Written by Peter Emerson, Director of the de Borda Institute
“Are you Russian or Ukrainian?” they asked. And now they’re killing each other. But the two are not opposites: (they are perhaps dissimilar in Siberia, but to the West of the Urals), both are mainly Slav and mainly Orthodox, both use the Cyrillic script, and linguistic differences are few.
“Are you Serb or Croat?” was a second loaded question, implying that a denominational difference – the former Orthodox, the latter Catholic – was an ethnic one. But these Christians are both Yugo- (i.e., southern-) Slavs, and both speak the same language, albeit in different scripts.
While in Northern Ireland, “Are you Protestant or Catholic?” was yet another binary dichotomy to cause violence and bloodshed. As it happens, the author’s father was an Irish Protestant from Cork, his mother an English Catholic from Cheshire; because the future referendum will ask if we want to be either in the UK or in a united Ireland, collectively, the Belfast Peace Agreement does not cater for the ‘ethnically unclean.’ As in war, it’s either/or… as it was throughout The Troubles. In a nutshell, the peace agreement will not enable anyone to vote for peace.
Part of the problem lies in the often-quoted principle of consent: it refers only to a/the majority. If two people are to live together, both must consent, 100%; but if two communities are to live together, then, according to the Peace Agreement, the only requirement is the agreement of the bigger half, at least 50% + 1; it is a marriage without a bride.
Why, then, especially in conflict zones, do we still use a decision-making process which may all but disenfranchise those who are partners in, or the adult children of, mixed relationships, as well as, more importantly perhaps, any who might want to vote for peace? Or let’s put it this way: in our modern society, with high-tech devices at all levels of society, why in (business and) politics do we still use an ancient, divisive, exclusive and often inaccurate methodology, especially when other more precise procedures are available?
Binary Voting
Either/or questions in political decision-making go back 2,500 years, and there are two types: singletons like “Option X, yes or no?” or pairings such as, “Option X or option Y?” With singletons (as with Brexit in Theresa May’s indicative votes, or as with children at lunchtime when offered a choice of, say, swedes, parsnips, turnips or broccoli), there might be a majority against everything; but with pairings, (swedes or parsnips?) there will always be a definite answer. {In Brexit, both David Cameron and Theresa May used singletons, but Boris Johnson, (the political …..), posed a pairing: “Do you want either the worst possible deal, i.e., ‘No Deal,’ or ‘My Deal’?” So he won. But of course he won! ‘Any Deal’ would have beaten the worst possible ‘No Deal.’ And no-one knows whether or not his ‘My Deal’ was more or less popular than many another option.}
Over the years, many clever minds have realised that, when a debate has three or more options on the table, asking binary questions is inadequate. The first was Pliny the Younger in the year 105, and hence, his plurality voting. But politicians seldom like a decision-making methodology which they cannot control. With binary voting, if they choose either the singleton or the pairing, they are in complete control of the debate, if not indeed the outcome. So in 1770, for example, when Jean-Charles de Borda proposed a non-majoritarian form of decision-making – today’s Modified Borda Count MBC – Napoléon Bonaparte didn’t like it very much. He wanted to control only everything. So he reverted to majority voting, held a singleton referendum, chose himself to be the only candidate, and became l’empereur… a ‘democratic’ dictator, he might have said.
There is nothing extraordinary in the fact that powerful individuals use means by which they can retain control; what remains most odd, however, is that numerous politicians, journalists, academics and the like regard binary voting as the main form of decision-making, and they don’t even consider multi-option mechanisms like – to name just four of them – plurality voting, the two-round system TRS, the MBC, and the alternative vote AV (otherwise known as the single transferable vote STV or, across the pond, as ranked choice voting RCV).
They often debate various electoral systems, all of which, apparently, are ‘democratic,’ if only in the opinions of those countries where they are deployed. They range from the binary votes used in North Korea (which thus calls itself a Democratic Republic); to the plurality votes or first-past-the-post FPTP of India, the UK and the US amongst others; to the single-preference forms of proportional representation PR which are in The Netherlands, for example; to the preferential forms like AV in Australia and the Irish system but British invention of PR-STV. And of these, the authors of the Belfast Agreement chose the best: PR-STV: the voters, they argued, must be allowed to cast their preferences... in elections. On decision-making, however, apparently, they must not be allowed any preferences at all!
Now the Greeks of old were aware of the majority-against-everything problem, so to take a simple example of a motion A, the status quo B, and two amendments C and D, it was decided that the order of any democratic debate shall be:
i) choose the more popular amendment; C v D
ii) adopt of reject this amendment, to get the substantive; (C v D) v A
iii) decide, either the substantive or the status quo; {(C v D) v A} v B
In all, then, with four possible outcomes, everything shall be decided in three majority votes, all of which shall be pairings. So there will always be a definite outcome, (even though it may be opposed by a majority).
Imagine, then, a debate of 9 committee members, all of whom are agreed that the status quo B must be replaced; so there are three possibilities – the motion A, or as amended by either C or D. Let us assume their preferences are as in Table 1.
Table I A Voters’ Profile
Preferences | Number of Voters | ||
4 | 3 | 2 | |
1st | A | C | D |
2nd | C | D | A |
3rd | D | A | C |
So A is more popular than D, by 6:3; which is written,
A > C = 6:3
Furthermore,
C > D = 7:2
and
D > A = 5:4.
It all means that
A > C > D > A…
and it goes round and round forever; the famous paradox of binary voting.
