The People's Plea and The Politicians' Prayer
Updated: Sep 17, 2020
The People’s Plea:
“LEADERS, LEAD US NOT INTO DIVISIONS.”
We shall begin with a plea to the politicians. “Dear Leaders…” is how we might start if we were North Koreans, but we’ll omit the ‘dear’.
“Leaders, don’t lead us, just deliver us from dreadful dichotomies. Instead, be more democratic and give us consensus voting. Amen.”
The methodology was mooted by Ramón Llull in 1199, outlined by Nicholas Cusanus in 1435, analysed and refined by Jean-Charles de Borda in 1774, re-iterated by Charles Dodgson (Lewis Carroll) in 1874, and recorded by Duncan Black in 1958.
The scientists know what we have to do; the computer programs have already been written; it just requires the world’s Drab politicians to restrain their lust for power and control, thereby to allow us and our representatives to be the intelligent, nuanced creatures we all are.
The Politicians’ Prayer:
“DEAR LORD, GIVE US CONSENSUS… BUT NOT YET.”
The ‘Brilliant Party’ has acquired a bright, colourful property, with just one defect: the front door is Drab… very, very Drab. The three exec. cte. members – Ms i, Mr j and Ms k – agree, unanimously, “that’s dreadful,” says one; “yes, terrible,” “indeed, horrible.”
So there’s a consensus on what they don’t want, and the door must be re-painted. But what colour do they want in its stead? Ah-ha; a debate ensues.
“Anything but Drab,” says Ms i, and she moves a motion: ‘paint it Amber’. “That’s worse than Drab,” Mr j counters, so he proposes an amendment: ‘delete Amber, insert Beige.’ “But Beige is bland!” opines Ms k, and she proposes a second amendment: ‘Crimson’.
The committee is indeed split, and there’s no consensus on a new colour… not yet anyway.
Altogether, we may observe, there are four options: A, B, C plus the status quo ante D, and the three members have the following preferences:1
Being committed democrats, they follow standard procedure. Firstly, they choose the more preferred amendment, B or C; and a majority of 2, i and j, prefer B. Next – is the motion to be amended? – so it’s A versus B; and another majority, i and k want A, the motion unamended.
Finally, it’s this substantive A or the status quo D, and both j and k select D.
So D is the outcome, their majority vote decision (which we call their social choice): by a majority of 2:1 or 67%, the exec. cte. votes to keep the door Drab, very. Democratically? Oh yes, very.
But (the table tells us), all three prefer C to D. Not just 67% but all of them, 100%, like C more than D.
With binary voting, however, that which is the least popular actually comes out on top! In this example, the majority vote outcome is wrong, and couldn’t be more wrong.
So here (and, we hasten to add, in many another setting), majority voting just doesn’t work well.
As a tool for measuring opinions, binary voting is as crude an instrument as a Covid-19 thermometer with only two calibrations: ‘hot’ or ‘cold’. If the suspected patient’s temperature is actually normal, any and every temperature reading on such a binary device will be wrong.
Well, it’s not much better with binary voting and, as we’ve just seen, the outcome of any binary decision-making process may also be wrong. In the above example, A is more popular than B, which we write as A > B, but so too B > C, C > D and D > A… so no matter what the outcome, there is always a majority in favour of something else!
A more accurate measure of an individual’s opinion is one in which he / she can express degrees of support: on any one colour for the door, is he cool, luke warm, hotly in favour, or whatever. Is B really worse than D, as Ms k suggests, and so on. Well, if they were to use a preference points system in which a 1st preference gets 4 points, a 2nd gets 3 and so on, the scores would be A-7, B-8, C-9 and D-6, so the social choice would be C.
In fact, with majority voting, the answer could be anything! If the original motion was ‘paint it Beige,’ with amendments for Amber and Crimson, then with the above preferences, the democratic outcome would be Beige: again, we follow procedures, A v C = C; next C v B = B; and then B v D = B. Or start with Crimson and they’d agree on Crimson; while starting with Amber, as above, they get Drab. Furthermore, if the door had already been Amber, Beige or Crimson, with someone moving a change to Drab and colleagues suggesting the other two colours as amendments, then again with the above preferences, the outcome would always have been, ‘no change’.
In a word, binary voting, ‘hot’ or ‘cold’ – this ‘good’, that ‘bad’! – is Orwellian in its simplicity. No wonder the outcomes are sometimes wrong.
With preferential points voting, however, we get not only a social choice as the most popular – option C – we also get the committee’s social ranking – C-B-A-D – and Drab, option D, is indeed their least popular option. In other words, the vote shows that, collectively, the committee wants the door to be re-painted, preferably Crimson.
Binary ballots are blunt; preferential points voting is more inclusive, informative and accurate. And if it’s more accurate, then it’s also more democratic.
At the moment, in politics, (business, and the community at large), decisions are often made on the basis of binary votes, initially on amendments and then on substantive motions, and everything is done in the laid down sequence of amendment-substantive-decision (not least because, otherwise, the outcome could vary).
The more accurate methodology of preferential points voting would list all the options (or on very complex matters, a short list of about five of them), and allow those voting – the people in a referendum or the elected representatives in a parliament – to cast their preferences.
In majority voting, there are just two calibrations, two ways of voting: ‘for’ or ‘against’, ‘hot’ or ‘cold’, and that’s that.
In a preferential points vote on three options, there are six ways of casting your preferences: A-B-C, A-C-B, B-A-C, B-C-A, C-A-B and C-B-A. With four options, A, B, C and D, there are some 24 ways of submitting a full ballot. So the voter may indeed express a more nuanced opinion. “Anything’s better than D,” says Ms i; so that’s her last preference. "Amber, that’s worse than D,” responds Mr j, so D is his 3rd choice, while his last preference is A. And so on.
