For the people to have their say on Brexit, how best can the multi-option conundrum be resolved?

Conservative MP Justine Greening who backs a 'series of plurality votes' to give the British people the final say on Brexit. NurPhoto/press Associatiion. All rights reserved.

Whenever a problem is complex, binary ballots are not the
best.  Politicians, however, often reduce
everything to either an “option ‘x’ or ‘y’?” choice or an “option ‘x’, yes or
no?” question – as in “the eu withdrawal
or ‘no deal’?” – because if ‘x’ is what they want, such a stark dichotomy
increases the chances of their success.

The outcome of such a vote, however, is often unclear: do
people really want ‘x’, or do they just dislike ‘y’?  And would they have preferred ‘z’?

Take, for example, the 2011 referendum on the electoral
system.  The vote (‘x’ or ‘y’?) was first-past-the-post,
fptp, or the alternative vote, av? 
But lots of people wanted (‘z’), pr,
proportional representation.  If the
question had been different, as it was in New Zealand… see below.

Take Kosova.  In 1991,
(‘x’, yes or no?), 99 per cent voted for independence.  If the question had offered (‘y’, yes or
no?), ‘unity with Albania?’ or (‘z’, yes or no?), ‘a Greater Albania?’ the
outcome would again almost certainly have been in favour.

Consider the 1973 Northern Ireland (‘x’, yes or no?) border
poll.  The Protestants voted, the
Catholics did not, and the ‘democratic’ decision was again 99 per cent in
favour.  It resolved nothing.

Iran.  In 1953, they
voted for socialism, 99%, (‘x’).  Ten
years later, 99% wanted capitalism, (‘y’). 
And in 1979, they wanted neither but an Islamic Republic instead, (‘z’),
yet another 99%.  Well, the Shi’a wanted
one: the Sunni Turkmen minority abstained.

Nearly all of these votes meant almost nothing.  Basically, you cannot identify the general
will of (parliament or) the people if some of the (mps or) public vote ‘no’, if they say only what they do not want.  Furthermore, this is how Hitler got to power:
he chose a minority – the Jews, gays, gypsies, any minority will do – and thus got
a majority.  Binary voting is the
catalyst of populism.  The dangers are
huge, for if we say ‘no’ to everything, we will finish up with nothing.

                                        ______________

Some electoral systems are not much better. Trump. Choose a
minority – Mexicans, immigrants, any minority will do – and anybody can win.
Only because of the lousy electoral system. It’s not just the Electoral
College, the American fptp is part
of the problem, as is the blatantly two-party structure of us politics … a form of ‘democracy’
which George Washington called “a frightful despotism.”[1]
In effect, us elections are binary
contests, it is Democrat or Republican, and for many voters, it is like an ‘x’
or ‘y’ majority vote?  Some people vote
‘for’ something, but lots vote ‘against’ what they regard as the opposite.

Britain’s first past the
post (FPTP) is no better, and here too, its consequences are numerous. Indeed,
if the uk had pr, there might not have been a Brexit
referendum at all! Secondly, if Britain was not so mesmerised by what Sir
Michael Dummett called “the mystique of the majority,”[2]
the uk would not now be in the
ridiculous position whereby a tiny rump party of extremists, the dup, is in government, while other much
larger parties are not! Thirdly, if the uk
did have pr, the dup would be even tinier.

                                         ______________

So, Brexit 

Brexit is a multi-option choice.  The fact that binary voting cannot best cope
with a multi-option problem was first noted in ce
105 by Pliny the Younger, and preferential voting was first mooted in 1199 by
Ramón Llull.  For some reason, however, while
Britain and many other countries believe in majority rule – which is quite
right – people often assume that a majority opinion can be identified in a
majority vote – which, when the question is multi-optional, can be quite wrong. 

Majority voting is primitive, divisive, ancient and, in many
instances, hopelessly inaccurate. If the
problem is multi-optional, the question should be multi-optional, and the
ballot paper should be a (short) list, usually of about 4 – 6 options.  With a multi-option problem like Brexit, we
all have opinions, we all have preferences. So how best can it be resolved?

Take, for example, 14 persons – (mps or) voters – with 1st, 2nd, 3rd
and 4th preferences on four options – A, B, C and D
– as shown.

 

Preferences

Number of Voters

5

2

3

1

3

1st

A

B

C

D

D

2nd

B

C

D

B

B

3rd

C

D

A

A

C

4th

D

A

B

C

A

On the face of it, option A appears to be very divisive;
opinions on D
are also split; C
is a bit better; but maybe B, the 1st or 2nd preference of 11
voters, best represents the collective will, so the correct social ranking is perhaps
B-C-D-A.

But what happens in practice?  Let us assume that, in any “option ‘x’,
yes-or-no?” type of majority vote, people vote ‘yes’ for their 1st
preference and otherwise they vote ‘no’; and that in any “option ‘x’ or ‘y’?”
type of ballot, they vote for whichever they prefer.

So, when it’s “A, yes-or-no?” a majority of 9 say ‘no’.  B loses by a majority of 12, C by 11, and D by 10.  So there’s a majority against everything –
which is probably today’s situation in the Commons on Brexit, and maybe too
amongst the electorate.

