Abstract
With the help of a grant from the Joseph Rowntree Charitable Trust, the de Borda Institute and the New Economics Foundation did some research into decision making. The binary majority vote is often inadequate and inaccurate, and it was thought that perhaps a multi-option procedure of preferential voting would be more suitable for a modern, pluralist society. As part of that project, an experiment was conducted on the web, based on a Modified Borda Count. The subject of discussion was the UK controversy about how to fund the political process. After a critique of dichotomous decision making and an introduction to consensus voting, this article describes the experiment, analyses the vote and makes recommendations for any future exercise.
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Notes
Thanks are due, first of all, to the Joseph Rowntree Charitable Trust, the funders. They have long been supporters of a more consensual approach to decision making, not least because of their Quaker tradition, and, as always, they were the most gentle of taskmasters. To conduct the experiment, the New Economics Foundation – www.neweconomics.org – and the de Borda Institute – www.deborda.org – commissioned open Democracy – www.opendemocracy.onet/ – to devise a web page for the debate. At the same time, Equality Studies of University College Dublin – www.ucd.ie/esc/ – was asked to design the ballot and to be the independent tellers for the count. Our thanks must therefore go to Jon Bright and John Baker, respectively, both of whom were both highly efficient and very enthusiastic. In any consensus debate, the role of the consensors is crucial, so a special word of thanks is also due to Professor Elizabeth Meehan, who provided both expertise and experience to what then became a four-person team.
He often talks about the consequences of majority voting in decision making -- the fact, for example, that societies often tend to divide into two, but he does not discuss decision making as such (Duverger, 1955: 387). He does, however, consider the effects of different electoral systems.
A full list of ‘democratic dictators’ can be found in Emerson (2002: 104–110). Majority voting has been used by some, such as Napoleon, in referendums, and by others, such as Lenin, in internal party votes. Indeed, in its original meaning, the very word ‘bolshevik’ signified ‘a member of the majority’, ‘bolshinstvo’; meanwhile the ‘menshevik’ belonged to the minority, ‘menshinstvo’.
Here Horowitz is talking about conflicts in Africa and other parts of the developing world.
7 February 1999.
He did not use the specific term ‘Borda count’, but he did say, ‘The right way … is to ask all of us to rank the seven options from one to seven and then add up those rankings. If one's most preferred option is ranked one and one's least preferred option is ranked seven, once the rankings are added up, the option with the lowest total ranking is the preferred option’ (Hansard, 22 January 2003).
Taken from an interview with Alexandra Runswick, which was published by Unlock Democracy in Spring 2005: http://www.unlockdemocracy.org.uk/wp-content/uploads/2007/01/2-robin-cook.pdf. He did not specify which type of preference voting he would have advocated. It would appear that he wanted, initially, to get acceptance for the principle, and later debates could focus on the detail.
Statements such as, ‘Democracy rests upon the principles of majority rule …’ from the US Department of State (http://usinfo.state.gov/products/pubs/principles/what.htm) are often interpreted to mean that ‘Democracy works on the basis of a decision by the majority’ (Report of the Constitution Review Group, Government of Ireland, 1996, p. 398). The majority vote referendum is described as ‘blunt’ by Vernon Bogdanor (1981: 92), but binary decisions in Parliament are often equally crude. Margaret Thatcher's two-option vote on the poll tax, for example, was meant to be a vote on local government finance; other options such as a local income tax and a land tax, however, were not on her agenda.
Given the role of the consensors and the possibility of compositing, it is probably fair to say that the MBC is even less prone to abuse.
Ramon Lull may have suggested this methodology in the twelfth century (McLean and Urken, 1995: 16–23). When M Jean-Charles de Borda first suggested this methodology in 1784, he was unaware of any earlier suggestions.
To put it more generally, in a BC ballot on n options, those who cast their first, second … penultimate and last preferences shall effect n, n−1 … 2, 1 points.
If in a BC all the voters express only a first preference, the procedure degenerates into a plurality vote, which is of course adversarial and unconsensual. The same is true of approval voting, if and when the voters approve or disapprove of just one option (Brams, 2008).
