To celebrate the AV Referendum and in response to statements
that it is a highly complex mathematical model there follows an
with Noel Edmonds
Mathematics at Mr Blobby college Birmingham
(WARNING - this
page contains multiple images of leaders of the Conservative Party and right wing politicians.
Readers are advised only to read
this page on an empty stomach)
As a scientist
people often ask me what's the difference between FPTP, AV and Deal or
Deal. The answer is nothing - All three involve guessing what's
inside a box before it is opened so as to make a seemingly important
tactical choice on no real statistical information using a very poor
grasp of elementary mathematics.
However, as both the Yes and No to AV campaigns seem to have totally
avoided any real statistical analysis here is some elementary
mathematic analysis of AV what I carried out as part of a software beta
AV is a form of runoff voting. Runoff voting has a long history
and was invented by the political class as a way of getting on with
each other just enough for mutual survival because voters dont tend to
vote for parties that are split.
Runoff voting is where instead of one ballot you have a series.
Eliminating the lowest polling candidates one at a time till there are
two left. Sometimes the balloting must continue until not only is
there a winner but they have passed a set threashold. Classic
examples of runoff
voting are the selection of Popes ....
...who require a 75% threashold....
....and of leaders of the Conservative
party or any other situation where the
electorate cannot be open about
their real opinions and the candidates cannot be seen to be openly
canvassing for support. Either because it might be seen as
disloyalty or because it's supposed to be down to the Holy Spirit and
not a political process at all...
In the latter quarter of the 20th century voting system problems
plagued the Parliamentary
Conservative Party when they
decided to remove Ted Heath and later Margaret Thatcher. Their
challengers could not be seen to openly canvass for support so rules
were invented that in the first round ballot the winning candidate must
get more than 50%. Such runoff ballot systems are traditionally
utilised for leadership elections. Another reason that runoff
ballots are utilised in such elections...
(or were till
Iain Duncan Smith & David Cameron who were elected
Runoff combined with a full membership vote)
...is that often such
elections are not secret ballots so the leader has the advantages of
intimidation to secure their 50% support. Thus it used to be felt
that if the leader couldn't rely on the open support of at least 50% of
the parliamentary party they were ...erm... not a leader as by
definition the party had split. Thus a new leader was
required. As FPTP creates a two and a half party system for
reasons explained below
the main parties are regularly split over a large number of issues ;
Europe, Immigration, whether or not to support the AV referendum, the
Iraq War, the 10p Tax rate and all the other issues that never make it
into any manifesto but seem to become very important once party in
power has been elected.
Also it is VERY important for the leaders of the main parties to
visibly have over 50% party support for Constitutional reasons. Technically
appoints the Prime Minister. Of course this is a bit of a fairy
tale in the 21st century (no disrespect
to the Queen she's a very good compere) so to keep it alive we
are now supplied with photographs of the appointment process...
Which look remarkably like the title card of an old episode of
Minder. However, the meaning of this odd ritual is that the PM
now has the right to he appoint the hugely well paid government jobs -
so the LEADER
is required to have enough support in the House of Commons to avoid his
government being terminated by a vote of no confidence resulting in an
immediate General Election. During the Coalition talks David
Cameron ( who spent the previous 3 years calling for an "immediate
general election") suddenly became extremely worried about how wrong
it was for parliaments to be disolved early. Not having a
full majority Mr Cameron worried about the viability of a 5 year
with the Liberal Democrats attempted to fix this constitutional problem
with a proposed increse in the majority needed to disolve parliament
from 50% + 1
a general election being triggered by a vote of no
confidence but abandoned the scheme when it was fiercely ridiculed even
within his own party. To quote Christopher Chope the Secretary of the
in party leadership elections < 50% wont do.
Indeed in the 1990 election for leadership of
the Conservative Party the barrier the PM needed to break to win the
first round was actually 50% and “a lead over the 2nd place candidate
of 15%" - so Mrs Thatcher was effectively eliminated with 53.8% because
she was 1.3% off the lead over Michael Heseltine needed for a decisive
first round win. This was a bit ironic really as she'd actually
only needed 53.3%
to win the
job of Leader of the Party back in 1974 ....
...but the rules of the Conservative Party leadership election process
were, of course, designed to disadvantage the incumbent.
Under the somewhat abstract rules the 1st round
runoff led to a second in which candidates who were not in the 1st
round could enter. In the 2nd round John Major polled only 49.7%
- not enough to win. This was supposed to lead to a third and
final ballot to be decided via AV but Michael Heseltine and Douglas
Hurd withdrew with only 35.2% and 15.1% as by this time everyone was
Interestingly when Edward Heath stood for party leader in 1965 he
didn’t achieve a 15% lead either but Reginald Maudling
dropped out and no other candidates came forward and there was no
incumbent to beat so the 15% margin did not apply. For some
there tend to be more candidates entering in the 2nd round of the
runoff system when the party is in Government.
In the 1997 election for leadership of the Conservative Party William
Hague who verhmently condemns AV for allowing the person who comes 2nd
or 3rd to come 1st was, of course, in 2nd place during the 1st and 2nd
ballots until John Redwood's elimination from the competition allowed
him to push Kenneth Clarke into second place.
