing.  The m rule is neutral: as noted, the difference is always 1 point.  This Modified Borda Count MBC as his original is now called, is unweighted and unbiased, (while the n rules are mistakenly called a BC).

An example of a 6-option ballot, the author’s guesstimate, is shown in Table II.  Doubtless, the options chosen by a citizens’ assembly would be wiser.

Table II                      A Preferential Ballot

 

NI’s constitutional status.

 

You may vote, in your order of preference,

for one or more options, as you wish. 

 

You should cast a 1 for your 1st preference; you may also cast a 2 for your 2nd preference, a 3 for your 3rd preference, and so on, as you wish.

If you cast just one preference,     your 1st preference gets 1 point;

if you cast two preferences,          your 1st preference gets 2 points, and

                                                  your 2nd choice gets       1 point;

and so on.  Therefore,

if you cast all six preferences,      your 1st preference gets  6 points,

                                                 your 2nd choice gets        5 points,

                                                 your 3rd choice gets        4 points,

                                                 your 4th choice gets        3 points,

                                                 your 5th choice gets        2 points, and

                                                 your 6th choice gets        1 point.

 

OPTION

Preference(s)

  A

NI to be wholly in the UK, under direct rule from London.

 

  B

NI to remain devolved in the UK, (the status quo).

 

 

  C

NI to be under joint British and Irish

Authority.

 

 

  D

NI to be in Ireland, in a W-I-S-E (Wales, Ireland, Scotland, England) federation.

 

 

  E

NI to be in a two-part federal Ireland, 6 counties plus 26 counties.

 

 

  F

The 6 counties of NI to be absorbed into a unitary state 32-county united Ireland.

 

 

 

In the count, preferences cast shall be translated into points,

and the option with the most points shall be the winner.

Now it could be that she whose favourite is option A might have a 2nd preference of option B; that he who thinks option C is best could compromise on option D, and so on.  So for those who cast all six preferences, (i.e., for those who choose to recognise the valid aspirations of their neighbours – an important feature of any reconciliation process), she whose 1st preference is option B might vote

B-A-C-D-E-F

or perhaps

B-C-A-D-E-F.

Likewise, he who thinks option D is the best might vote

D-C-E-B-F-A

or perhaps

D-C-B-E-A-F

and so on.

In other words, most peoples’ preference sets will be what are called ‘single-peaked curves’, such as can be seen in Table III.  And with this methodology, the m rule, J-C de Borda’s formula:

 

 …if (almost) everyone casts a single-peaked set of preferences, the collective will, the collation of all these single-peaked curves, will itself be single-peaked.

 

In the example shown in Table III, Ms i, in blue, has preferences of

B-C-A-D-E-F

so the points she gets for these options are, respectively,

B-6- C-5-A-4-D-3-E-2-F-1

so when listed, in A-B-C-D-E-F order, her vote becomes

4-6-5-3-2-1.

In like manner, Mr j in brown has a preference set of

D-C-B-E-F-A

which corresponds to:

1-4-5-6-3-2

and likewise, Ms k’s set in grey

E-D-F-C-B-A

becomes

1-2-3-5-6-4

If we add these three sets of points, we get:

4    6    5    3    2    1

1    4    5    6    3    2

1    2    3    5    6    4

6  12  13   14  11    7

the collective will.  It peaks at option D.  So this is the answer: and by examining the steepness of the curve, we can calculate, exactly, if this ‘peak’ – a mound, a hill or a mountain – represents the best possible compromise, a consensus or even an alpine collective wisdom.

Table III                     Single-peaked Preferences

Suffice here to say that very few people will have sets of preferences which are not single-peaked, something like

C-A-E-B-D-F.

Ratification

There are many who hold that the democratic process is majoritarian; that decisions should be based on questions ‘yes-or-no?’ or ‘for-or-against?’  That even if only by 50% +1, the winners then win everything and the losers get nuttin’. 

Democracy would perhaps be more peaceful if the voting procedure enabled voters (and/or their representatives) to vote only positively, albeit in order of preference; in other words, if no-one voted ‘no’. 

If such were the norm, political controversies could be regarded as multi-optional, and all concerned could cooperate,{not voting (‘for’ or) ‘against’ each other, but} first talking and then voting with each other, each stating what they want, but each also stating their compromise option(s).  We could then identify the collective compromise: at best the option with the highest average preference, if, that is, that average has surpassed a certain threshold, i.e., if its collective single-peaked curve isn’t just an undulating plateau. 

Society may nevertheless prefer to regard the multi-option vote as non-binding.  So the two most popular options could then be put to a final, binding, binary vote.  Final, that is, for this generation.  And maybe, by the time the next generation takes over, society will have replaced the 2,500-year-old binary vote with a decision-making voting procedure which is a little more inclusive, robust, accurate… and modern!

 

Postscript

“Would you like to [send in a] submission?” asked the UCL’s Working Group on Unification Referendums on the Island of Ireland on 4.8.2020.  OK said I.  “Great.”  But it was ignored.  It was unlisted in the final report.  And we were not invited to its webinar launch.  “Our exchange [is now] closed.” 28.7.21. 

Sadly, despite numerous historical examples of horrible binary voting, many people in academia and the media, (let alone lots of political activists Scottish, Irish, Catalan… and Russian), still regard binary voting as adequate.

 

References

Dalai Lama     1998, Freedom in Exile, Abacus, London.

Emerson, P.     2022, The Punters’ Guide to Democracy, Springer, Heidelberg.

Reid, A.           2003, The Shaman’s Coat, Phoenix, London.           

Riker, W.H.    1988, Liberalism against Populism, Waveland Press Inc., Illinois.

 


[1]           See, for example, the postscript.

[2]           If all the voters cast all n preferences, so if m always = n, the BC and MBC are the same.  If some voters express only some preferences, however, if in some ballots, m < n, the overall outcome might be very different.

[3]           Вот наш Ольстер, ‘Vot nash Ol’ster’.

[4]           Croatia is mainly Catholic Slavs, but the Krajina were settled years ago by Orthodox Slavs from Serbia, a bulwark against the Ottomans.

[5]           As a Russian/English translator in the EUMM in 2008-9, the author helped today’s Tánaiste Micheál Martin meet refugees fleeing from Akhalgori

[6]           Ireland was divided without referendums, but NI was concocted to give the Protestants a ‘permanent’ majority.

[7]           2014 also saw the Scottish referendum, and the word Scotland, ‘Shotlandiya’ was used in Luhansk by Russian separatists, to ‘justify’ the unjustifiable.  (The author was in Ukraine, as an OSCE elections observer.)

[8]           The 2014 referendum asked, ‘independence (from Ukraine), yes or no?’ while the 2022 plebiscite posed something quite different, ‘incorporation into Russia, yes or no?’

[9]           It is used in Ireland, but it was a British invention, in 1821.

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