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A second referendum on the deal with the EU: a multi-option poll

More than anything else, perhaps, the UK now needs something which is not just accurate but also inclusive.

lead Ramon Llull/Raimundus Lullus (1232? - 1316. Wikicommons/ from the collection of Friderici Roth-Scholtzii Noriberg. Some rights reserved.To identify the nation’s collective will, we need to collate the voters’ individual wills. This cannot be done in a ‘yes-or-no?’ (‘remain-or-leave?’) vote in which some people say only what they do not  want. So, logically, the 2016 referendum did not and could not identify “the will of the people.” This is confirmed by the fact that, today, nobody knows what the collective will actually is, and hence all the arguments about whether Brexit is to be ‘soft’ or ‘hard’ or whatever? Nobody knows what the collective will actually is, and hence all the arguments about whether Brexit is to be ‘soft’ or ‘hard’ or whatever...

If that ballot had been multi-optional – something like ‘the UK in the EU, the EEA, the Customs Union or the WTO?’ – each voter could have voted for what they actually wanted, and, if people had voted ‘sincerely’ rather than ‘tactically’ – to use the terms from social choice science – the most popular option could have been identified.

The correct procedure would have been to set up an independent commission, so to determine which options best represented the national debate; this was done in New Zealand in 1992, before they had their five-option referendum on their electoral system.

Multi-option polling

Consider the theory. When the House of Lords debated Lords reform in 2003, they took five majority votes on five options, but lost all of them.

If Brexit had been four majority votes on the above four-options, and if, as in the Lords, voters had cast a preference only once, then ‘in the EU’ could have got 48% and each of the other three a part of 52%.  In other words, the 2016 referendum should probably have been a victory for ‘remain in the EU’. The 2016 referendum should probably have been a victory for ‘remain in the EU’.

So what should happen now?  At the very least, academia and the media, not least the BBC, should begin talking about multi-option decision-making. (It has been in the public domain for over 800 years, after Ramón Llull first raised the subject. And he, of course, was a Catalan!)  It must further be recognised that some jurisdictions have actually used multi-option referendums, like Westminster.  Ha!  The precedent was set in 1949, when after protests in Halifax, Newfoundland was eventually allowed a plebiscite of three-options. Later, in 1982 in Guam, six options were presented to the electorate; not only that, a further option was left blank, so anyone(s) who wanted to (campaign and) vote for a seventh option could do exactly that.

In summary, a pluralist democracy is possible; and ideally, as Ramón Llull implied, the appropriate voting procedures should be preferential.

Preferential polling

In multi-candidate elections or multi-option decisions, a voter cannot express his/her opinion accurately if, á la George Orwell, he is able to say, in effect, only “This one ‘good’ and those ones ‘bad’.”  Furthermore, any calculation of the collective based on such inaccurate data will obviously also be inaccurate.  Therefore, individuals should indeed be allowed to cast their preferences. Individuals should indeed be allowed to cast their preferences. 

In let’s say a five-option debate, he who casts one preference (and says nothing about the other options) gives his favourite 1 point (and zero to the other options). She who casts two preferences gives her favourite 2 points (her 2nd choice 1 point, and zero to the other three options). And so on. So he who casts all five preferences gives his favourite 5 points, (his 2nd choice 4 points, his 3rd 3, etc.). The difference is always 1 point; there is no especial weighting.

Wanting to win, the protagonist will ask her supporters to give her option the maximum 5 points, that is, to cast full ballots. In all, she will need lots of high preferences, a few middle ones perhaps, but very few low ones; accordingly, she should try to persuade any opponents to give her option not a 5th but a higher preference. 

This points-system of voting – the Modified Borda Count, MBC – was considered by Ramón Llull in 1199, formally proposed by Jean-Charles de Borda in 1774, and then adopted in the French Academy of Sciences ten years later.  (Alas it was replaced in 1800 by majority voting, on the orders of one not best known for his democratic ideals, Napoléon Bonaparte.)  The MBC identifies the option with the highest average preference… and an average, of course, involves every voter, not just a majority of them.  The methodology, therefore, is inclusive.  And more than anything else, perhaps, the UK now needs something which is not just accurate but also inclusive.

Any second (or fresh) referendum

Accordingly, the government should task an independent commission to receive submissions and then draw up a multi-option referendum of between 4 – 6 options. The subsequent ballot should allow the voters to cast their preferences; the count should be conducted according to the rules laid down for an MBC; and the option with the highest points total should be declared the winner. 

About the author

Peter Emerson, the child of an English Catholic mother and Irish Protestant father, is the director of the de Borda Institute, a Belfast-based NGO which specialises in voting systems for decision-making.  He has worked in several other conflict zones as well, in the Balkans, the Caucasus and East Africa.  His latest book is From Majority Rule to Inclusive Politics, (Springer, 2016).


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