Scottish independence? United Ireland? Catalonia? Hong Kong? Referendums may indeed be called, but they need not be binary – yes or no; for or against; black or white. Sadly, in both British and Irish politics, policies are invariably decided on the basis of only two options. But pluralism is possible.

Part of the problem is the fact that majority voting is an idée fixe. The Electoral Commission does not consider multi-option voting; the BBC does not (yet) discuss it; and academia is also, largely, silent. Many politicians like majority voting, partly because it’s ‘win or lose’. They like to win and win everything, and some are prepared to lose, if only in the hope that they might win next time. As often as not, and especially in a two-party state, neither side likes to compromise.

Furthermore, lots of people actually think that to be democratic, a decision must be taken in a majority vote. Other voting procedures, such as multi-optional or even preferential voting – anything that might give compromise options a chance – are seldom even on the agenda.

So it is that, on the question of decision-making, the authors of many constitutional settlements – the Belfast Agreement, the Dayton Accords, Germany’s 1949 Basic Law, the US Convention of 1776 – confine themselves to binary voting. Electoral systems are discussed in detail: the Belfast Agreement agreed to stick with proportional representation (PR) and the single transferable vote (PR-STV), Bosnia chose PR, the Germans adopted mixed-member proportional representation (MMP), and our American cousins wanted the States to be represented proportionally.

On decision-making, however, debates were stuck in a binary groove and multi-option voting procedures were not even contemplated. For example, the introduction of the 1998 edition of Germany’s Basic Law says: “The fact that members of the Bundestag take decisions on behalf of the whole German people… is a requirement… for majority decision-making.” This, might I suggest, is pure gobbledegook.

You can see the trouble caused by the addiction to majority voting in UCL’s major new report on any future unification referendums in Ireland, which contains the following oxymoron: “[The]Good Friday Agreement… stipulates that majorities of 50%+1 would be required. But the ethos of consensual politics should be upheld as far as possible.” But what if we looked for an alternative to majority voting?

Beyond yes and no

“Asking ‘yes-or-no?’ questions is very unAfrican,” went a memorable comment at a 2003 press conference in Kigali, the capital of Rwanda. One of European colonialism’s biggest mistakes was to give that country and others majority rule – Nelson Mandela called it a “foreign notion” – based on binary/majority voting. In Rwanda, doing so pitted Hutu against Tutsi: the 1994 genocide started with the slogan Rubanda nyamwinshi, “we are the majority”.

Philosophers and scientists have been campaigning for preferential voting for nearly 1,000 years. And yet, some 3,000 years after first being deployed in Ancient Greece, binary voting is still in use today, even though this most primitive and Orwellian of all voting procedures sometimes produces inaccurate results.

On the Brexit vote last Christmas Eve, for instance, UK prime minister Boris Johnson asked the Commons: “My deal: yes or no?” But did ‘yes’ imply support for ‘his deal’, or opposition to ‘no deal’? Did ‘no’ suggest a desire for Scottish independence? In any multi-option debate, binary voting can be at best ambiguous, at worst, a manipulation.

Logically, in a multi-option debate, when there’s no majority ‘for’ any one option, there’s a majority ‘against’ every option. So, when debating three options, A, B and C, if three people on a committee each have preferences of A-B-C, B-C-A and C-A-B respectively, then A is more popular than B (which we write as A > B), and B > C, and C > A, and in fact A > B > C > A > B… and it goes round and round in circles, forever.

If, then, there are lots of options ‘on the table’ – one motion plus various amendments – and especially if there is no majority for any one option, there must be some sort of decision-making structure. Otherwise, the outcome could be anything. As Pliny the Younger wrote almost 2,000 years ago: “In ancient times… [the Greeks] learned how to introduce an amendment [and] the whole of senatorial procedure.”

It works like this. You choose the best amendment; next, you choose the substantive (the motion amended or unamended); and then you make the final choice: the substantive or the status quo. Imagine, then, a committee of nine people debating tax rates for the rich, which are currently set at 40%. They all think this is far too low. Let’s also assume that four have first to fourth preferences of 70-60-50-40; three prefer 60-50-40-70; and the remaining two opt for 50-40-70-60.

Following those ancient procedures, the committee first chooses the more popular amendment, 60 or 50, and 60 wins by 7:2. Next, it’s this amendment versus the motion, 60 v 70, and 70 wins 6:3. And finally, this substantive versus the status quo, 70 v 40, which 40 wins by 5:4.

So they all agree, democratically, that what they want... is what they don’t want. The result is fake, to coin a phrase. Doctors don’t use binary thermometers: is the patient hot or cold? Nor do pilots use binary altimeters: is the plane high or low? Only politicians use a binary tool. And, as in this example, binary decision-making is just not fit for purpose. The outcome is sometimes wrong.

