Peter Emerson on how to improve voting and referendums

BRITAIN IS outside the European Union after a referendum to leave in 2016, and now the Scots are eyeing another referendum on whether to remain in the United Kingdom. But back in 2016, few Brexit supporters contemplated that the country might also leave arrangements like the European Economic Area or customs union, which it has. How did it come to this?

One factor, obviously, was the choice of the majority of voters (to Remainers’ dismay). But a bigger, less obvious factor was the ballot and voting process itself. The conventional binary voting method is outdated and needs to be modernised to produce outcomes that hew to the will of the people.

Majority voting dates back not only to Ancient Greece, but also to China’s Imperial Court of the Han Dynasty, which began around 200BC. There were no political parties at the time (and only men could vote); the majority-wins method worked fairly well. In Greece, the citizens’ decisions were then implemented by an executive, initially elected but later chosen by sortition, that is, random selection. In China the executive, the emperor, usually accepted the majority views of his ministers.

However this classic form of majority, binary voting that characterises the democratic tradition is as archaic as wearing togas or driving a chariot. A major limitation was identified by Pliny the Younger, a senator in ancient Rome.

In the year 105 AD a consul was murdered and his servants stood accused. The jury was faced with three options: acquittal, banishment or capital punishment (memorable as A, B or C). The wise senator realised that if they took a binary vote on, say, “execution: yes or no?” the A and B proponents would collude against the C crowd. With “acquittal, yes or no?” B and C might both oppose A. And so on. If the breakdown of support for A, B and C were, say, 40, 30 and 20, there would be a majority of 70:20 against capital punishment, 60:30 against banishment and 50:40 against acquittal.

In other words, if there is no majority for any one option, then there is a majority against every option. If the issue entails multiple options, it will be hard to spot majority preferences—and society will suffer. People grasp the idea of ranked preferences when it involves weighing up several candidates in an election—in New York City’s mayoral primary in June, voters can rank up to five candidates—but politicians often misframe political questions in terms of a dichotomy, where broader thinking is needed most. As a way to gauge public sentiment for decisions and referendums, more sophisticated voting methods are needed, since binary systems do a poor job of settling complex issues.

Consider the case of Bosnia and Herzegovina. In 1991 this multi-ethnic region of the former Yugoslavia was barely at peace. The 1990 general election had produced a Muslim, Orthodox Christian and Catholic breakdown of 40, 30 and 20. A majority vote on any one option would therefore be inadequate. However, a European commission set up to arbitrate the tensions insisted that Bosnia have a binary referendum. Rather than resolve the issue of Bosnia’s constitutional status, the referendum a year later stoked the conflict.

There is a different way. In the late 1700s, a French mathematician and former naval officer, Jean-Charles de Borda, was frustrated at the simplicity of binary voting processes, as was the philosopher and scientist the Marquis de Condorcet. They both devised alternatives, today known as the Modified Borda Count (MBC) and the Condorcet Rule. In both, the voters cast their preferences. The MBC can identify the option with the highest average preference, whereas the Condorcet count examines each pair of options, to see which option wins the most pairings. Think of it like a football league: the MBC winner is the option which scores the most goals, the Condorcet winner is the option which wins the most matches.

With multi-option preference voting, there are several ways of analysing the results. We can choose the option with the highest number of first preferences—basically, the plurality voting we’re familiar with (notably in the “first past the post” electoral system). But we can also use a two-round system or an “alternative vote” method known as ranked-choice voting (RCV) or single-transferable vote (STV), along with the MBC or Condorcet approach.

Which system is most accurate? Consider the case of 15 people choosing among four outcomes, w, x, y and z.

Opinions on w and x are polarised; maybe y or z best represent the collective will? Watch how the views pan out under different systems:

Plurality voting: six people think w is best; nine say it’s the worst, but w wins with six: it is the largest minority.

Two-round system: Nothing has a majority; so the two leading options, w and x, go into a second round and, if everyone’s preferences stay the same, x wins since it has a majority, nine to six.

