The human race must work together. Just as you can no longer fight a war during a pandemic – and hence the Covid-19 cease-fire in Yemen – so too we may not survive if we continue to talk and vote against each other.

Binary voting is a blunt instrument. We cannot best measure the temperature of a coronavirus victim with a thermometer which registers only ‘hot’ or ‘cold’. Likewise, we cannot best identify an individual’s opinion with a tool which is calibrated only ‘for’ or against’. Furthermore, majority voting and its consequence, majority rule – majoritarianism – has been a major cause of countless tragedies: the civil war in Yemen we mentioned, as well as those in Syria and Ukraine; ‘the Troubles’ in Northern Ireland; the genocide in Rwanda – it was initiated with the slogan “rubanda nyamwinshi” (we are the majority); the break-up of Yugoslavia, where “all the [1990s] wars started with a referendum,” (Oslobodjenje); the anti-rightist campaign in China, in which Máo Zédōng wanted “to smash the minority”; and in the Soviet Union… well, the Russian word for ‘majoritarianism’ is ‘bolshevism’.

Now you cannot identify “the will of the majority” in a binary ballot without (a politician) ‘identifying’ it earlier and putting it on the ballot paper. Secondly, a yes-or-no vote is inadequate if we want to know what everybody wants, because some people will say only what don’t want – that is, they’ll vote ‘no’. So perhaps we should ask, “What do you want?” Or maybe we should pose a different question: “What do you think is best for the collective?”

In the year 105, Pliny the Younger realised that, when there is no majority for any one thing, there is a majority against every single thing. So majority voting is not the means by which a conflict can be resolved; it is a recipe for conflict… as in Brexit; or war… as in the Balkans.

Little wonder, then, that some have advocated a more accurate measure: preferential voting. The first was Ramón Llull in 1199, and others like Jean-Charles de Borda in 1784 have studied the problem in detail. After all, when people are expressing preferences, we could identify the option with the highest number of 1st preferences (plurality voting); or have a knock-out (single transferable vote); or run a league, with the winner being the option with the highest average preference (a Borda count), or whatever. M de Borda opted for the average, because an average includes every voter, not just a majority of them.


It works like this. Those concerned debate the problem and, if there is no verbal consensus – in other words, if there are still quite a few options ‘on the table’ – a ballot paper is drawn up and the participants then cast their preferences.

In the count:

  • The person who casts only one preference gives his/her favourite just 1 point;

  • The person who casts two preferences gives his/her favourite 2 points (and his/her 2nd choice 1 point);

and so on, so in an n-option ballot,

  • Those who cast all n preferences give their 1st preference n points [their 2nd choice (n-1), their 3rd (n-2), etc.].

The formula reads as follows: in a ballot on n options, (and n is normally between 4 and 6), a voter may cast m preferences, so needless to say n ≥ m ≥ 1. Points shall be awarded to preferences cast according to the rule:

(1st, 2nd … last)

(m, m-1 … 1) Rule (i)

Unfortunately, someone changed this to:

(n, n-1 … 1) Rule (ii)

which is the same, mathematically, as:

(n-1, n-2 … 0) Rule (iii)

and rules (ii) and (iii) are both called a Borda Count, BC.

Now ideally, as noted, we work with each other. So nobody votes ‘no’. We cast our 1st preference, but we also state our 2nd and subsequent preferences, our compromise option(s). In so doing, the voter recognises the validity of his/her neighbours’ aspirations and, as it were, acknowledges that, even if the democratic will is for her last preference, she will nevertheless abide by this democratic decision.

Unfortunately, people sometimes assume that a 1st preference, if cast, shall get n or (n-1) points, as in rules (ii) or (iii), regardless of whether or not the voter has cast his subsequent preferences. So the incentive is to cast just one preference… but if everyone does that, the voting procedure morphs into a plurality count, which M de Borda critiqued at length. He advocated rule (i), which today is called the Modified Borda Count, MBC. Of course, if everyone casts full ballots, analyses by all three of the above rules will produce the same outcome. If however some voters cast partial votes for only one or some of the options listed, the outcome under rule (i) might be very different from that of rules (ii) or (iii). An Taisce has used the MBC at recent AGMs.


The science of climate change can be quite complex. The science of social choice can also become pretty complicated. The main point, however, is this: while unanimity may be difficult or, in international gatherings, COPS and so on, almost impossible, there are lots of ways of identifying a majority opinion. Relying on a verbal consensus might – and often does – take all night. A preferential vote can be expedited efficiently, and more fairly; no one wins everything, but everyone wins something. Voting should not be a win-or-lose contest but a win-win compromise. And the diversity of our species should be enjoyed.

by Peter Emerson, The de Borda Institute