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Most parliaments use (simple or weighted) majority votes, hence most debates are for or against; therefore politics is adversarial.  It need not be so. 

Accordingly, this article looks at the inadequacies of all binary voting, in parliaments, referendums and constitutional conventions. Next it considers the theories of multi-option voting. Thirdly, it critiques that which is based on majority voting, namely, majority rule.  And finally, it outlines the basis of any constitutional convention.

Binary voting in parliaments

A vote on the highest rate of income tax – ‘x’ per cent, yes-or-no? – could mean that those who want it to be higher or lower both vote against – an unholy alliance. Indeed, in any pluralist parliament in any one debate, with lots of parties and opinions, there might be a majority against every motion.

In 2002, on reforming the House of Lords, there were five options: fully elected, 80/20, 50/50, 20/80 and fully appointed. So they took five majority votes… and lost the lot. A recipe for impasse.

Majority voting, which is also used in international gatherings like the UN Security Council,[1] may be simple, weighted, qualified, consociational or twin.[2] What’s more, in tight situations, results can be swung by the voting behaviour of maybe just one individual who has been ‘persuaded’ – bribed, threatened or seduced – to change sides.[3]

Is there not a better form of decision-making?

Binary votes in referendums

The 2011 referendum on the electoral system was a choice of either first-past-the-post, FPTP, or the alternative vote, AV. That is, David Cameron’s 1st preference or his 2nd. Neither is proportional. To ask any PR supporter the question – FPTP or AV? – is like asking a vegetarian, beef or lamb?

Before the Edinburgh Agreement, the SNP advocated three options for the 2014 Scottish referendum: independence, devo-max and status quo. But Cameron reckoned his favourite, status quo, would win a two-option contest against independence. So binary it was. Many wanted devo-max; nobody voted for it because they couldn’t – it wasn’t on the ballot paper; yet it 'won'. Scotland’s referendum was used as ‘justification’ by those wanting separatism in Ukraine: not the Edinburgh Agreement bit, but the binary nature of the ballot.

Thus the tragedy of the Balkans was repeated. In 1991, with wars already in Slovenia and Croatia, the EU's Badinter Commission insisted on referendums. As a result, there were umpteen plebiscites: a few were recognised; others, as in Herzeg-Bosna and the Sandżak, were not. But “all the wars in the former Yugoslavia started with a referendum,” (Oslobodjenje, Sarajevo’s now legendary newspaper, 7.2.1999).

In 2002, a referendum was incorporated into the Machakos Protocol for South Sudan. Six months later, there was renewed violence in Darfur. After all, if one region can fight, hold a referendum, and thus gain its political objective, why not another? South Sudan has since imploded. 

Was it wise to promote self-determination by referendum – in a word, Balkanisation – in Africa, a continent replete with borders geographical, historical and tribal?

Binary votes in constitutional conventions

In Egypt’s Tahrir Square, the people were united – young, old, male, female, Muslim and Copt. But then they held a referendum. Two-option voting is divisive. So they divided. And then they fought.

In Iran, in 1953, 99.8 per cent voted for socialism. Ten years later, 99.9 per cent wanted capitalism. In ’79, they voted for an Islamic Republic, by (a mere) 99.3 per cent.

In 2007, Venezuela held a constitutional referendum. In the first of two ballots, voters were asked to vote a single yes-or-no on a list of 33 questions; in the second, on 36. Both ballots were lost by 49 to 51 per cent.

Must even the most complex of questions be reduced to a dichotomy?

Binary voting in general

Stalinist results are not confined to non-western democracies: the majority in favour of the Northern Ireland border poll of 1973 was 99.7 per cent. As often happens, the majority votes in favour while the minority abstains (Crimean Tatars), boycotts (Northern Ireland nationalists), or resorts to violence (Bosnian Serbs). Where the communities are evenly balanced, as in Quebec in 1995, both sides do participate, but the outcome was in part determined by neither side.[4]

On matters of contention, then, majority voting is inadequate. As implied above, it often allows those in power to determine the question. Supposed democrats have thus abused the democratic process, but so too have unabashed dictators like Napoleon, Mussolini, Hitler, Duvalier and Saddam Hussein.

