The majority vote is over 2,500 years old. It is the most ancient and most inaccurate measure of collective opinion ever invented...although, to be fair, it was only meant to be a decision-making process, an alternative to dictatorship.
The first person to criticise majority voting was Pliny the Younger who, in AD 105, suggested a form of multi-option voting: the plurality vote. But it, too, is very adversarial. The real moves towards consensus voting came with Ramon Lull in 12th century Spain, at a time when many Europeans were, of course, illiterate. The clergy were not only well educated, however, they were often the decision-makers. Lull proposed that which is now known as a Condorcet count, and some say he also laid the foundations for the Borda count (BC).
Then, in the year 1435, on the question of who was to be the Holy Roman Emperor, Cardinal Nicholas of Cusa suggested a BC, with only one variation in the rules to what is used today, namely, that the tellers should first say Holy Mass. Alas, his proposal was not adopted, and the majority vote remained.
The next steps came in 18th century France, when many were aware that the days of the ancien régime were numbered. The Académie des Sciences discussed two alternatives - the proposal of Le Maquis de Condorcet and that of M chevalier Jean-Charles de Borda - but eventually, in 1784, they adopted the BC. In both voting procedures, voters cast their
preferences on a range of options: in a Condorcet count, options are compared with each other in pairings, to see which of the two is more popular, and the option (if any) which wins the most pairings is the winner; while in a BC, preferences mean points, and the winner is the option with the most points. Both systems are very good. It's a bit like a sports league, in a way, where the winner could be the team which wins the most matches, (Condorcet), or the one which scores the most goals (BC). In most years, the winner will be the same under both systems, but obviously, there can be exceptions.
Initially, then, l'Académie adopted the BC as an electoral system, and it worked well. Alas, a few years later, a new member was not too enamoured by this consensus business. So the closed-question majority vote was re-instated. It should be said that this particular individual was not well known for his democratic idealism: his name was Napoleon Bonaparte.
Since then, many other dictators have followed Napoleon's example and resorted to the yes-or-no, for-or-against majority vote. It is, after all, a brilliant way of manipulating people, because the latter often think that they are not being manipulated. These dictators include Lenin, Mussolini, Stalin, Hitler, Duvalier, Pinochet, Khomeini and Mugabe, along with many others less obviously malign, like Messrs. Blair and Bush in the UN.
Social Choice Theory
Consensus voting re-appeared on the scene, although not under that name, in 1958, when Duncan Black wrote his now famous The Theory of Committees and Elections (footnote 3). In his introduction, he said he was not going to write about the history of decision-making because he "did not even know it had one". Today, however, both the history and the science of voting are firmly established, there are over 300 different voting methodologies to choose from, and some of them are, to varying degrees, consensual.
M. de Borda and Condorcet were both mathematicians. M de Borda recognised that the BC could be manipulated: inorder to boost the chances of his 1st preference over that which is nevertheless his 2nd preference, a voter could give the latter his last preference; the BC "is designed for honest men," he concluded. At the same time, Condorcet discovered the paradox of voting: if in a 3-option ballot, 43% have preferences A-B-C, 33% prefer B-C-A and 23% C-A-B, then in the majority vote pairings, a majority (of 66%) prefer A to B, a majority of 76% prefer B to C, and a majority of 56% prefer C to A. So A > B > C > A ... ad infinitum.
It should also be noted that while both procedures take all the preferences cast by all the voters into account, a Condorcet count can still be dominated by a majority. Furthermore, a BC can be
subject to what is known as an irrelevant alternative. When voting on options A,
B and C,
it may be that A is the most
popular; but if another option, option D is added, then when voting on A,
B, C and D,
the winner might be B
So, as Kenneth Arrow pointed out, nothing is perfect. A Condorcet count suffers from the paradox, a BC does not; a BC suffers from the irrelevant alternative, a Condorcet does not. Little wonder, then, that many have tried to combine the two.
In view of all of the above, a development of the BC has been adopted for consensus voting: it is called the modified Borda count or MBC, and it lays down procedures not only for the vote and the
subsequent count, but also for the debate which precedes the vote and count. Whether that debate is done directly or electronically, it proceeds as follows.
- An independent chair calls for the election of three impartial consensors.
- When the debate starts, participants are asked to submit proposals, which the consensors then form into a list (summarised on a computer screen).
- As the debate proceeds, questions may be asked, amendments proposed, and new ideas suggested. If at any time there is unanimous support for two or more options to be composited into one, or for one particular option to be removed altogether, then the consensors will adjust the list accordingly.
- If at the end of the debate, only one option remains, this may be adopted as the verbal consensus. If however there are a number of options still ‘on the table', then the chair may ask all concerned to proceed to a multi-option preference MBC vote.
- In a vote on, say, 5 options, a 1st preference gets 5 points, a 2nd preference gets 4 points, and so on... if, that is, the voter has cast a preference for all five options. If a voter casts only one preference, then his favourite gets only 1 point; if a voter casts two preferences, then her favourite gets 2 points and her 2nd preference gets 1 point; and so on. Thus the counting procedure encourages the voters to cast all five preferences.
- The winner is the option with the most points.
The reader may already have noticed an even bigger advantage: in the debate, everyone will know that the count does indeed take every preference cast by every voter into account. Therefore, the proposers will have tried to persuade (almost) everybody that their particular option is good if not brilliant, that it deserves a 2nd preference if not a 1st, and thus people will talk to their erstwhile (majoritarian) opponents. Consensus voting actually helps people to come to a consensus, long before they proceed to a vote! Indeed, on some occasions, the very procedures involved in consensus voting may actually facilitate the identification of a verbal consensus.
