18th November, in the National University, “Kyiv-Mohyla Academy,’ Kiev, everyone was on-line, and so was the vote! The report starts:
In any post-war parliament, a consensus may be just as important as it is in war! Accordingly, after an introductory critique of majority voting and a description of some other decision-making voting procedures, every participant was asked to propose that which they might consider to be a suitable decision-making voting methodology. Thus would a ballot be formed; from 4 – 6 options is usually regarded as being optimum, especially for any subject of complexity. And finally, the participants would cast one or more preferences, so to identify their most popular option.
An Overview
It was a huge mistake
for the colonial powers
+ to give – or impose – majority rule on Rwanda;
for Britain
+ to give majority rule to Northern Ireland;
for the UN, in their ‘right of self-determination’
+ to suggest a minority may secede if a majority of that minority so decide;
for the world’s parliaments and congresses
+ to regard a whole host of electoral systems as democratic, while in the main using only one form of decision-making;
and
+ to practice majority rule, so to imply that the exclusion of any Arabs from the Knesset in a majority coalition of ‘the others’ is democratically justifiable.
In a nutshell, taking a majority vote in a situation where there are more than two options ‘on the table’ is often inaccurate and may even be dangerous. In a simple scenario, a debate of four possible outcomes – a motion, option A; two possible amendments, options B and C; and the status quo, option S – is often subject to three binary votes:
{(B v C) v A} v S = ….
A better methodology might be to consider all four options, in turn, and then to hold just the one preference vote on these options.
The Experiment
As in Mykolaiv, so too in Kiev, the workshop first considered the ubiquitous use of majority voting, even in debates where more than two options are ‘on the table’. In most forums, differences are resolved – or not, as the case may be – in a series of majority votes; but such debates are open to manipulation and, in many settings, abuse.
Accordingly, the workshop:
+ considered several voting procedures;
+ formed a ballot of four or more options;
+ proceeded to a preferential vote using the software – www.debordavote.com on the participants’ mobiles; this analyses a voters’ profile according to the rules laid down for a Modified Borda Count MBC;
and
+ thus identified the voters’ consensus.
The difference between the two events was that, while only the vote in Mykolaiv was on-line (as a result of a power-cut), in Kiev everything was on-line (and, from that point of view, it was a de Borda first).
Binary Ballots – a Critique
In a setting: where 5 people want A, 4 prefer B and 2 opt for C;
where their 1st-2nd-3rd preferences are:
5 A-B-C
4 B-C-A
2 C-A-B
A is more popular than B, A > B = 7:4
B > C = 9:2
and C > A = 6:5
which means that
A > B > C > A > B > ….
and it goes round and round for ever.
It also means that
{(B v C) v A} = A
but, if the debate is restructured
{(C v A) v B} = B
and
{(A v B) v C} = C
In other words, the order of voting can be determined to give whatever result the chair desires. In a preferential vote, in contrast, with 4 points for a 1st, 3 for a 2nd, etc., the results would be A 23, B 24 and C 19, so the winner would be B. This result is close – see below on consensus coefficients – but it is unambiguous and all very transparent.
Other Voting Procedures
Many forms of decision-making are possible. Those numbered – i) to iii) – were not listed on the subsequent ballot: those lettered A to G were included.
i) majority voting on simpletons – “Option A, yes or no?” In a debate on n options, there might be a majority against every option;
ii) majority voting on pairings – “Option A or option B?” There may be majorities in favour of (n-1) options;
D plurality voting is a single preference on a choice of three or more options. The winner may have majority support, or maybe only the largest minority;
B the two-round system, TRS, is a plurality vote followed, if need be, by a majority vote pairing between the two leading options;
The following may be multi-optional.
iii) approval voting is non-preferential; a voter may ‘approve’ of one or more options;
A range voting: every voter has x points, and gives all to one or some to two or more candidates;
The following are preferential.
F Borda count BC is a points system. In a ballot of n options, a 1st preference gets n points, a 2nd preference, if cast, gets (n-1), etc.;
E In a modified Borda count MBC, if the voter casts m preferences, a 1st preference gets m points, a 2nd, if cast, gets (m-1), etc.;
G the Condorcet rule analyses all the pairings: A-B, A-C, A-D… C-D, C-E… F-G, all 21 of them, to see which (if any) wins the most pairings;
C STV or RCV or AV is a knock-out system of plurality votes; the votes of each eliminated option are transferred to its 2nd or subsequent preference, until an option gets a majority.
In summary,
+ a single-preference procedure prevents the voter from casting a 2nd and subsequent preferences;
+ some multi-option procedures allow the voter to cast more than one preference;
+ option E actually encourages the voter to thus cross the gender gap, the party
divide, and even any sectarian chasm.
The seven options – all multi-optional, some preferential – were as listed: option A came from the ‘floor’, the remaining six from the speaker. On the e-ballot, they should have been cast in random order – ideally, options E and F should not have been alongside each other.
The Vote
In a full ballot on seven options, a 1st preference gets 7 points, a 2nd gets 6, etc., so a full ballot is worth
7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 points.
14 people voted; 13 were full ballots, of 28 points each; 1 was a partial ballot of only two preferences. So, on a turnout of about 70%, the total number of points used was:
13 x 28 = 168 + 1 x (2+1) = 364 + 3 = 367
Consensus Coefficients
If, as is the case in this event, one or more persons casts only a partial ballot, we cannot use average preference scores as an accurate comparison. Instead, we use consensus coefficients:
the option’s MBC score [divided by]
the maximum possible MBC score = 14 in number 1st prefs = 14 x 7 = 98
The maximum consensus coefficient CC is always one; the minimum may vary a little, according to the number of options on the ballot. In the above poll:
maximum 1.00
mean 0.57
mimimum 0.14
In any multi-option ballot, the chances of a multi-draw are all but zero. Some options will be above the mean, others below.
If the leading option is < 0.60, there is no clear winner, no consensus, and so no decision should be taken; instead, the debate should be resumed at a later time. If, however,
0.60 < the winner < 0.70 it is the best possible compromise;
0.70 < ” < 0.80 the consensus
0.80 < ” the collective will.
These figures are somewhat arbitrary, and may vary as experience suggests.
The Results
Option Points Consensus coefficients
A range voting .67 67 / 98 = 0.68
B TRS .63 63 / 98 = 0.64
C STV .56 56 / 98 = 0.57
G Condorcet .49 49 / 98 = 0.50
D Plurality voting .47 47 / 98 = 0.48
F BC .43 43 / 98 = 0.44
E MBC .42 42 / 98 = . 0.43
Total = 367
and 3.74
And 3.74 / 7 = the mean = (c 0.50) = 0.53
The Analysis
The outcome, therefore, the best possible compromise, is option A on a score of 67 points, with a consensus coefficient of 0.68.
Post-script
This outcome is not as I would have wished. Range voting encourages selfish, uncompromising behavior: if given 10 points to allocate as he/she may wish, the intransigent voter may well tend to plomp all 10 points onto his 1st preference, while the more consensual voter might give her 1st preference, let’s say, 5 points, her 2nd choice 3 and a 3rd choice 2 points.
The event nevertheless shows that consensus voting is possible.
Acknowledgements
My thanks go to Veronika Nazarko who guided me to the correct department when I was hopelessly lost; to the Dean, Liudmyla Zubrytska, who hosted the event; and to Maryna Moskalenko who, prior to the e-vote, solved all the e-lectronic problems which would have flummoxed this old e-diot.