2019-33 Moscow workshop on "Decisions..."

DECISIONS, DECISIONS…

PART I

Report on a workshop held

on Monday 18^th November,

in the International Laboratory of Decision Choice and Analysis

of the High School of Economics, University, Moscow,

at the invitation of

Professor Fuad Aleskerov.

Peter Emerson

www,deborda.org

www.debordavote.org

1          The Task

a)         firstly, to decide how to choose… and then

b)         to decide what to choose as an electoral system for Russian parliamentary elections.

2          To Decide how to Decide

Decisions can be taken in any number of ways: the worst methods involve violence, other processes can require protracted negotiations, and maybe a more pragmatic methodology is to vote.  But there are over 600 electoral systems in the world, so maybe it would be better to have a debate, to choose a short list, and then to vote on just these.

3          Consensus Voting

Most formats of consensus voting require a chair, a team of consensors, maybe too a timekeeper, and the participants.  In this role-play, both the chair and the consensors were a singleton, the lecturer; there was no timekeeper; and everyone else was a participant.

In principle, all concerned could propose an option.  The lecturer introduced four voting methodologies already well know in Russia and elsewhere: majority voting; plurality voting; a two-round system, trs; and the alternative vote, av, (sometimes known as the single transferable vote, stv, or instant run-off voting, irv).  To these four were then added a Borda procedure, the modified Borda count or mbc, and the Condorcet rule; both were well known to all the participants. 

They were then asked if they would like to add any other methodologies: a Copeland[1] variation of the Condorcet rule, suggested one; another proposed a refinement to the mbc; a third suggested Coombe’s[2] method.  As the first two suggestions were regarded as variations on the two themes mentioned, while the third could be a lengthy process, the consensor suggested the participants should proceed with the above 6-options, and leave any adjustments to a further debate, if indeed either Condorcet and/or the mbc proved to be the most popular.

3.1       The Ballot Paper

In theory, decisions can also be taken by majority vote but, in this example, assuming participants vote in favour of their 1^st preference only, every option loses: A by 0-9, B by 2-7, and the others by 1-8, 3-6 and 3-6 respectively.  So in a multi-option debate, binary voting is at least inappropriate, if not ineffective (as was discovered recently in the British House of Commons’ so-called “indicative votes”), if not hopelessly inaccurate… (but is used extensively).  Hence the ballot paper, as shown in Table I. 

Table I           The Ballot

Options		Preferences
A	Plurality voting
B	The two-round system, trs
C	The alternative vote, av, stv or irv
D	The modified Borda count, mbc
E	The Condorcet rule

3.2       The Vote

Nine participants then voted on their smart phones – (a few did not have their devices with them) – casting a 1 for their 1^st preference, a 2 for their 2^nd choice, and so on.  All nine were full ballots.  The vote (which of course is now closed) can be found on  www.debordavote.org  under “Ballots”, page 2, and the ballot name is “Russia decides 1”.

3.3       The Results

In a plurality vote, the count considers the 1^st preferences only, and the result is A-0, B-2, C-1, D-3, E-3, so it’s a draw for D and E.

The trs second round is a contest between D and E and, if the participant’s preferences stay the same, the outcome is E on a score of 5 to D’s 4.

With av, option A on 0 is out automatically; option C with 1 is next to go, and its 1 vote goes to D, for a score line of B-2, D-4, E-3; so B is now eliminated, and its two votes got to E; as happens quite often in the more simple voters’ profiles, the trs result is the same as the av result: E 5, D 4.

With the mbc, the score line is A-17, B-26, C-27, D-31, E-34; and with the Condorcet rule, the results are A-0, B-1, C-2, D-4, E-5.  So a full set of results is as shown in Table II.

Table II         The Results

Options		Social Choice	Social Ranking
A	Plurality voting	D/E	D/E-B-C-A
B	The two-round system, trs	E	E-D
C	The alternative vote, av, stv or irv	E	E-D
D	The modified Borda count, mbc	E	E-D-C-B-A
E	The Condorcet rule	E	E-D-B-C-A

The outcome then, at this stage, is E, the Condorcet rule: E is definitely first and D is equally definitely second.  The workshop then considered consensus voting in a little more detail.

