13/15th May, the National University of Mongolia debated traffic pollution in Ulaanbaatar, with an MBC analysis. Here's the report.
TWO MODIFIED BORDA COUNTs, MBCs,
on the question of:
“pollution in Ulaanbaatar.”
MONGOLIA NATIONAL UNIVERSITY
(a) on 13th and (b) on 15th May, 2025.
DEFINITIONS
+ MODIFIED BORDA COUNT MBC A preferential voting procedure for decision-making and
elections. In decision-making, it can facilitate the
identification of an electorate’s social choice – its most
popular option – or its social ranking – its prioritisation.
Uniquely, the MBC is egalitarian; it is non-majoritarian. For a decision, a social choice, it can identify from a short-list of
usually about 5 options, the option with the highest average
preference… and an average, of course, includes every voter
(and not just a majority of them).
For a prioritisation, the range of options can be greater;
usually a maximum of 20 options; and the count can identify
those options with the best consensus coefficients (see
below).
+ SINGLE-PEAKED CURVE A graph of a voter’s preferences which, when presented on an x-axis of options and a y-axis of preference, has a single
peak.
+ CONSENSUS …is defined as that option which, with an average preference
score above the mean, best represents the collective will
it is identified as the option with the highest average preference, (if, that is, everyone has
cast a full list of six preferences);
or as the option with the most points or the best consensus coefficient;
or as the option as represented by the peak in a collective single-peaked curve.
+ CONSENSUS COEFFICIENT An option’s CC is defined as its MBC score divided by the
maximum possible score.
THE SOFTWARE
All participants were first asked to register on
This ‘app’ can be used:
+ by the facilitator, to add or subtract options to the ballot, as per the wishes of the participants;
+ by the participants, to cast their preferences;
+ by all, to see the results and analyses.
BACKGROUND
It is widely recognised that pollution in Ulaanbaatar is far too high. Some is caused by the excessive use of coal, while much is due to the very high levels of motorised traffic. The two role-plays, (a) and (b), aimed to identify which policy or policies should best be adopted to tackle traffic pollution.
(a) and (b) In (a), a ballot of five options was prepared by the de Borda Institute. In (b) nothing was prepared.
(a) One further option was added in debate – Option F, a nuclear power station – (but I’m afraid the correction was not saved, so option F on the software ballot paper continued to be just “……….” – my mistake).
(b) Participants were presented with the format of a ballot paper (on the computer screen and their smart phones), but no options were listed; the page was blank. The debate was a little slow, but once started, almost impossible to stop. Certainly, there were lots of ideas, and if time had permitted, each could have been debated in a little more detail.
(a) and (b) Herein, of course, lies the advantage of deliberative democracy: the very process encourages more participation, and the generation of better options.
(a) and (b) In any MBC, if the number of options listed is < 10, the voter is asked to submit a full ballot,
(a) so with six options, a full (a) ballot consisted of six preferences.
(b) and a full (b) ballot listed all ten preferences.
(a) and (b) In casting a preference for all the options listed, a voter in effect recognises the validity of all the options, the aspirations of all of his/her neighbours. If, of course, there is something the voter most definitely does not like, then he/she just gives it no preference at all.
(a) A full ballot consisted of six preferences, of 6-5-4-3-2-1 = a total of 21 points.
There were 12 valid votes: 10 full votes of 6 preferences, and 2 partial votes of 5 preferences
= 5-4-3-2-1 = a total of 15 points.
10 x 21 = 210
+ 2 x 15 = 30
Total = 240 points.
If the ballot paper had spelt out option F, then maybe these two votes would also have included all six preferences.
(b) A full ballot consisted of ten preferences, of 10-9-8-7-6-5-4-3-2-1 = a total of 55 points.
There were 18 valid votes, all of 10 preferences, for a total of
18 x 55 = 990 points.
(a) and (b) If and when every voter does cast a full ballot, results may be based on the options’ average preference scores; when some cast a partial ballot, it is wiser to rely on consensus coefficients.
THE OUTCOME
When making a social choice, we identify the option with the highest average preference score (or consensus coefficient); if the results are very close we might consider the possibility of a composite of the two most popular options.
In any prioritisation, however, we choose those options with a good score, and to choose all options which may be regarded as ‘popular or very popular’. If this involves a list of (a) four or (b) seven options, then, well and good. If however, in (a) the fifth, or in (b) the seventh is very close, then it may well be wiser to choose (a) the top five, and (b) the top seven policy options.
