In a role-play in Tiānjīn University, participants (debated and) voted on the optimal size of Tiānjīn's population, and here's the report:
A MODIFIED BORDA COUNT MBC
on the question:
“What should be the size of Tiānjīn’s optimal population?”
TIĀNJĪN UNIVERSITY, 2025-04-24
DEFINITIONS
+ MODIFIED BORDA COUNT MBC A preferential voting procedure for decision-making and
elections. Uniquely, it is egalitarian; it is non-majoritarian;
from a choice of usually about 5 options, it can identify the
option with the highest average preference… and an average,
of course, includes every voter (not just a majority of them).
+ SINGLE-PEAKED CURVE A graph which, when presented on an x-axis of options
and a y-axis of average preference score, 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 with the most points;
or as represented by the peak; in the graph below, it is about
14.9 millions.
THE SOFTWARE
All participants were first asked to register on
This 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.
BACKGROUND
Tiānjīn currently has a population of about 17 millions. The question posed was as follows:
“Tiānjīn should aspire to what size of population?”
A ballot was prepared by the de Borda Institute, and no deletions or additional options were suggested. The ballot paper therefore consisted of six options, and a full ballot of six preferences gives a total of 21 points. There were about 30 participants, some working individually, some in groups of two or three, and not all managed to register (for some e-reason). In total, there were 13 valid votes, and all of them were full ballots of 6 preferences; this led to a grand total of (21 x 13 =) 273 points cast.
possible average
score preference score
So a maximum (of six 1st preferences) 6 x 13 = 78 points = 1.00
a minimum (of six 6th preferences) 1 x 13 = 13 points = 6.00
an average (of say three 3rd
+ three 4th preferences) 3.5 x 21 = 45.5 points = 3.50
THE ANALYSIS
Prior to the vote, all concerned may agree to the following:
If, come the vote, the option with the highest average preference is:
< 4.00, there is no consensus, and no decision shall be taken.
> 4.00 the outcome is the best possible compromise;
> 4.50 ” a consensus
> 5.00 ” the collective wisdom.
THE FACILITATION
In practice, choosing these scores, and facilitating the choice of options, should all be done by a team of four independent ‘referees’ – a chairperson and three ‘consensors’ as they are called. Their functions are:
+ to allow all options which comply with the UN Charter on Human Rights;
+ to determine and publicise the rules for the analysis;
+ to facilitate the formation of the ballot, so that (on most occasions) it consists of about 4 – 6 options;
+ to analyse the results.
THE OPTIONS
A < 12 million
B < 15 million
C = 17 million (the status quo)
D < 20 million
E < 25 million
F > 25 million
THE VOTE
In a ballot of, say, five options:
+ he who casts just one preference gets his favourite just 1 point
(and the other options get nothing0;
+ she who casts two preferences gets her favourite 2 points
(and her 2nd choice 1 point);
and so on; accordingly,
+ those who cast all five preferences get their favourite 5 points,
(their 2nd choice 4, their 3rd option 3 points, etc.).
In effect, then, every voter is thus encouraged to cast many if not all 5 preferences, rtheir favourite as well as their compromise option(s)… and if (nearly) every voter does that, the collective compromise can easily be identified: the option with the highest average preference or the most points.
THE RESULTS
actual average
The official results of the vote were as follows: Option score preference score
A 48 points 0.38
B 57 points 0.45
C 52 points 0.41
D 48 points 0.38
E 37 points 0.29
F 25 points 0.20
so, as seen in the following table, these results form a single-peaked curve… implying that the participants have come to a logical outcome.
TABLE I THE RESULTS: A SINGLE-PEAKED CURVE
AVERAGE
PREFERENCE
SCORES
|
55 |
|
. |
|
|
|
|
|
|
50 |
|
|
. |
|
|
|
|
|
45 |
. |
|
|
. |
average |
preference |
score |
|
40 |
|
|
|
|
|
|
|
|
35 |
|
|
|
|
|
. |
|
|
30 |
|
|
|
|
|
|
|
|
25 |
|
|
|
|
|
|
. |
|
20 |
|
|
|
|
|
|
|
|
OPTIONS |
A < 12 |
B < 15 |
C = 17 |
D < 20 |
|
E < 25 |
F >25 |
|
|
millions, the population of Tianjin. |
||||||
Taking the outcome to one decimal point, the graph’s ‘single-peaked curve' peaks at < 14.9 millions.
THE OUTCOME
If some of the voters submit only partial ballots, casting 1 or more, but less than 5 preferences, the figures used in the analysis will be affected. Until consensus voting becomes more widely understood, therefore, a final analysis should perhaps use lower average preference scores. On this occasion, with an average preference score of 4.5, the outcome of the above MBC ballot is as follows:
“The participants’ consensus is that the population of Tiānjīn should be no more than 14.9 million.”
Tiānjīn 2025.04.24