By contrast, a preferential vote on four options – A-B-C-D, D-C-A-B, C-B-D-A etc. – allows for 24 different opinions and nuances. It reduces both ambiguity and the possibilities for manipulation. So with four options and four preferences, an average preference score can vary from the highest score of 1.00 (all first preferences) to the lowest of 4.00 (all fourth preferences). In the above example about tax rates, 70, 60, 50 and 40% get average preference scores of 2.44, 2.11, 2.23 and 3.22; so the collective will, a composite between 60 and 50, is exactly 56%.

Alas, politicians like binary voting. Usually, with majority voting, the political leader chooses the question – and usually, the question is then the answer. Hence the majority votes for ‘democratic’ dictators like Napoléon, Lenin and Hitler, as well as those of ‘dictatorial’ democrats.

In the three-option debate in Scotland in 2014 – independence, the status quo or ‘devo-max’ – David Cameron thought there was a Scottish majority for the status quo. So he dictated a binary question: independence versus status quo. The campaign ensued. The SNP was gaining ground. In Westminster, there was panic. The ‘status quo’ option morphed into ‘devo-max’ – and devo-max won. But nobody voted for it, since it wasn’t on the ballot paper.

The 2011 referendum on the UK’s voting system was another nonsense. After all, asking a supporter of PR “first-past-the-post (FPTP) or alternative vote (AV)?” is like asking a vegetarian “beef or lamb?”

In conflict zones, binary questions are far worse. Asking someone from Belfast “Is Northern Ireland British or Irish?” all but disenfranchises people in mixed relationships and their children. Or to quote Sarajevo’s legendary newspaper, Oslobodjenje in February 1999: “all the wars in the former Yugoslavia started with a [binary] referendum.”

What are the options?

Multi-option voting was first used in China in 1197, by the Jurchens in the Jīn Dynasty. Two years later in Spain – no connection – Ramón Llull spoke of preferential ballots. The world’s first referendum to embrace pluralism was in New Zealand in 1894, with three options. There, too, in 1992, an independent commission produced a referendum shortlist of five electoral systems – PR-STV, FPTP, plus three in the middle. After two rounds of voting, the winner was half-PR-list and half-FPTP. In other words, a compromise.

Some binary referendums are sort-of OK: the 1998 Belfast Agreement was one such, as was Ireland’s 2018 referendum on abortion. So was Norway’s 1905 referendum on independence: 99% on an 85% turnout. Preferential voting, though, might have been even better.

Sadly, UCL’s Working Group on Unification Referendums on the Island of Ireland did not consider multi-option voting procedures. There are in fact quite a few ways of identifying a democratic majority opinion. The first two might indicate only the option with the largest minority.

• Multiple majority votes, as in Slovenia’s three-option ballot in 1996, in which nothing got a majority, but the largest minority was 45%, and so this was the winner
• Plurality voting, as in the Danish parliament

The next three can definitely indicate an option with majority support:

• The two-round system, as in New Zealand, Finland and Guam (see below), which was also deployed by Britain in a 1948 referendum for Newfoundland.
• AV, which was the SNP’s referendum policy in 1997 and initially in 2014
• A modified Borda count (MBC), forms of which are used in elections in Nauru and Slovenia, and once in 2003 in decision-making in Dublin City Council

Perhaps the most inaccurate referendum of all was the Brexit vote: a multi-option debate, but a majority vote on only one of the options. If there had been other majority votes on the other options – the EEA, the customs union, the WTO – maybe they, too, would have lost. And at maybe 48%, ‘Remain’ was perhaps in fact the winner, as it would have been in Slovenia. Binary voting can be hopelessly inaccurate.

In contrast, the best referendum was perhaps the one held in Guam in 1982, a constitutional plebiscite with six options on the ballot paper, plus a seventh left blank so anyone with another idea could campaign and vote for exactly that. Complicated? Not at all. The proportion of invalid votes was 0.85%.

But back to Northern Ireland. The Belfast Agreement does not preclude people from thinking and talking about different options. Alas, in its report, the UCL working group acts as if the agreement does indeed preclude even a preliminary, non-binding, multi-option vote. There might be one or perhaps two binary polls, it says, while the agreement itself stipulates a possible ‘never-end-um’; a binary referendum every seven years or so. But a non-binding preferential poll as a preliminary? Such an idea was proposed, but not mentioned let alone discussed, and not even listed in the final document. The binary vote idée is indeed fixed. God help us all if it is ever used in Kashmir (as per UN Resolution 47) or Xīnjiāng.