We might also note that this procedure is similar to that which is used in mediation. In conflict resolution work, the professional mediator asks open questions, so to identify all possible options; then, in an open (i.e., multi-option procedure) he asks all parties to state their preferences; and finally, she identifies the most acceptable compromise, namely, that option which has the highest average preference.
The Proof of the Pudding
Consensus voting has been used in a number of settings. The most famous instance took place in 1986, eight years before the IRA cease-fire, when over 200 people met in a public meeting in Belfast. They included members of Sinn Féin and the Official Unionists, along with others from the political wing of the UDA. There were politicians and paramilitaries, priests and pastors, the public and the police. The fact that they all came together was achievement enough; but the second fact, that they actually managed to identify their common consensus, was at least twelve years ahead of its time.
In 1991, with an even broader spread of participants, the exercise was repeated with electronic counting. In addition, a guest from Sarajevo was present, and thus an attempt was made to warn of the dangers of holding a majority vote referendum in Bosnia. Alas, six months later, at EU insistence, that is exactly what they did do... it started the war.
Further demonstrations have been conducted both throughout these islands and abroad. In addition, consensus voting (the MBC) has been used in an industrial dispute by Mediation Northern Ireland, and often by the Irish Green Party, most recently when electing its chairperson. All of these votes have been successful.
A Consensual Polity
Let us now return to the theory. Consider a hypothetical five option ballot, with options A, B, C, D and E, and let us assume that the electorate of one hundred voters casts all five preferences. If option B gets the 1st preference of everybody, it gets the maximum, the highest average preference score of 1, or 500 points. If option D gets everybody's 5th preference, then it gets the minimum average preference score of 5, just 100 points. If option A gets the 3rd preference of everyone, or if option C gets 50 2nd preferences and 50 4th preferences, then both A and C would get an average preference score of 3 or 300 points, the mean.
In real life, something(s) will always be above the mean, and something(s) else below. If in just such a five-option ballot, the winning option gets a very high average preference score, between 1 and 1.5, then this option may be said to represent the (almost) unanimous opinion of all concerned. If the winning score is from 1.5 to 2, then the winner may be called the common consensus. If it gets between 2 and 2.5, then maybe it is better to call it the best possible compromise. And if it gets a score of, say, 2.9, which is only just better than the mean of 3, then obviously all of the other options are getting very similar scores of 3 or 3.1, in which case, it is wiser to resume the debate.
In any democratic structure, it would be advisable to lay down the minimum levels of consensus required for various types of decision. During the transition stage in South Africa, they used the expression "sufficient consensus"; in Northern Ireland, they spoke of ‘key' decisions; and in the Dayton Agreement, reference was made to "national interests". None of these terms were defined in an inclusive mathematical way, and the consequences of such imprecision have often been sad.
The degree of mathematical exactness in the MBC means that it can be used at any stage of the decision-making process. If something comes out on top, with a score above the pre-determined consensus threshold, the vote may be regarded as the decision-making process, and this particular outcome may be deemed the winner. If on the other hand lots of options are very popular and a cluster of them are obviously more popular than the remainder, then the chair may regard the vote as a straw poll and resume the debate, concentrating on the cluster. Or if all the options are on roughly the same level of support, then, as already suggested, this vote should also be regarded as a straw poll, as an inconclusive one, and the open debate should be resumed.
Finally, in parliamentary circles, it is recommended that the count should be conducted according to the rules of both an MBC and a Condorcet count. If the outcome from both is the same, then
everyone may know that this outcome is a most accurate reflection of "the will of parliament"; if the two outcomes do not coincide, the debate should be resumed in a search for more options. If the one outcome is clear cut, however, (and if the parliament has been elected under a fair electoral system), then this outcome may indeed be said to represent "the will of the people".
The de Borda institute
A full description of the MBC is in Designing an All-Inclusive Democracy, Springer-Verlag, 2007.
 When used in elections, this methodology is known as first-past-the-post... even though there is no post! If there are only two candidates, one needs at least 50% + 1 of the vote to win; if there are ten candidates, a winner could scrape by on just 10% + 1; and the world record is held by Papua New Guinea where, with a multitude of candidates, a member of parliament was elected on only 6.3% of the vote. (Electoral System Design, IDEA, 1997.)
 In one form or another, the BC is used in elections in Kiribati, Nauru and Slovenia. Variations of the BC are also used in events like grand-prix motor racing and the Euro-vision song contest. The Condorcet count is not used in any national democratic structure.
 Duncan Black, The Theory of Committees and Elections, Cambridge, 1958, p 180.
 In the Oct. 2002 debate on Iraq, only one draft of resolution 1441 was on the table; this led to the ridiculous situation when France voted in favour of something she did not like!
A fuller list of ‘democratic dictators' is in the author's Defining Democracy, The de Borda Institute, 2002.
 ...though nothing like to the extent of a majority vote.
 The Impossibility Theorem. Kenneth Arrow, Social Choice and Individual Values, Yale, 1963.
 The consensus of those present was as follows: "Northern Ireland to have devolution and power-sharing with a Belfast-Dublin-London tripartite agreement". It was, if you like, a mini-Belfast agreement, twelve years ahead of its time.
BC - Borda count
EU - European Union
IDEA - Institute for Democracy and Electoral Assistance
IRA - Irish Republican Army
MBC - modified Borda count
UDA - Ulster Defence Association