THE MATHS
(a) average consensus
score preference score coefficient
So
maximum (of six 1st preferences) 6 x 12 = 72 points = 1.00 = 1.00
minimum (of six 6th preferences) 1 x 12 = 12 points = 6.00 = 0.17
a mean (of say three 3rd
+ three 4th preferences) 3.5 x 12 =. 42 points = 3.50 = 0.58
and
(b) average consensus
score preference score coefficient
So
maximum (of 18 in all 1st preferences) 10 x 18 = 180 points = 1.00 = 1.00
minimum (of 18 in all 10th preferences) 1 x 18 = 18 points = 0.10 = 0.10
a mean (of say some 4th and 5th,
+ some 6th and 7th preferences) 5.5 x 18 = 99 points = 5.50 = 0.55
THE ANALYSIS
Prior to the vote, all concerned may agree to the following:
If, come the vote, the option with the highest consensus coefficient is:
(a) (b)
< 0.60 0.55 there is no consensus, and no prioritisation shall be taken.
> 0.60 0.65 the outcome is the best possible compromise;
> 0.70 0.70 ” a consensus
> 0.80 0.85 ” the collective wisdom.
THE OPTIONS
(a)
A A ban of all SUVs in City limits.
B One car per family / household of 2 adults.
C Even number registrations on Mon, Wed and Fridays; odd numbers on Tues, Thurs and Saturdays.
D Cycle lanes separated from cars by posts or hedge.
E Cycle traffic lights, with priority over car traffic lights
F ……. (A nuclear power-station).
(b)
A Build a metro
B Traffic congestion ‘app’
C Stricter driving licenses
D Build more roads
E Even number registrations on Mon, Wed and Fridays; odd numbers on Tues, Thurs and Saturdays.
F More parking lots
G Private parking lots
H More u-turn possibilities
I More roundabouts
J Separate cycle lanes
There was very little overlap between the two role-plays. (a)’s option C and D are the same as (b)’s options E and J. Accordingly, any future role-play should allow for more time for debate.
Secondly, the options could have been improved. In (b), for example, options F and G could perhaps have been combined; again, more debate is recommended.
THE VOTE
In a ballot of (a) six and (b) ten options:
+ he who casts just one preference gets his favourite just 1 point
(and the other options get nothing);
+ she who casts two preferences gets her favourite 2 points
(and her 2nd choice 1 point);
and so on; accordingly,
+ those who cast
(a) all six preferences get their favourite 6 points,
(their 2nd choice 5, their 3rd option 4 points, etc.).
(b) all ten preferences get their favourite 10 points,
(their 2nd choice 9, their 3rd option 8 points, etc.).
In effect, every voter is thus encouraged to cast many if not all of their preferences, their favourite as well as their compromise option(s)… and if (nearly) every voter does that, the collective compromise can easily be identified: the options with the most points, or the highest average preferences, or again the best consensus coefficients.
THE EXERCISE
There are, of course, lots of policies which could be initiated to help reduce pollution levels. Accordingly,
(a) it was decided to adopt every suggestion with a good level of support – a consensus coefficient > 0.60 – options D, A and C, with the priority going to the option with the highest score;
and
(b) The three options – option D, A and F – were on top. Nothing had a score < 0.70 but > 0.60, and option C was the only other option to gain a score greater than the mean of 0.55.
THE RESULTS
The results (shown in bold) were as follows:
(a)
actual consensus
Option score coefficient
D 50 points 0.69 cycle lanes
A 46 points 0.64 SUVs banned
C 44 points 0.61 even/odd registrations
E 40 points 0.56
B 38 points 0.53
F 22 points 0.31
(b)
actual consensus
Option score coefficient
D 136 points 0.76 more roads
A 128 points 0.71 a metro
F 128 points 0.71 more parking lots
C 106 points 0.59 stricter licensing
E 98 points 0.54
J 94 points 0.52
G 92 points 0.51
B 77 points 0.43
H 69 points 0.38
I 62 points 0.34
THE OUTCOME
(a) Because two of the voters submitted only partial ballots, casting 5 rather than 6 preferences, decisions are based on consensus coefficients and not on average preference scores.
(a) and (b) When consensus voting becomes more widely understood, a final analysis should perhaps use lower CCs.
CONCLUSION
Allowing for the final analysis of the voters’ profile to be based on an MBC encourages all concerned to be more inclusive both in debate and in the vote which follows. As seen in both role-plays, of those who voted, all submitted full or very nearly full ballots. Deliberative democracy works.