4          Consensus Decision-making

Binary voting is very adversarial: it is all win-or-lose, and even if only by 50% + 1, the winner gets everything while the loser gets nothing.  In consensus voting, a different atmosphere prevails.

4.1       An mbc Count

In an n-option Condorcet or mbc count, a voter may cast m options, and obviously n ≥ m ≥ 1. What follows relates more to the mbc, in which points are awarded to (1^st, 2^nd … last) preferences cast, according to the rule (m, m-1 … 1).[3]  And the winner is the option with the most points.

This has the overall effect of encouraging the voters to cast full ballots.  Furthermore, it incentivises the protagonist – the first is a he – to engage positively with everyone, not only with his supporters who he hopes will cast their 1^st preference for his option and do so in full ballots, but also with any (erstwhile majoritarian opponents) whom he might be able to persuade to give his option a 3^rd or even a 2^nd preference.  In a nutshell, the negativity of binary voting is replaced by a more convivial discourse.

4.2       The mbc Results

A consensus coefficient cc, for any one option is that option’s mbc score divided by the maximum possible score – which would be a 1^st preference from everybody.  In this particular example:

• The number of options, n                               =          5
• The number of voters, v                                 =          9
• The total number of points in a full ballot      =          5 + 4 + 3 + 2 + 1         =          15
• So the total number of points cast                  =          9x15                            =         135
• The maximum cc        (all 1^st preferences)      =          5x9/5x9                        =          1.00
• The minimum cc         (all last preferences)    =          1x9/5x9                        =          0.20
• So the mean cc            (if everyone casts a full ballot)                                   =          0.60

The results are shown in Table III.

Table III        The Results

Options		mbc points	Consensus Coefficient
A	Plurality voting	17	0.31
B	The two-round system, trs	26	0.48
C	The alternative vote, av, stv or irv	27	0.50
D	The modified Borda count, mbc	31	0.57
E	The Condorcet rule	34	0.63

3.5       The Consensors’ Composite 

In binary voting, the two options are usually regarded as mutually exclusive (even when they are not).  In consensus politics, in a 5-option ballot, it is highly unlikely that all five options will be totally mutually exclusive of all the other four.

As it happened, the most popular option was Condorcet, the second most popular, the mbc.  So the consensor (the lecturer and author of this report) then decided that the actual outcome would be, as suggested by one of the participants, the Copeland variation of the Condorcet rule.

3.6       A Second Role-play 

A further role-play was conducted, with participants acting as if they were members of a political party.  And sure enough, ‘United Russia’ likes majority voting, usually on one option or maybe involving a choice of two; in extremis, it would opt for plurality voting.  In contrast, smaller parties are much more likely to have their option included in the debate and the vote, if the latter is multi-optional.

The workshop then proceeded to use a Condorcet count to choose an electoral system.  The proceedings of this second part of the workshop are in Part II of this Report.

_______________

DECISIONS, DECISIONS…

PART II

1          The Task

To decide what to choose as an electoral system for Russian parliamentary elections.

2          The Methodology

As resolved in Part I of the role-play, the choice of electoral system would be made by (the Copeland variant of) the Condorcet rule

3          The Ballot Paper

Of the 300 electoral systems available, the participants opted for a ballot paper of eight options: fptp, the British system; trs, à la France; av, which is used in Australia; pr-list, of which there are several types, closed (as when Israeli voters choose a party only) or open (when the voters can opt for a particular candidate of a particular party, as do the Danes, or more than one candidate of one particular party, like the Belgians, or more than one candidate of more than one party, the Swiss variant); a parallel system of ‘half-and-half’,[4] of fptp (as in Russia) or trs (in Georgia) mixed with a form of pr-list – parallel systems are only semi-proportional; a fully proportional system may be again ‘half-and-half’, but in Germany’s multi-member proportional mmp system – half fptp and half pr – the result is adjusted to be proportional overall; the seventh system, pr-stv, is also fully proportional and is used in Ireland, North and South; and lastly, option H, the bc, which is used in part of Slovenia’s electoral system, but the bc (or the mbc) is not proportional.

