2025-26 Majority voting on non-dualities

MAJORITY VOTING MAY BE ACCURATE IF, AND ONLY IF, THE TWO OPTIONS ARE A DUALITY

- THE BINARY BIND

1          The Chinese wouldn’t vote, “Yīn or Yáng?”  The two are a unity, not a duality.    

2          Likewise, the citizens of Donetsk shouldn’t vote, “Russian or Ukrainian?” – these two adjectives are also not a duality.  Apart from the Crimean Tatars, most Ukrainians are of a Slav ethnicity, speak a Slavic language and (as if it matters) share a Christian religion, either Orthodoxy or (Uniate) Catholicism.  In effect, that dichotomy – “Russian or Ukrainian?” – was the question in every oblast (province) in the 1991 referendum, and again in just three oblasts – Crimea, Donetsk and Luhansk – in 2014.  

+          In the ’91 ballot, everywhere voted for independence by 80% or more… except Crimea, on only 54%.  Was it wise to assume such a small margin was a 100% victory?  Should the Crimean ballot not have included some compromise options, like ‘joint authority’?  

+          The second poll coincided with the Scottish referendum… and the word ‘Shotlandiya’ (Шотландия) {Scotland} was used by Russian separatists in Luhansk.  “Everything is connected,” as a Buddhist might say; ‘Vsyo svyazano’ (Всё связанное), to quote one Vladimir Vernadsky.

3          Brexit was also not a duality.  At its simplest level, there were four options ‘on the table’ – in the EU? the EEA? CU (Customs Union)? andWTO?  Alas, Brexit was a ‘yes-or-no?’ (‘remain or leave’?) question on only one option.  Now in first-past-the-post elections, many MPs fail to get an absolute (50%+) majority but nevertheless get elected.  In like manner, if there had been majorities against all four options, ‘in the EU’ at 52% might have been the least unpopular.  Which is the most popular.  The winner!  

So this paper first analyses majority vote decision-making, politically and mathematically, before then describing a more holistic polity.

A POLITICAL ANALYSIS

In 1985, Mikhail Gorbachev’s coming to power marked the end of the Cold War.  (Westminster then declared it had no strategic interests in Northern Ireland, and hence, later that year and 16 horrible years overdue, the Anglo-Irish Agreement.)  Change was also afoot in the USSR, now to split into its 15 republics, with privatisation and democratisation.  

But economies should never be privatised at a time of basic deficits!  Sadly, on western advice, the rouble was floated.  It sank.  For Europe, Siberian oil was now cheap.  For Russians, it prompted lots of speculators to go to the supermarkets – ‘Producty,’ as they are still called – buy up all the foodstuffs and then sell them outside the metro stations… at ‘x’-times the price!  Hence the oligarchs.

Secondly, a binary form of democratisation should never be introduced into a binary society like that of Nagorno-Karabakh.  1988 marked the first of many Caucasian ethno-religious clashes – this one was Armenian v Azeri, Christian v Moslem – and a Moscow headline read, “This is our Northern Ireland,” ‘Vot – nash Olster,’ (Вот – наш Ольстер).  

History, yes, repeats itself.

+          In the 1920s, albeit without referendums, Ireland opted out of the UK… and Northern Ireland opted out of Ireland: hence The Troubles;

+           in 1991/2 in the Balkans, “all the wars in the former Yugoslavia started with a referendum,” (Oslobodjenje, Sarajevo’s newspaper, 7.2.1999).  At the same time, in the USSR, (a) Georgia and (b) Ukraine opted out of the Soviet Union, so (a) Abkhazia and South Ossetia opted out of Georgia, so the region of Akhalgori opted out of opting out and opted back into Georgia; and (b) in 2014, Donetsk supposedlyopted out of Ukraine, so a part of Donetsk, the region of Dobropillya, supposedly (but unsuccessfully) also opted out of opting out, like Akhalgori, and opted back into Ukraine.  

+          Later, in 2022, Putin changed his mind: he now wanted Donetsk to be, not independent, but incorporated into Russia.  Accordingly, in another Donetsk referendum, a majority vacillated in exactly the same way, supposedly.  

Initially, Russia criticised these referendums – it was all part of ‘matrioshka nationalism,’ apparently, so called, after those famous Russian dolls – until, that is, 2006, when Putin took advantage of a referendum in South Ossetia.