With the other “option ‘x’ or ‘y’?” type of binary question,
A
is more popular than B by 8:6; B is more popular than C
by 11:3; C is more popular than D by 10:4; and D is more popular than A
by 9:5.  So A > B > C > D > A > B >
…………… and it goes round and round for ever – the ‘paradox of [binary] voting’,
as it is called; no matter what the outcome, there is always a majority who
would want something else.

The conclusion is clear: majority voting is inadequate,
maybe it produces no answer, or maybe it produces the wrong answer. So would a
multi-option vote be better?  Majority voting is inadequate,
maybe it produces no answer, or maybe it produces the wrong answer…  would a
multi-option vote be better?  

Well, in plurality voting (which is like an fptp election) the social choice is A,
with a score of 5, and the social ranking is A-D-C-B, 5-4-3-2. 

In a two-round system, trs,
(as in French elections), which Professor Vernon Bogdanor has spoken of,[3]
if no one option gets a majority in the first round plurality vote, there is a
second round majority vote between the two leading options – in our example, A
on 5 and D on 4 – which D then wins in a social ranking of D-A,
9-5.

An alternative vote (the Australian electoral system), as
proposed by Justine Greening MP,[4]
is a series of plurality votes, with the least popular option eliminated and
its votes transferred as its voters would have wished, until one option gets a
majority.  So, in our example, the score
is A
5, D
4, C
3, B
2; so option B is out and its 2 votes go to C for a score of A
5, C
5, D
4; so that’s the end of D, and its 4 votes go (not to B
which has been eliminated but) 1 to A and 3 to C, for a final score of A
6, C
8, so the winner is now C in a social ranking of C-A,
8-6.

Lastly, in a preferential points system – in this example, a
1st preference gets 4 points, a 2nd gets 3, a 3rd
2 and a 4th gets 1 point – option A gets 20 + 0 + 8 + 5 =
33; B
gets 8 + 27 + 0 + 3 = 38; C gets 12 + 6 + 16 + 1 = 35;
and
D
gets 16 + 9 + 4 + 5 = 34.  So
the social choice is now B, and the social ranking, 38-35-34-30,
is
B-C-D-A
, which is what we assumed was the best expression of the
general will.

So maybe the most accurate methodology is this preferential points
system, the Modified Borda Count, MBC,
as it is called. It is interesting to note that the mbc social ranking, B-C-D-A, is the exact opposite of
the plurality vote, fptp, social
ranking A-D-C-B.  In other words, FPTP can sometimes be wrong and occasionally
could not be more wrong. It is useless. This semi-binary electoral system
should not be used as a means of resolving the Brexit problem. And nor should a
binary referendum. Maybe some pluralism could help.[5] The world’s first
multi-option referendum was in New Zealand in 1894. They did it again in 1992.

                                             ______________

In 1990, very few New Zealanders knew what AMS and MMP
were (see below).  But an independent
commission was tasked to examine their electoral system.  People wrote submissions, the commission held
meetings, the press published articles, the tv
conducted interviews, and by the time the electorate was presented with a referendum
with five options on the ballot paper – FPTP, AMS, AV, MMP and PR-STV[6] –
lots of New Zealanders had made up their minds as to which system they wanted. In
1992 and ’93, they voted in a TRS
system, and they chose MMP, mixed
member proportional, the German system.

In effect, the New Zealand electorate could vote ‘yes’ for whatever
they wanted, and maybe nobody voted ‘no’ to anything. When everybody says what
they want, it should indeed be possible to see which option is the most
popular.

This is certainly true with preferential points voting.  In a four-option MBC ballot:

  • –  he who casts just one preference gives his
    favourite only 1 point (and nothing to anything else);
  • –  she who casts two preferences gives her
    favourite 2 points (and her 2nd choice 1 point); and so on; thus
  • –   those who cast all four preferences give their
    favourite 4 points (their 2nd choice 3, their 3rd 2 and
    their 4th preference 1 point).

The difference is always 1 point.  A voter’s xth preference, if cast,
gets 1 point more than his (x+1)th preference, regardless of whether
or not he has cast that (x+1)th preference.

In effect, the voter is thus encouraged to cast a full
ballot.  What’s more, the protagonist
will want, not only her supporters to cast full ballots, but also her erstwhile
(majoritarian) opponents to give her particular option at least a 3rd
if not a 2nd preference.  In
other words, the campaign which precedes the vote will be much more nuanced. People
will have a reason for listening to each other and engaging in debate.

At best, the outcome will be the option with the highest
average preference, and an average, of course, involves every one who votes,
not just a majority of them.  The mbc is cohesive, robust, and most
importantly, accurate.  If politicians
really wanted to bring the country together (again), they would use just such a
inclusive voting procedure, either in parliament and/or in any future multi-option
referendum.  Politics, they say, is the
art of compromise; the MBC is its
science.

 


[1]
         His farewell address of 1796.

[2]
         Principles of Electoral Reform, 1997, OUP, p 71.

[3]
         Vernon Bogdanor: A second Brexit referendum?

[4]
        Justine Greening: Give the British people the final decision on Brexit.  

[5]
        Gina Miller has also asked for a multi-option ballot, (Today, 21.9.2018).

[6]
        Additional member system and pr-single transferable vote

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