About us

.

A MAJORITY VOTE

MAY BE ACCURATE

IF, AND ONLY IF,

THE TWO OPTIONS

ARE A DUALITY.

 

 

DEMOCRACY IS FOR

EVERYBODY, NOT

JUST FOR A (OR

THEMAJORITY.

 

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Another journey to China, via Baku (COP29), Georgia, India, and return via Mongolia, Russia and (therefore) Ukraine.  Here's the blog: https://deborda.substack.com/p/debordaabroad2

 

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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!

« 2025-31 Letter from Ukraine: another binary! | Main | 2025-29 UKRAINE: A POST-WAR POLITY »
Tuesday
Nov182025

2025-30 Ukraine: An on-line debate + decision

18th November, in the National University, “Kyiv-Mohyla Academy,’ Kiev, everyone was on-line, and so was the vote!  The report starts:

In any post-war parliament, a consensus may be just as important as it is in war!  Accordingly, after an introductory critique of majority voting and a description of some other decision-making voting procedures, every participant was asked to propose that which they might consider to be a suitable decision-making voting methodology.  Thus would a ballot be formed; from 4 – 6 options is usually regarded as being optimum, especially for any subject of complexity.  And finally, the participants would cast one or more preferences, so to identify their most popular option.  

An Overview

It was a huge mistake 

for the colonial powers

+          to give – or impose – majority rule on Rwanda; 

for Britain

+          to give majority rule to Northern Ireland; 

for the UN, in their ‘right of self-determination’ 

+          to suggest a minority may secede if a majority of that minority so decide; 

for the world’s parliaments and congresses

+          to regard a whole host of electoral systems as democratic, while in the main using only one form of decision-making; 

and 

+          to practice majority rule, so to imply that the exclusion of any Arabs from the Knesset in a majority coalition of ‘the others’ is democratically justifiable.  

In a nutshell, taking a majority vote in a situation where there are more than two options ‘on the table’ is often inaccurate and may even be dangerous.  In a simple scenario, a debate of four possible outcomes – a motion, option A; two possible amendments, options B and C; and the status quo, option S – is often subject to three binary votes:

{(B v C) v A} v S       =          ….

A better methodology might be to consider all four options, in turn, and then to hold just the one preference vote on these options.

The Experiment

As in Mykolaiv, so too in Kiev, the workshop first considered the ubiquitous use of majority voting, even in debates where more than two options are ‘on the table’.  In most forums, differences are resolved – or not, as the case may be – in a series of majority votes; but such debates are open to manipulation and, in many settings, abuse.

Accordingly, the workshop:

            +          considered several voting procedures; 

+          formed a ballot of four or more options; 

+          proceeded to a preferential vote using the software – www.debordavote.com  on the participants’ mobiles; this analyses a voters’ profile according to the rules laid down for a Modified Borda Count MBC;

and

+          thus identified the voters’ consensus. 

The difference between the two events was that, while only the vote in Mykolaiv was on-line (as a result of a power-cut), in Kiev everything was on-line (and, from that point of view, it was a de Borda first). 

Binary Ballots – a Critique

In a setting:     where 5 people want A, 4 prefer B and 2 opt for C;

                                    where their 1st-2nd-3rd preferences are:

                                    5                      A-B-C

                                    4                      B-C-A

                                    2                      C-A-B

A is more popular than B,           A > B              =          7:4

                                                B > C              =          9:2

and                                          C > A              =          6:5

which means that

A > B > C > A > B > ….

and it goes round and round for ever.

It also means that        

{(B v C) v A}             =          A

but, if the debate is restructured

{(C v A) v B}             =          B

and

{(A v B) v C}             =          C

In other words, the order of voting can be determined to give whatever result the chair desires.  In a preferential vote, in contrast, with 4 points for a 1st, 3 for a 2nd, etc., the results would be A 23, B 24 and C 19, so the winner would be B.  This result is close – see below on consensus coefficients – but it is unambiguous and all very transparent.

Other Voting Procedures

Many forms of decision-making are possible.  Those numbered – i) to iii) – were not listed on the subsequent ballot: those lettered A to G were included.

i)          majority voting on simpletons – “Option A, yes or no?”  In a debate on n options, there might be a majority against every option;

ii)        majority voting on pairings – “Option A or option B?”   There may be majorities in favour of (n-1) options;

D         plurality voting is a single preference on a choice of three or more options.  The winner may have majority support, or maybe only the largest minority;

B         the two-round system, TRS, is a plurality vote followed, if need be, by a majority vote pairing between the two leading options;

The following may be multi-optional.

iii)       approval voting is non-preferential; a voter may ‘approve’ of one or more options;

A         range voting: every voter has x points, and gives all to one or some to two or more candidates;

The following are preferential.