M de Borda first proposed that which is now called the Borda count in his Mémoire sur les élections au scrutin in 1781. For a voter’s bottom preference, next one up etc., he suggested the formula a, a+b, a+2b …, as well as a=1 and b=1 (Black, 1987: 158). So a voter who casts, say, three preferences awards 1, 2 and 3 points to his third, second and first favourites. This is a formula that caters for partial voting. Some have interpreted de Borda’s paper in reverse order to suggest that in an n-option ballot, points should be awarded to first, second … and last preferences according to the formula n−1, n−2 … 0, which does not cater for partial voting (Ibid, p. 59); many now follow this rule. Because the difference is so profound, the dBI uses the term MBC, as defined in the next footnote.
In the MBC, as advanced by the de Borda Institute, those who cast their preferences for all n options shall affect n, n−1 … 2, 1 points, while those who vote for only m options, where m<n, shall affect m, m−1 … 2, 1 points. In mathematical terms, this reads as follows: a voter's xth preference, if expressed, gets 1 more point than her (x+1)th preference, whether or not she has expressed that next (x+1)th preference.
There have been three suggestions as to how a partial vote should be counted. In a five-option ballot, a voter exercising a full ballot would cast his first-second-third-fourth-fifth preferences; for a voter who casts a partial ballot, voting for, say, only her first-second preferences, the points awarded may be allocated either as in a BC or by averaging out the points for those preferences uncast, or as in an MBC: BC: 5-4-0-0-0 averaged: 5-4-2-2-2 MBC: 2-1-0-0-0 The first two methodologies incentivise the voter to cast only one preference, the first more so than the second; the MBC, in contrast, is mathematically neutral.
The person who submitted this blank ballot participated at (rather too much) length in the debate and was ‘happy to support [this] intellectual exercise’, he said, by talking … but not by voting.
During the transition stage in South Africa, the term used was ‘sufficient consensus’, but it was never defined (Mandela, 1994: 714). In the Belfast Talks, in contrast, a ‘triple-lock mechanism’ was defined as ‘the support of parties representing a majority of the total valid poll, a majority of both communities as represented by the parties in the negotiations, and a majority of the parties involved in the talks’ (de Bréadún, 2008: 28).
Compositing may take place (i) only if the participants are forewarned of the possibility; (ii) only if the most popular options are compatible and ‘adjacent’; and (iii) only if voters have expressed ‘single-peaked preferences’ for these options. A single-peaked preference is best described via an example: in a five-option debate on dog licenses, if the options were A – €10, B – €5, C – €2, D – €1 and E – €0, then if someone's first preference was, say, option D, one would expect his second preference to be either C or E and so on, that is, to be ‘single-peaked’, and one would definitely not expect the following order, for example: D, B, E, A, C, an order that, if displayed graphically, has two ‘peaks’. If, then, in the count, options B and C were equally popular, doubtless the consensors would decide to set the final figure at €3.50.
The theorem states that there is no such thing as the perfect voting system, that is, a counting procedure the transitive outcome of which complies with conditions of non-dictatorship, independence, Pareto optimality and universality (Arrow, 1963).
A Condorcet count is not prone to the irrelevant alternative; a BC/MBC is not in practice subject to a paradox. Therefore, if the count is conducted according to both methodologies, the outcome is more likely to be highly accurate. Hence, the theories of Nanson, for example (Emerson, 2007: 17).
In a five-option ballot, as noted earlier, if everyone submits a full ballot, the highest possible average preference score would be 1 and the lowest 5. In a nine-option ballot, again with full ballots, the lowest would be 9. In the former case, the mean average preference score would be 3; in the latter, 5. In other words, it varies, depending on the number of options. For this reason, it is easier to use a different measure: the consensus coefficient. For each option, it is the ratio of that option's MBC total divided by the theoretical maximum number of points it could have received. This consensus coefficient varies from good to bad, from one to zero (Emerson, 2007: 166). An option's final result, its MBC total, average preference score or consensus coefficient, is a reflection not only of its level of support among the voters, but also of the level of participation that all voters have given to the decision-making process.
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Emerson, P. Consensus Voting and Party Funding: A Web-Based Experiment. Eur Polit Sci 9, 83–101 (2010). https://doi.org/10.1057/eps.2009.40
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DOI: https://doi.org/10.1057/eps.2009.40