If the subject in question is not contentious, a simple ‘show of hands’ may be perfectly adequate. Disputes, however, especially in any democracy aspiring to be pluralist, should not be reduced from a discussion of many options to an (argument and) ballot on just two options.  Given, furthermore, modern cybernetics, it is now possible to use electronic preference voting, at least in the elected chamber.[5]

The theory of voting

The democratic process should determine the will of the people, (or that of their representatives). If every voter in a referendum (or MP in parliament) says what they want, it should be possible to identify the average or collective will. This cannot be done in a yes-or-no ballot,[6] but it can be done in a multi-option poll, and done well if that poll is preferential.  As in New Zealand,[7] an independent commission should consider public submissions and then draw up a (short) list, while in parliament the Speaker could consider all options and do the same.

Now, in a two-option ballot, voters may express only one of two points of view, (that or abstain): A or B. In a three-option ballot, six full sets of preferences are possible: A-B-C, A-C-B, B-A-C, B-C-A, C-A-B and C-B-A.  With four options, it’s up to 24; with five 120, and so on.

So, returning to the question of income tax, the highest rate could be 45 per cent, or 40, or whatever; presumably, nobody would argue for zero or 100 per cent. So, have the debate, consider the options, and produce a (short) list. Let’s assume it consists of five options, 40, 45, 50, 55 and 60, as on the x-axis of Table 1, while the y-axis shows the points awarded, 5-4-3-2-1 for 1st-2nd-3rd-4th-5th preferences.

She who wants 55 will presumably have a 2nd preference of either 50 or 60, while her 3rd and subsequent preferences will be even further away from 55. She will therefore have a ‘single-peaked’ set of preferences, something like 55-60-50-45-40 or 55-50-60-45-40 (shown as dotted lines, series 1 and 2).

Likewise, he who has a 1st preference of 40 will probably have a single-peaked set of 40-45-50-55-60 (shown in long dashes, series 3).

A rather incongruous set of preferences of, say, 45-55-40-60-50, (an unbroken line, series 4), would have two ‘peaks’.

Table 1           Single-peaked preferences

CLICK TO ENLARGE

Accordingly, if any MP does cast a set of preferences with more than one ‘peak’, constituents and journalists should have cause for concern. Granted, other multi-option debates might not sit so easily on a spectrum; for the moment, however, we talk only of voting theory.

And in that theory, if everyone does cast a single-peaked set of preferences, the collective opinion will also have a single-peak.  Furthermore, depending on the ‘steepness’ of that peak, this summit can be regarded as the consensus, and if that peak is between, say, 50 and 55, the exact average opinion can be calculated, 52.7 per cent or whatever.

The appropriate voting methodology is called the Modified Borda Count, MBC. Voters may cast as many preferences as they wish and points are then awarded in proportion to the preferences cast.[8] In a five-option ballot:

• - he who casts only one preference gives his favourite one point;
• - she who casts two preferences gives her favourite 2 points (and her 2nd preference 1 point);
• - And so on.
• - So he who casts all five preferences gives his favourite 5 points, (his 2nd preference 4 points, etc.).

The difference is always one point.

In effect those who,

• - abstain have no influence on the result;
• - participate partially have a partial influence; and
• - participate fully have a full influence.

Voting for only your intransigent 1st preference gives that option a one point advantage over the option you like the least. Casting five preferences gives a four-point advantage. Thus this voting procedure encourages every voter to cast a full slate, that is, to recognise the validity of their neighbours’ aspirations. This principle of inclusivity applies, even when the options cannot be conveniently positioned on a spectrum, as was the case with tax rates.

Majority rule

Democracy is often based on a decision taken by a majority. Therefore many elected chambers divide into two, a single majority party or majority coalition government versus an opposition.