Such are the advantages of preference voting, each may express a more accurate summary of their views; and if every individual opinion is more accurate, then the collation of that data into a collective opinion may also be more accurate.
Now in some debates, there may be those who want only one particular option, no ifs, no buts, no compromise: for them, democracy is win-or-lose. So they may want to cast only a 1st preference and leave the rest blank.
In a "Modified Borda Count" (MBC), as this form of preference points voting is called, he who votes for only one option (and says nothing about the others) gets 1 point for his favourite option (and nothing for the others). She who casts two preferences gets 2 points for her favourite (and 1 point for her 2nd preference). And those who, in a ballot on four options, cast all four preferences, get 4 points for their favourite, (3 for their 2nd choice and so on).
The option with the most points is the winner.
So the system is fair: a voter’s 2nd preference, say, always gets 1 point more than his 3rd preference, regardless of whether or not he has cast that 3rd preference. And the system is inclusive: the protagonist will want as many points as possible, so not only will she want all her supporters to give her option their 1st preference, and to do so in full ballots; she will also find it advantageous to campaign for a 2nd or at least a 3rd preference amongst the other members of society.
Now mathematically, if everyone does submit a full ballot, the winning option, the one with the most points, is also that which gains the highest average preference, and an average, of course, involves every voter, not just a majority of them. The MBC is indeed inclusive.
So, to be technical for a moment, in an MBC on n options, the voter – a member of the public in a referendum or an elected representative in parliament – may cast m preferences, and (n ≥ m ≥ 1). Points are awarded to (1st, 2nd … last) preferences cast, according to the formula (m, m-1 … 1). The MBC is often confused with the Borda Count (BC), where points are awarded as per (n, n-1 … 1) or (n-1, n-2 … 0), and if every voter submits a full ballot, then, no matter which formula is used, the social choice outcome is always the same. If however there are no rules for truncated votes, the BC may incentify the intransigent to submit only a 1st preference, and if everybody does that, the BC is not much better than a plurality vote. In contrast, in an MBC, which is actually M de Borda’s original rule, everyone is encouraged to participate in the democratic process and to the full.
Majority voting is not only divisive and exclusive; as shown above with the Drab door, it sometimes produces the wrong outcome. Furthermore, it (might perhaps ratify but it) cannot identify “the will of the people” or the will of parliament, because the winning option has to be identified earlier if it is to be already on the ballot paper; so the author of the question, be he a dictator or he/she a democrat, controls the agenda if not indeed the outcome.
For some extraordinary reason, however, nearly every country, democratic and communist alike, uses majority voting in decision-making. Mathematically, such ballots are often next to meaningless.
It was used by Napoléon in referendums, which by the way he won, all three of them, by over 99%; by Lenin when he founded the Bolsheviks – the very word means ‘members of the majority’ – but in fact, he only had the largest minority; and by Hitler in a 2/3rds weighted majority – the Enabling Act of 1933.
While today, this 2,000-year-old procedure is used by Washington, Westminster, Moscow and Beijing, again, as often as not, as an instrument of control.
The British sometimes have meaningless votes as when, on Brexit, Theresa May asked the House of Commons, “Option X, yes or no?” three times! Her campaigning slogan, remember, was ‘democratic leadership’.
Chinese majority votes can also be meaningless, as when Xí Jìnpíng was elected by 2,952 votes to 1 with 3 abstentions; and he uses a similar oxymoron, ‘democratic centralism’. On other voting occasions, the Communist Party methodology of majority voting has itself been a determining factor: the 1989 decision to authorise a military intervention into Tiān’ānmén Square was taken, it is said, by a margin of just one vote.
Yes, binary voting is ubiquitous: it is even enshrined in the North Korean constitution, both simple majority and 2/3rds. But it’s no good.
In a pluralist debate – i.e., when there are more than two options ‘on the table’ – if there is no majority in favour of any one thing, there is a majority against every (damned) thing… (as was the case in Brexit). This truism was first pointed out by Pliny the Younger, 1900 years ago.
In contrast, with an MBC those participating in the decision-making process (or their elected representatives) also play a part in drawing up the options. The MBC can be very inclusive; it can also be extremely accurate.
Why can’t we embrace our human diversity and enjoy preferential decision-making? Many countries have multi-candidate elections. We wouldn’t want any of those “Candidate X, yes-or-no?” elections, would we? That’s the sort of nonsense they have in North Korea. Why then, in referendums and in parliamentary ‘divisions’ (as such ballots are called in the House of Commons), do we have “Option X, yes-or-no?” decision-making? In many instances, a binary ballot is no less illogical than the shenanigans of Pyongyang.
So why can’t we follow the science, as the good environmentalist might say, the science of social choice?
In a nutshell, politicians who want to unite the party / country / whatever, should not contradict themselves by using a voting procedure which is inherently divisive, and especially not the most divisive of all – this Orwellian binary vote.
After all, you cannot best get a consensus in a majority vote because – with so many votes ‘for’ and so many ‘against’ – it measures the very opposite, the degree of dissent. Logically, they should aim to unite the said electorate in a voting procedure which is cohesive, in which those voting state not only what they want but also their compromise option(s), recognising in so doing the validity of these other options and acknowledging their neighbours’ different aspirations.
The most accurate voting systems for use in decision-making are undoubtedly the MBC and / or the Condorcet rule. And the former is also non-majoritarian. It allows the voters to identify their common good, if such exists. In other words, if the MBC social choice passes a pre-determined threshold level of support, this outcome can be termed their consensus… or, if higher still, their collective wisdom.
1 This example is taken from the author’s Democratic Decision-making, 2020, (Springer, Heidelberg), forthcoming.
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