Our voting system is binary. But the solution to Brexit isn’t.

To humankind’s enormous cost, democracies use simplistic voting procedures like first-past-the-post in elections and binary ballots in decision-making.

As exemplified by individuals like Bolsonaro and Trump, these voting systems are a threat to the planet.

They say democracy is majority rule. The outcome of a majority vote, they continue, is the will of the people. Logically however, this may not be true.

Firstly, the will of the people has to be identified earlier in order to appear on the ballot paper.

Secondly, to find the collective will, you must first identify the individual wills – what do people want? This is impossible if some people are saying not what they want, but only what they don’t want. In an ‘Option X, yes or no’ ballot, if someone votes ‘No’, we don’t know what they actually do want.

How can we address this?

Would “Option X or option Y?” questions work? That leaves the question ‘what about options Z, or W?’   

Take for example the 2011 UK referendum on electoral reform, which offered a choice between the Alternative Vote (AV) and First Past the Post (FPTP). AV or FPTP? - for anyone wanting Proportional Representation (PR), that was like asking a vegetarian “beef or lamb?”  

(In 1992, New Zealand solved their electoral problem with a 5-option referendum.) 

Binary ballots don’t work when there are multiple options

A binary ballot might work if there are only two options.  When contentious problems are under discussion in a pluralist democracy, however, such moments should be rare. 

And even when the topic is dichotomous there may be more than two ways of voting. Take the question of ‘which side of the road shall we drive on?’ It seems to have only two options. But when Sweden had a referendum on this subject in 1995, they actually offered three options: ‘left’, ‘right’ and ‘blank’.  

In an election, we insist that there should be a range of candidates. Those North Korean elections which simply ask, ‘Candidate X, yes or no?’ we all recognise as ridiculous.

Similarly, when it comes to decision-making votes, we should demand a range of options. As we now know, ‘Option X, yes or no’ (‘Remain’ or ‘Leave’) decision-making is also ridiculous.  Multi-option voting is required. 

Now, if you know the number of options, you could just have that number of binary votes. The problem with this was noted as far back as AD 105 by Pliny the Younger who pointed out that if there’s no majority for any one thing, there’s a majority against everything.

We saw this exact scenario play out recently during Parliament’s ‘indicative votes’ on Brexit options when Theresa May was Prime Minster. So, as suggested by Ramón Llull 800 years ago, they should try preferential voting. 

How voting systems struggle to express ‘the people’s will’

Consider 14 people debating four options. Here’s how they vote:

Opinions on option A, it seems, are polarised.  Option B is not much better.  C has slightly more overall support.  So maybe D, the 1st or 2nd preference of everybody, best represents the collective will.

With this as the state of opinion, what is the outcome?

• With plurality voting, like in First Past the Post, A wins with 5 votes.   
• In two-round voting, as in France, it’s A vs B in round two, which B wins 9 to 5.
• With AV, as used in Australia and partially in Ireland’s Single Transferable Vote system, D is out and its 2 votes go to C, so B is next eliminated and C wins with 9 votes to A’s 5.
• In a points system where a 1st preference gets 4 points, a 2nd 3, and so on (as used in part of Slovenia’s elections) the scores are A-29, B-31, C-36, D-44, so D wins. 

Here we see that the results of the points system vote is not just different to the plurality vote – it’s the total opposite! This points system is also known as a ‘Modified Borda Count’ or MBC. It’s much more precise than plurality voting.

It is also non-majoritarian. If the MBC points system were to replace majority voting, all-party power-sharing could replace binary majority rule. So the whims of Trump or Bolsonaro would be at least trimmed.

And what could this mean for Brexit? The final decision, whether it’s taken by the new Parliament or by the people in another referendum, should be taken in a multi-option and, ideally, preferential vote. 

In this way, it may be possible to achieve that which a majority vote could never facilitate: consensus and reconciliation.

Peter Emerson is author of Majority Voting as a Catalyst of Populism (Springer, Heidelberg). www.deborda.org