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David Cameron and the Three ‘Whiches’

By Peter Emerson

This is a saga of sadness, a tragic tale of three ‘whiches’: a fairy ‘which’, a whichsoever ‘which’ and a wicked ‘which’.  In initiating each of three referendums, David Cameron said, “You have a choice, ‘this’ or ‘that’, which do you want?”  So all three ballots were binary, and while the first two delivered what he wanted, the last one was, in effect, political suicide.

All three outcomes were inaccurate reflections of ‘the will of the people’.  Let’s have a look, and then let’s consider a better methodology.

The 2011 referendum on the electoral system

After the 2010 general election, the UK had a coalition government: Cameron’s Conservative Party (Tories) and the Liberal-Democrats.  And he probably thought to himself, “How can I rid myself of the Lib-Dems’ persistent pursuit of proportional representation, PR?”  Hence the first ‘which’, so to silence any further debate on electoral reform.

Some people liked single-seat constituencies, either the UK’s first-past-the-post, FPTP, a plurality vote; or France’s two-round system, TRS, a plurality vote followed by a majority vote. Both are single preference systems. Or there is the Australian alternative vote, AV, a preference vote which is like a knock-out competition – in a series of plurality votes, the least popular is eliminated after each round and his/her votes are transferred to the voters’ second or subsequent preference, until a candidate gets 50%. Meanwhile, many wanted pr in multi-member constituencies. There is the German half FPTP and half pr-list system called multi-member proportional, MMP. There is PR-List – in Israel, you vote for a party; in the Netherlands, for a candidate of one party; in Belgium, for one or more candidates of one party; and in Switzerland, for those of more than one party.  Or there’s the Irish PR-single transferable vote, PR-STV, where voters can vote cross-party in order of preference. ATV is like av except that success depends on (not a majority but) just a quota of votes. Overall, then, the choice was huge.

But Cameron’s first preference was FPTP and his second was av. So that was the 2011 referendum, the first ‘which’: “FPTP or AV, which do you want?”  For countless (and uncounted) supporters of pr, this was like asking vegetarians, “Beef or lamb?” Now maybe FPTP was the most popular but, based on data from just a two-option poll, impossible to say.

For Cameron, however, it was a dream: he chose the question, and the question determined the answer, just as any fairy godmother would have wished: a massive 67.9 to 32.1%.  Magic. Furthermore, the Electoral Commission said the question was fair. Amazing. The Ombudsman agreed. Incredible. And many thought this was all democratic. So that was the end of that argument. So why not a second fantasia, another referendum?

Scotland 2014

“Double, double, toil and trouble,” said the witches in Macbeth, “the Scottish Nationalist Party, SNP, always on about independence. How can I rid myself of these skittish Scots?” This was Cameron’s second problem, and so, as if on a broomstick from the darkest recesses of Westminster, the second ‘which’ enters the political stage.

There were three options: (a) the status quo, (b) maximum devolution or ‘devo-max’ as it was called, and (c) independence.  Thinking that (a) would easily beat (c) in a two-option contest, just as FPTP had wiped out AV, Cameron waved his wizard’s wand and demanded a binary ballot.  So the second ‘which’ was again dichotomous: “(a) or (c), which do you want?”

In the campaign itself, however, the gremlins were grumbling, option (c) was gaining ground.  Cameron et al twitched; no – panicked; and so, as if at the witches’ coven, a vow was made – zap! – and option (a) morphed into option (b). On the ballot paper, however, there was no switch, the ‘which’ was still “(a) or (c)?”  So the result was a stitch-up: 55.3% and 44.7% respectively were highly inflated levels of support for (a) and/or (c). Furthermore, the winner was (b)… but no-one had voted for it!

For Cameron, though the potion was fading, the plebiscite was still successful, and that was the (very temporary) end of that argument too.  We return to the diviners’ den.

The EU referendum

Believing as it does in majority voting, the Tory Party (and many another) is a beast of two wings and no body; little wonder that this weird creature is often in a flap, especially over Europe. “Those cursed Europhobes,” he might have muttered.  And then, stage extreme right, another scary monster, the UK Independence Party, UKIP.  “Oh how can I rid myself of these damned devils?”  Ah-ha, the third… but this was the wicked ‘which’.

The wrong side won.  The Electoral Commission’s semantic change from ‘yes-or-no?’ or ‘in-or-out?’ to ‘remain-or-leave?’ did not change the poisonous potent of the poll, its binary bind, its divisive ‘positive-or-negative’ nature.  The question – “Which do you want?” – was again adversarial.  The campaign was horrible. And the result?  48.1% chose ‘remain’ to 51.9% ‘leave’.  But nobody knows what the latter actually want!  To suggest, then, that this outcome is ‘the will of the people’ is, again, bunkum.  Meanwhile, politically, Cameron is dead, impaled on his own petard; in a word, ‘bewhiched’.

Democratic theory and practice

So what should have happened? Well, consider first a hypothetical example. The average age of the electorate cannot be identified by a majority vote. If such a piece of research were to be attempted, the question would probably be, “Are you young or old?”  In which case, no matter what the answer and by what percentage, it would be wrong!  If, however, the question were multi-optional, “Are you in your twenties, thirties, forties, etc.?” the answer could be pretty accurate.

With average age or collective opinion, as in a German constructive vote of confidence, voters should be positive. No-one should vote ‘no’ or ‘out’ or ‘leave’; instead, everyone should be in favour of something: for the UK to be in the EU, or like Norway in the EEA, or like Switzerland in a looser arrangement, or independent of both organisations, or whatever.