Alternative vote: This is a system of elimination. With STV and RCV, on the first count the least popular z is out and its two votes go to y for a second count of: w-6, x-4, y-5. Still nothing has a majority, so x is eliminated, and its four votes also go to y. So now y wins with a majority, nine to six.

Modified Borda Count: In full ballots, a first preference gets four points, a second preference gets three, and so on. The final scores are w-33, x-32, y-42, z-43, so this time z wins.

Condorcet: Every pair of options is analysed, to see which option wins the most pairings. There are six pairs: w-x, w-y and so on, all the way to y-z. In this last pairing, 6 + 2 voters prefer z to y, while 4 + 3 of them prefer y to z, so by 8:7, z is more popular than y. The final scores of all pairing victories are that w did not win any, x had one, y had two and z won three. Hence z wins again.

Both the MBC and Condorcet take all preferences cast by all voters into account, always. Little wonder, then, that they are the most accurate. In many voters’ profiles, the MBC winner is also the Condorcet social choice (just as, in most football seasons, the MBC winner—the team with the best “goal difference,” ie, goals for minus goals against—is also the team which wins the most matches, the Condorcet winner).

The MBC has one further advantage: it is non-majoritarian. It can identify the option which is the voters’ highest average preference—and an average involves all votes, not just the majority’s. So in parliaments, the MBC could defuse polarisation and be the basis of cross-party power sharing. No majority has the right to dominate, no minority has the right to veto; instead, all have a responsibility to seek the common good.

However, there are some shortcomings to these approaches. It’s more complicated than binary voting, so public-information campaigns are needed to explain how it works. And the choice of options must be made independently, or it could favour certain outcomes. Moreover, the option with the highest average preference score may need to surpass a threshold to be regarded as the best possible compromise—if under that threshold, then maybe there is no agreement and debate should continue. Still, for intricate sets of choices, these systems work better than yes-or-no questions.

Or in-or-out ones. For Brexit, the situation was inherently multi-optional. Britain could have chosen to stay in the EU (option a) or leave the EU but stick with the EEA (b), Customs Union (c), or World Trade Organisation (d). The referendum result showed 52% of voters against option a. Doubtless the other options would also have lost any corresponding majority votes. So at 48%, maybe option a had the “largest minority”: was option a perhaps the winner?

We’ll never know because the vote was structured in an overly-simplified, binary ballot. It did not match the reality of how such a complex question should best be decided, and failed to clearly reveal public sentiment. But it isn’t always this way.

When Slovenia held a referendum on its electoral system in 1996, three options were on the table. None of them won a majority of support, so the Constitutional Court validated the option with the biggest minority, which was 45%. When New Zealand held a referendum on its electoral system in 1992, it included no fewer than five options on the ballot. (Britain, meanwhile, has long been stuck in a binary mindset: a referendum on electoral reform in 2011 offered the choice of first-past-the-post or alternative vote. For supporters of proportional representation, that was like asking a vegetarian, “beef or lamb?”)

Applying preferential-choice voting to political decisions is not hard. All that’s needed is for an independent election commission to redesign ballots and restructure their vote-counting processes, along with educating voters to understand the new system—fairly basic tasks. The simplicity helps explain why America has been adopting rank-choice voting systems for municipal elections (as well as for the Oscar for Best Picture).

In the case of Scotland, one could imagine such a commission being set up to accept submissions from the public on questions to be brought before voters: on whether an independent Scotland would have its own currency, embassies, army, monarchy and yes, rejoin the EU. These questions are complex and can best be captured, not in a simplistic stay/go dichotomy, but as a series of options. At the very least, framing the decision this way would allow for a more nuanced debate.

As well it should, since a preferential system corresponds more neatly to how individuals make decisions in life: it’s rarely between two stark alternatives but usually about choosing among a myriad of options. The method also tends to result in centrist positions, not polarised extremes. Whether working out a punishment in ancient Rome or deciding constitutional questions today, society needs to adopt a multi-option method of decision-making to identify more accurately the collective will.

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Peter Emerson is the director of the de Borda Institute which advocates for reform of voting systems globally