F         Borda count BC is a points system.  In a ballot of n options, a 1st preference gets points, a 2nd preference, if cast, gets (n-1), etc.;

E        In a modified Borda count MBC, if the voter casts m preferences, a 1st preference gets m points, a 2nd, if cast, gets (m-1), etc.;

G         the Condorcet rule analyses all the pairings: A-B, A-C, A-D… C-D, C-E… F-G, all 21 of them, to see which (if any) wins the most pairings;

C         STV or RCV or AV is a knock-out system of plurality votes; the votes of each eliminated option are transferred to its 2nd or subsequent preference, until an option gets a majority.

In summary,

+          a single-preference procedure prevents the voter from casting a 2nd and subsequent preferences;

+          some multi-option procedures allow the voter to cast more than one preference;

+          option E actually encourages the voter to thus cross the gender gap, the party 

divide, and even any sectarian chasm.

The seven options – all multi-optional, some preferential – were as listed: option A came from the ‘floor’, the remaining six from the speaker.  On the e-ballot, they should have been cast in random order – ideally, options E and F should not have been alongside each other.

The Vote

In a full ballot on seven options, a 1st preference gets 7 points, a 2nd gets 6, etc., so a full ballot is worth 

7 + 6 + 5 + 4 + 3 + 2 + 1        =          28 points.

14 people voted; 13 were full ballots, of 28 points each; 1 was a partial ballot of only two preferences.  So, on a turnout of about 70%, the total number of points used was:

13 x 28 = 168              +          1 x (2+1)                     =          364 + 3            =          367

Consensus Coefficients

If, as is the case in this event, one or more persons casts only a partial ballot, we cannot use average preference scores as an accurate comparison.  Instead, we use consensus coefficients: 

                       the option’s MBC score                      [divided by]

the maximum possible MBC score = 14 in number 1st prefs = 14 x 7 = 98

The maximum consensus coefficient CC is always one; the minimum may vary a little, according to the number of options on the ballot.  In the above poll:

maximum                                            1.00

mean                                                   0.57

mimimum                                           0.14

In any multi-option ballot, the chances of a multi-draw are all but zero.  Some options will be above the mean, others below.

If the leading option is < 0.60, there is no clear winner, no consensus, and so no decision should be taken; instead, the debate should be resumed at a later time.  If, however, 

            0.60     <          the winner       <          0.70                 it is the best possible compromise;

            0.70     <                      ”          <          0.80                 the consensus

            0.80     <                      ”                                              the collective will.

These figures are somewhat arbitrary, and may vary as experience suggests.

The Results

                 Option                                            Points                               Consensus coefficients

A                     range voting                .67                  67 / 98 =                      0.68

            B                     TRS                             .63                  63 / 98 =                      0.64

            C                     STV                            .56                  56 / 98 =                      0.57

            G                     Condorcet                   .49                  49 / 98 =                      0.50

            D                     Plurality voting           .47                  47 / 98 =                      0.48

            F                     BC                               .43                  43 / 98 =                      0.44

            E                     MBC                           .42                  42 / 98 =                  .   0.43

Total    =          367

                                                                                                                            and 3.74 

                                    And 3.74 / 7    =          the mean  =     (c 0.50)            =          0.53

The Analysis

The outcome, therefore, the best possible compromise, is option A on a score of 67 points, with a consensus coefficient of 0.68.

Post-script

This outcome is not as I would have wished.  Range voting encourages selfish, uncompromising behavior: if given 10 points to allocate as he/she may wish, the intransigent voter may well tend to plomp all 10 points onto his 1st preference, while the more consensual voter might give her 1st preference, let’s say, 5 points, her 2nd choice 3 and a 3rd choice 2 points.

The event nevertheless shows that consensus voting is possible.

Acknowledgements

My thanks go to Veronika Nazarko who guided me to the correct department when I was hopelessly lost; to the Dean, Liudmyla Zubrytska, who hosted the event; and to Maryna Moskalenko who, prior to the e-vote, solved all the e-lectronic problems which would have flummoxed this old e-diot. 

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