In a nutshell, President Wilson’s right of self-determination is inadequate; (he later confessed he hadn’t known there were so many Germans in the Sudetenland).  Majority rule may perhaps be fine; but a majority opinion cannot be identified in a binary vote if the question posed is a non-duality.  

Despite its appalling history, many westerners believe in majority voting; that we are democratic; and, in a word, that we know, well, everything.  Which implies, of course, that others, like Mikhail Gorbachev, know little.  So, back to 1985 and his perestroika.   He knew what to do: to privatise, to democratise… but, we thought, he didn’t know how to do it.  Accordingly, lots of ‘monolingual experts’ rushed over to Moscow to say, “Mr Gorbachev, you need majoritarianism.”  This translates to, ‘Mikhail Sergeyevich, Vam nuzhen (you need) bolshevism!’  (Вам нужен большевизм!)  Alas, we are all little Bolsheviks.  So too today’s Chinese: “the minority obeys the majority,” ‘shǎoshù fúcóng duōshù,’ (少数 服从多数).  And in Article 97 of its constitution, even the DPRK talks of majority voting.

BLUNT BINARY BALLOTS

It was the Greeks, of course, 2,500 years ago, who first used this voting procedure, and then the Chinese, about 400 years later.  Majority rule was obviously better than any minority diktat, and this (very binary) logic endured... and still endures.  Even in 1776, when Jeremy Bentham spoke of the superlative of the superlative, “the greatest happiness of the greatest number,” people still adhered… and still adhere, to this comparativevoting procedure!  

Yet several multi-option decision-making methodologies were by now available.  Already over 1,000 years old, plurality voting was first used in China in 1197 by the Jurchen Jīn Dynasty; (alas, in 1206, a Mongolian assembly or Khuriltai then elected Chinggis Khan).  So back to Europe where, after the Dark Ages, approval voting (1268) and the Borda Count (1433) became quite popular.  Next, in France, not least because you cannot use binary ballots to best identify (an average height, “small or tall?” or) an average opinion, la volonté général – “left- or right-wing?” – l’Académie des Sciences devised the Modified Borda Count MBC in 1770, the two-round system of 1775 and, ten years later, the Condorcet rule.  1821 saw the English Alternative or Single Transferable Vote – it’s also called Ranked Choice Voting – and all these voting procedures can be used in decision-making.

But first, in 1789 in France, la revolution, l’Académie became l’Institut Français, and its new boss ditched the MBC and reverted to majority voting.  So he could choose the options.  He chose just one, himself.  And in a non-duality, a binary referendum in 1803, Napoléon thus became l’empereur, a ‘democratic dictator’ he might have said. 

A MATHEMATICAL ANALYSIS

Politically, then, in democracies and autocracies, and especially in conflict zones, majority voting is at least inadequate, at worst a provocation.  It’s now time to consider a mathematical analysis, and there are two types of binary ballots:

           singletons           like “Option X, yes or no?” 

and

            pairings,             such as “Option X or option Y?”

Consider a simple example, a committee of twelve where, all are agreed, the front door needs repainting.  Five move the motion, “Let it be Amber.”  Four propose an amendment, “delete ‘Amber’ and insert ‘Black’,” and three suggest, ‘Claret’, A, B and C.  Let us assume their preferences on the four options – the motion A, the possible amendments B and C, and the status quo S – are as shown:

Preferences	Number of Voters
	5	4	3
1st	A	B	C
2nd	B	C	S
3rd	C	S	A
4th	S	A	B

With singletons, options A, B and C lose majority votes by 7, 8, and 9 votes, respectively, and S loses, 0-12.  There is indeed a majority against everything.  So singletons are no good.  

While with pairings, A > B by 8:4, B > C by 9:3, and C > A by 7:5, so A is more popular than B, B more than C, and C than A, so that

A > B > C > A > B ….

which goes round and round for ever!  The so-called ‘paradox-of-binary-voting.’  So the outcome could be anything; there are three possible winners: A or B or C.  So pairings aren’t much good either.  We also see that S > A, B > S, and C > S.  

The Greeks were aware of these complications.  Accordingly, they devised the following procedure: in this simple example where there are four possible outcomes – A, B, C or S: 

            first,                  select, the more popular amendment                                      B v C

            next                  choose the substantive, the motion original or amended          (B v C) v A

            and finally          make the decision                                                              {(B v C) v A} v S

So, with these three votes, all pairings, there will always be a definite decision, even when a majority doesn’t like that result.  In this instance:

{(B v C) v A} v S =          {B v A} v S         =          A v S                 =          S.