As implied earlier, in some plural societies, no one individual or party (or ethno-religious group) can represent a majority, so there might always by a majority against no matter who is in power or what is proposed. Syria is at war, partly because, in the aftermath of the Arab Spring, a majority was opposed to Bashar al-Assad. But in such a country, majority rule is part of the problem. 

Elsewhere, too, it has been a cause of much suffering, as in Northern Ireland, the Balkans, the Caucasus, and the Middle East. Similarly, in Rwanda, the Interahamwe launched its genocide with the slogan, Rubanda Nyamwinshi, the majority people. In China, Máo Zédōng urged his supporters to smash one ‘minority’ after another, the nationalists, rightists and revisionists.  While in the Soviet Union, where the Bolsheviks caused the deaths of yet further millions, the very word bolshevik means ‘member of the majority’ or bolshinstvo, while the Mensheviks belonged to the menshinstvo, the minority.

So consider the democratic logic. If the collective opinion of a parliament could be determined more accurately by a voting process which was non-majoritarian, the very basis of majority rule would be undermined. Instead, in an inclusive democracy, all could work for the common good. The people could elect the parliament, (ideally, by a system of PR), and that parliament could elect the government, again by a proportional methodology.[9]

Conclusions

Many people are obsessed with majority voting. Electoral systems may and do vary; but decision-making, seemingly, must be binary. The UK's Electoral Commission said the FPTP or AV question was just fine. The Ombudsman agreed. And a 2011 Radio 4 documentary on referendums implied that they were all yes-or-no, for-or-against. 

So, inter alia, any constitutional convention must ask, how should society make its collective decisions? The ancient Greeks decided the worst of all dichotomous forms of decision-making, violence, should be replaced by democracy: majority votes. But other decision-making methodologies include AV, the two-round system, the Condorcet rule, and the MBC.  Should not the people and/or their representatives use multi-option voting?

The convention should consider not only the (electronic) procedures for any future referendums or parliamentary votes. It must also decide how it itself should make decisions, and how the overall outcome of the convention should be endorsed. Would it be wiser for the convention to consider a range of possibilities, on which the voters may then be enabled to have the final say?

[1]           The debate on Iraq in 2002, was reduced to a dichotomy: Resolution 1441, yes-or-no?  France and Germany did not like part of that resolution, but they nevertheless voted in favour. Of such are the absurdities of binary voting.

[2]           Qualified majority voting is used in the eu. Consociational voting is deployed in some plural societies. Certain referendums in Switzerland require a twin majority, a majority of voters and a majority of cantons.

[3]           See http://www.deborda.org/won-by-one/

[4]           The vote was lost by 50.6 to 49.4 per cent, and having blamed this loss on “the ethnic vote” – the Cree Indians – Jacques Parizeau had to resign.

[5]           The de Borda Institute first used electronic preference voting at a cross-community meeting in Belfast in 1991, three years before the IRA cease-fire. And six months before the Bosnian war, a guest from Sarajevo argued against any two-option referendum, not least because with a Muslim:Orthodox:Catholic ratio of 40:30:20, there was no majority anyway. 

[6]           In 2003, 99 per cent of the electorate in Gibraltar voted to say they did not want to share sovereignty with Spain. The democratic process did not identify the voters’ will: it only identified one of presumably many things which they did not want.

[7]           In 1992, New Zealand used the two-round system of voting: in a ballot of five options, the most popular choice was multi-member proportional, MMP; this won the second round by 54 per cent.

[8]           In an n-option ballot, the voter may cast m preferences such that n ≥ m ≥ 1, and points are awarded to (1st, 2nd … mth) preferences according to the rule (m, m-1 … 1).

[9]           The matrix vote, an electronic tabular mechanism, allows every MP to choose, in order of preference, not only those whom they wish to be in cabinet, but also the portfolio to which they wish each of these nominees to be appointed. At best, the outcome will be an all-party coalition, each party represented in proportional due, each minister the one most suited to his/her portfolio.