Table I           The Ballot

Options			Preferences
A	fptp	uk
B	trs	France
C	av	Australia
D	pr-list	Denmark
E	Parallel: fptp + pr	Russia
F	mmp	Germany
G	pr-stv	Ireland
H	bc	Slovenia

3.1       The Vote

Ten participants voted, casting again a 1 for their 1^st preference, a 2 for their 2^nd choice, and so on.  The vote (which of course is now closed) is on  www.debordavote.org  under “Ballots”, page 2, and the ballot name is “Russia elects”.

3.3       The Results

In a plurality vote, the result is A-0, B-1, C-1, D-3, E-0, F-0, G-2, H-3, so it’s a draw for D and H.

The trs second round is a contest between D and H and the outcome is another D/H draw.

With av, options A, E and F on 0 are all out automatically; options B and C on 1 are next to go, and with such a small number of participants in a relatively large number of options, av becomes a bit of a lottery: an outcome (as per the de Borda Institute’s decision-maker program) is option D on 10.

With the mbc, the score line is A-24, B-40, C-54, D-53, E-39, F-48, G-43, H-44, so the social choice is C. 

With the chosen methodology of the Condorcet rule, the results are A-0, B-2.5, C-6, D-5.5, E-2, F-5, G-3.5, H-3.5, the winner is again C.  A full set of results is as shown in Table II.

Table II         The Results

	Electoral System
Decision-making methodology	Social Choice	Social Ranking
Plurality voting	D/H	D/H-G-B/C-A/E/F
trs	D/H	D-H
av, stv or irv	D	D
mbc	C	C-D-F-H-G-B-E-A
The Condorcet rule	C	C-D-F-G/H-B-E-A

The outcome then, as per the Condorcet rule, is C, av.  It should be observed that the mbc social choice is exactly the same as the Condorcet choice, and that the two social rankings are also almost identical.

4          Conclusion

As was noted in Part I of this role-play, a decision-making methodology of either an mbc and/or Condorcet is excellent: a chosen methodology, especially a variation which relies on a combination of both, is bound to be robust, inclusive and very accurate… and therefore very democratic.

With regard to the outcome of this second ballot, given the closeness of the result with option D, the consensor decided that the final outcome is a ‘half-and-half’ system.  This could be a parallel system based on av and pr-list, but a better combination would be a variation of mmp in which one ‘half’ was av and the other pr-list.

Whether or not such an electoral system would be the best – at least in the opinion of this author – is not so obvious, if only because the participants did not consider that which he regards as an even more accurate system – the quota Borda system, qbs, which will feature in the matrix vote lecture.

Peter Emerson

27.11 2019

Chita.

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[1]           A Copeland score is the number of Condorcet pairings won minus the number lost.

[2]           In av, the option with the lowest score is eliminated; in Coombe’s, it’s the option with the most bottom preferences.

[3]           Unfortunately, someone changed this to (n, n-1 … 1), and just to make the maths easier, another suggested (n-1, n-2 … 0).  Either is often referred to as a Borda count, bc.  Unfortunately.

Now if everyone submits a full ballot – if, in other words, m = n – then there is no difference between (m, m-1 … 1) and (n, n-1 … 1).  But the latter cannot cater for partial voting; indeed, in the worst case scenarios – in divided societies and/or on controversial topics – many voters might be tempted to cast only a 1^st preference, in which case the bc morphs into a plurality vote, which M de Borda opposed at length.  His original formula may be written as (m, m-1 … 1).

[4]           It’s usually 50% of the mps by a non-pr system, and 50% by pr; but any ratio is possible.