When New Zealand debated electoral reform in 1992, an independent commission produced a short list of options: FPTP, PR-STV, and three systems as it were in the middle, a five-option referendum. Thus (nearly) everyone could vote positively, and New Zealand now enjoys MMP.

A ‘which’s’ brew

If a question is binary, only one form of voting is appropriate: a (simple or weighted) majority vote.  (Very few questions should be binary, however, and even when the Swedes were asked, “Which side of the road shall we drive on?” the referendum ballot included three options: ‘left’, ‘right’ and ‘blank’.)

When there are several options, popularity can be measured in a number of ways: the option with the most 1st preferences, with the fewest last preferences, with the best average, or whatever, a points system, a league or a knock-out. Let’s have a look.

Imagine a scenario where, after a debate which leaves five options ‘on the table’: A, B, C, D and E, 12 persons have the following preferences.

Table I                        A Voters’ Profile

No of voters: 2 2 1 1 1 2 1 2
Options      A 1st 1st 5th 4th 5th 5th 5th 5th
B 2nd 3rd 1st 3rd 2nd 2nd 2nd 3rd
C 3rd 5th 2nd 1st 1st 3rd 4th 4th
D 5th 2nd 3rd 2nd 4th 1st 3rd 2nd
E 4th 4th 4th 5th 3rd 4th 1st 1st


A cursory glance would suggest option A is polarised, as four think it is the best while seven deem it the worst; option E is also divisive, while C and D have mixed support; so the option which best represents the dozen’s collective will is probably B, the 1st preference of only one voter, but the 2nd or 3rd of everyone else!

Now let’s do five analyses: (i) plurality voting; (ii) a points system – a 1st preference gets 5 points, a 2nd gets 4, and so on – the Borda count, BC; (iii) AV; (iv) a league system, the Condorcet rule, to see which option wins most of the ten pairings – A v B, A v C… B v C… D v E; and (v) TRS.  The results are as follows:

Table II          Five Social Choices

i Plurality voting A
ii BC – points B
iii AV/STV – knock-out C
iv The Condorcet rule – league D


In other words, it’s gobbledygook; like rabbits from the conjurer’s hat, the decision can be A or B or C or D or E, whichever! Democracy can be witchcraft, the sorcerer can still cast his spell. With this particular profile (and in many other circumstances), the outcome depends, in part, upon the procedure, so “It’s not the people who vote that count, it’s the people who count the votes,” to quote one Jozef Stalin.

Uniquely, the Borda and Condorcet rules take account of all preferences cast by all voters, and these two methodologies are the most accurate. Indeed, with many voters’ profiles, the Modified Borda Count, MBC (its full name) and Condorcet outcomes are the same.


In a plural society and a pluralist democracy, contentious and/or complex problems should not be reduced (and distorted) into dichotomies. For any future referendum, therefore, an independent commission should be tasked to draw up a (short) list, usually of about five options, and voters could then cast preferences on these options, prior to an MBC analysis.

Likewise, councils and parliaments everywhere should consider preference voting – a procedure demonstrated in Belfast in 1986 (and electronically in 1991) in a cross-community meeting in which over 200 participants included everything from professors to punters, from politicians to paramilitaries… but no witches.

A chronic chronicle

Once upon a time, in the Middle Kingdom during the Former Han Dynasty, advisers to the Emperor of China used binary voting, and so too did the (rich male) citizens in Greece. Democracy had taken its first step. In those days of old, however, there were no political parties, and voters could vote with each other today and against tomorrow, without falling into permanently opposed factions. Later, in ad 105, the Roman Pliny the Younger suggested plurality voting – step two.

After the Dark Ages, the 12th century Spaniard Ramon Llull considered multi-option voting. In the 15th, the German Nicholas Cusanus proposed a points system, today’s MBC. Another 300 years later, so too did France’s Jean-Charles de Borda and then England’s Charles Dodgson (so this is a fairy tale: his nom de plume was Lewis Carroll, the author of Alice in Wonderland). While today, with India’s Amartya Sen and America’s Kenneth Arrow, this science of many steps spans the globe.

Unfortunately however, evil men continued to practice majoritarianism, the likes of Napoleon (who had three 99%+ referendums), Lenin (the very word ‘bolshevik’ means ‘member of the majority’), Hitler (four plebiscites at 88%+), Máo Zédōng (“…we must win over the majority and smash the minority,”) and Saddam Hussein (one 100% referendum, an outcome first achieved by the Irishman, Bernardo O’Higgins, in Chile).  Furthermore, even when whole countries collapse into war as majorities/minorities fight minorities/majorities – in Bosnia, Rwanda, Syria and Ukraine, for example – people still believe in a myth, that democracy is majority rule, that a majority opinion can be identified in a majority vote, and that, inter alia, the outcomes of the three referendums mentioned above reflected ‘the will of the people’. The late Professor Sir Michael Dummett called it, “the mystique of the majority.”


So let us dream awhile. If the UK’s 2011 referendum had been multi-optional, with a multi-option choice as in a restaurant for (nearly) every taste, the UK would probably now have a form of PR. As a consequence, no one party would have a majority in parliament, so the UK would probably have a coalition government; in which case, there might not have been an EU referendum at all! And everything would be, well almost, happy ever after.

David Cameron and the Three ‘Whiches’

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