So having decided, verbally, that they don’t like S, they then decide, democratically, that they like S.  So majority voting is still no good!  Indeed, it’s worse.  If the motion is option B, to paint the door Black, and the two amendments are for A and C, the decision is: 

            {(A v C) v B} v S            =          {C v B} v S         =          B v S                 =          B.

Or again, it’s:

            {(A v B) v C} v S            =          {A v C} v S         =          C v S                 =          C.

So the answer can be virtually anything.  It depends on the order of voting.  So everything depends upon the chair.  “It’s not the people who vote that count,” as Jozef Stalin once said, “It’s the people who count the votes.”  Furthermore, if there’s a majority in favour of something which the chair doesn’t like, she can introduce another option, split that majority, adjust the order of voting… At its worst, majority voting is a form of ‘democratic’ divide-and-rule.

The methodology is divisive and exclusive.  As noted earlier, it is inappropriate politically.  And now we see, it is inaccurate mathematically… in all hopelessly inadequate.  In a word, it is manipulable; some politicians are manipulative; and many decisions have been manipulated… often with horrible consequences, as in non-duality independence referendums.  {Yet just such a binary poll is stipulated in the Belfast Agreement: a collective peace accord without the possibility of a collective compromise!?}

PLURALISM IS POSSIBLE

Scientific instruments are not binary: speedometers aren’t marked only ‘fast’ or ‘slow’, altimeters aren’t just ‘high’ or ‘low’; but in decision-making, we still rely on a blunt, binary tool, ‘yes’ or ‘no’.  A more accurate measure of opinions could be calibrated in preferences.

Now in majority voting, there are two ways of completing a ballot, A or B.  Thus inevitably, voters in referendums/MPs in parliaments/countries in the UN COPs, fall into two opposing camps; the procedure is exclusive, adversarial… it’s all win-or-lose.  

In an MBC, points are awarded to (1^st, 2^nd … last) preferences cast, according to the rule (m, m-1 … 1).  She who casts m preferences gets her favourite m points, her 2^nd choice m-1 points, and so on.  The winner is the option with the most points; it might be the 1^st preference of few, but if it’s the 2^nd or 3^rd preference of many, it may well represent the collective will.

Furthermore, if (nearly) everyone does cast a full ballot, this outcome will be the option with the highest average preference.  So everyvoter/MP/country is involved, not just a majority of them.  The MBC is inclusive, literally.  Voters/MPs/countries say ‘yes’ to something, or ‘yes’, in their order of preference, to two or more things.  But no-one votes ‘no’!  There is no veto in consensus voting.  

With three options, A, B and C, a full ballot of 1^st-2^nd-3^rd preferences might be A-B-C, A-C-B, B-A-C, B-C-A, C-A-B or C-B-A.  With four, there are 24 different ways a voter may cast all four preferences.  And with five options, 120 opinions or nuances may be expressed.  Thus inevitably, voters/MPs/countries could vote, not against, but with each other.  Like good Christians, Buddhists, whatever, they need not preach, “Love thy neighbours,” on Sundays, and “vote (‘for’ or) ‘against’ them!” on weekdays.  No; their exhortation is “Love and vote with!”  The procedure is inclusive, consensual… and it’s all win-win.  In a parliament, it could work like this.

A problem arises.  Every party may propose a motion, though the smaller parties might prefer a joint submission; let’s assume there are five options ‘on the table.’  Each is debated in turn.  Amendments may be incorporated, only if the option’s proposer(s) agree to that change.  And when all is said but still not done, the chair may move to a preferential vote, usually on about five options.  

The MBC is egalitarian and non-majoritarian.  If it were the democratic norm, governance at the national level could be based on all-party power-sharing.  And internationally, if adopted by the COPs for example, all 200 countries could reach agreements in the knowledge that no country ever wins everything, but (almost) every country wins something.

CONCLUSION

Collective decision-making on matters controversial may rely on majority pairings, if but only if, the two options are a duality!  Other matters may best be resolved with one or more MBCs.  In this way, countries may resolve even ethnic disputes with a compromise; the COPs may identify an international consensus; and collectively, we may proceed to a more ideal world: as stated by Longchenpa, a Buddhist monk of the 14th Century, “…the nonduality of right and wrong [is] the state of a buddha.”