It also means that a chairperson using binary voting can get whatever he/she wants, simply by adjusting the order of voting:
(A v C) v D = D
but
(C v D) v A = A
and
(A v D) v C = C
In summary, majority voting is manipulable; some politicians are manipulative; and many binary votes are manipulated. Little wonder then that, in any majoritarian polity, the position of chairperson is so important. And in many instances, the vote is only taken when those in power already know what the answer will be.
Multi-Option And Preferential Voting
Consider now another scenario, of 14 voters debating the re-painting of a front door: there’s the motion, “let’s paint it amber,” option A; the status quo, black, option B; and two possible amendments, “delete ‘amber’ and insert ‘cream’/‘denim’,” options C and D. And let’s now assume the 14 have the following preferences.
Table I I Another Voters’ Profile
Preferences | Number of Voters | |||
5 | 4 | 3 | 2 | |
1st | A | B | C | D |
2nd | D | D | D | C |
3rd | C | C | B | B |
4th | B | A | A | A |
In plurality voting, (like FPTP), only the first preferences are counted, so the result is A-5, B-4, C-3, D-2 and the winner is A on a score of 5. It’s not a majority, only the largest minority – but it wins.
In TRS, if no one option gets a majority in the first round, a second-round majority vote is held between the two leading options from the first round; in this instance, A and B. (TRS is often used in French elections.) And if everyone’s preferences stay the same, the result is now
A-5, B-9
so B is the winner on a score of 9 which is, of course, a majority.
AV, a knock-out system, is also based on a plurality vote. (As an electoral system, it is used as noted in Australia, while Ireland, North and South, uses the PR version – PR-STV.) And now, if no one option gets a majority in the first round, the least popular is eliminated and its votes are transferred to its 2nd (or subsequent) preference, and the procedure is repeated until an option does have majority support. In this example, the results are:
stage (i)
A-5, B-4, C-3, D-2
so D is out, and its two votes go to C for a score-line of
stage (ii)
A-5, B-4, C-5 .
and again, there’s nothing with a majority, so B is now eliminated and its 4 votes go (not to D which is no longer in contention, but) to C, for a result of
stage (iii)
A-5, C-9 . .
in which C does gain a (different) majority of 9.
And finally, for this analysis, the MBC, (a form of which is used for the ethnic minority in Slovenian elections); it is the only methodology discussed in this paper which always takes all the preferences of all the voters into account, and is indeed the most accurate. In this instance, a 1st preference gets 4 points, a 2nd gets 3 and so on; and the scores are:
A-29, B-31, C-36, D-44
so D is the winner on 44.
In other words, for this particular voters’ profile (and many another), the totally democratic decision is either A or B or C or D! The outcome depends upon the voting procedure. As Joseph Stalin used to say, (although he was referring to a different sort of abuse), “It’s not the people who vote that count; it’s the people who count the votes.”
Conclusion
Democracy is for everybody, not just a majority. The MBC is non-majoritarian. An MBC outcome is the option with the most points and at best – i.e., if everyone does cast a full ballot of all four preferences (see below) – it is the same, mathematically, as the option with the highest average preference. And an average, of course, includes every voter, not just a majority of them. Unlike the exclusive majority vote, the MBC is inclusive, literally; and surely, those who aspire to create an egalitarian society should use an egalitarian form of decision-making.
Now admittedly, some may cast just a partial ballot. But Jean-Charles de Borda stipulated that, in a four-option ballot,
- he who casts only one preference shall get his favourite just 1 point,
(and the other options shall get nothing);
- she who casts two preferences shall get her favourite 2 points,
(and her 2nd choice shall get 1 point);
and so on; accordingly
- those who cast all four preferences shall get their favourite 4 points,
(their 2nd choice shall get 3 points, their 3rd 2 points, etc.).
In effect, everyone is encouraged by the voting procedure itself to state, not only their favourite, but also their 2nd and maybe too their subsequent compromise option(s). And if (nearly) everyone does state their compromise option(s), it is easy enough to identify the collective compromise – the option with the most points.
In conclusion:
- majority voting prevents the voters from casting their 2nd preference;
- AV (STV/RCV) allows them to recognise the political aspirations of their neighbours; and
- the MBC actually encourages them to be inclusive, if need be to cross the
gender/party/religious/sectarian divides.
The MBC is unbiased: the difference is always just 1 point. A voter’s 2nd preference will always get just 1 more point than her 3rd preference, regardless of whether or not she has cast that 3rd preference.
Furthermore, the MBC is difficult to manipulate, by AI or by any other means. Both in elections and in decision-making, extremist politicians don’t like compromise, so they don’t like preferential voting procedures. And just as the success of the Alliance and Green Parties in Northern Ireland has been a direct result of our preferential electoral system, PR-STV, we may assume the converse is also true. The rise of the right in Europe and elsewhere is exacerbated by the use of simplistic voting procedures:
- (a) single-preference electoral systems like the USA’s and UK’s FPTP, or the Dutch PR-list system, for example;
and
- (bi) binary decision-making, as used in governance, in
- democracies everywhere,
- some theocracies
and even
- (when it suits them) autocracies – the word ‘bolshevik’ (большевик) means ‘member of the majority’;
and
(bii) as used in voting, in
referendums in Northern Ireland, the Balkans, Ukraine, and elsewhere;
and
elections, regularly, but only in North Korea!
Further Info
Find out more about Peter Emerson, Director of the de Borda Institute.