In the 2001 election for leadership of the Conservative Party the rules
were changed again so that the final two candidates had to be voted on
by the entire party. Although Micheal Portillo was the leader in
the 1st ballot (there were
actually 2 first ballots as the two
ranking candidates tied for last place and the Chairman of the
Committee couldn’t decide who to eliminate first which matters as the
runoff is not instant but on sequential days) when David Davies
Michael Ancram were eliminated most of their backers migrated to
Kenneth Clarke and Iain Duncan Smith so that Micheal Portillo was
eliminated in the penultimate round by 1 vote. The story of his
life. Many People blamed tactical 3rd round FPTP voting for
Portillo's disqualification. However, it is just possible that
actually no one likes him.
Notice how Michael Portillo's vote
drops in the "2nd first round". This situation is the result of
tactical voting during the repeat ballot based on information that
could only be gleaned from the results of the 1st first round vote.
Iain Duncan Smith then won the membership vote despite being 4 points
behind Kenneth Clarke in the MPs vote. Iain Duncan Smith’s narrow
margin in the MPs ballot meant he was in a very weak political position
and Michael Howard managed to usurp him 2 years later ....
In the 2005
election for leadership of the Conservative Party David
Davies was the front runner in the first round but when Liam Fox and
Kenneth Clarke were eliminated their supporters shifted their votes to
David Cameron who won both the MPs vote and the party vote.
in the 2nd Ballot David Davies's vote share falls only to rise again. This is the
result of the Runoff process not being "instant" but a series of
sequential FPTP ballots with a time
lag in between each allowing for tactical voting based on the results
of the previous round. This
situation is not possible in "Instant" Runoff Voting or AV - votes can
be reallocated but not switched. It is this
effect that instant runoff 1,2,3,4 ... style ballot paper is designed
Some Chickens explain the traditional
financially prudent Labour Party Leadership Contest "Chickening Out"
which has the added advantage of not involving any affliliates, unions
pesky party members.
Gordon Brown was famously "elected"
unopposed as any challenger would have needed to be nominated by 12.5%
of Labour MPs - the process favours the incumbent. No AV ballot
before the most recent has gone beyond 1 round since 1980 due to either
a limited number of candidates
personally very expensive to run) or one candidate getting an absolute
1st round majority. Unlike the Conservative Party, the Labour
Party likes to hang on to bad leaders for grim death. The last
election for leader was highly unusal in having 5
candidates and progressing through all 5 rounds of the AV process.
As we can see it is the reallocation of losing candidate Ed Balls, Andy
Burnham & Diane Abbot's votes that make the differece between Ed
and David Miliband winning or losing. On a slight tangent
one could also analyse which elements of the electoral college the two
finalists derived most support from which is interesting.
There is no doubt that politicians themselves think that runoff voting
is a better way of arriving at political stability than a simple FPTP
election. However, the reason that General Elections do not
utilise runoff voting is twofold.
Firstly cost. It would be extremely expensive to perform multiple
And secondly since there are 650 consituencies all electing MPs
simultaneously - if those where the result was close enough to
go to more
than one round the voters in the key marginals would have detailed
knowledge of the results of other constituencies to inform their choice
for the next round which would not be fair to other voters.
In order to solve the problem of how to run a runoff type election
without the voters knowing the results of the previous ballot at the
next round ...in 1871 American architect William Robert Ware invented
"instant runoff voting" or "AV" - a system whereby the voters
their candidates in order of preference 1,2,3,4 etc so that all the
"runoff rounds" can be contained and calculated from the numbered
preferences of one ballot paper.
The problem is that although the permutations through which every
voters choices are passed are equal (all votes are treated equally)
because they are expressed on one piece of paper instead of 3 it is
possible to claim that the votes are not of equal value because
physical recounting of every single ballot paper is not required once
they have been sorted at the end of each round. This actually
ended in a court case in the US (which uses AV for
the selection of Mayors) known as...
in 1975 at which Circuit Judge James G. Fleming decided that
Under the 'A.V.
System', however, no one person or voter has more than one effective
vote for one office.
No voter's vote can be counted more than once for the same candidate.
In the final analysis, no voter is given greater weight in his or her
vote over the vote of another voter, although to understand this does
require a conceptual understanding of how the effect of a 'A.V. System'
is like that of a run-off election.
The form of majority preferential voting employed in the City of Ann
Arbor's election of its Mayor does not violate the one-man, one-vote
mandate nor does it deprive anyone of equal protection rights under the
Michigan or United States Constitutions.
AV is often criticised as a highly complex mathematical model.
Critics such as Baroness Warsi claim that AV puts power in the hands of
extremists. Leaving aside the obvious point that FPTP would seem
to put extreme power in the hands of tiny parties... here's a graph
showing Andrew Pelling's 2005 Conservative majority for Croydon Central
of 75 votes displayed in proportion to the minor parties votes in that
election to give some indictation how sought after their votes are in a
It is easy to write of Lady Warsi as simply the person given the dirty
work of the Conservative party because she's the one who cant lose her
seat but the reality is a tad more complictated. Lady Warsi's
argument for the dangers of AV (as explained to the readers of "the
Sun") was that in Dewsbury where she stood in 2005 the BNP polled more
than the difference between the two major candidates (as we shall see
below this doesn't actually give their voters the ballence of power due
to threashold effect) but her arguments are worth considering as
Dewsbury in which both the Conservatives and Labour fielded asian
muslim candidates (the Labour candidate was Shaid Malik) in 2005 polled
the highest BNP vote in the country.
However, if we look at the data from 2001 to 2010 (there were some
minor boundary changes in 2010) we see a few interesting
undoubtedly an enormous BNP peek in 2005. And secondly the then
Ms Warsi seems to have actually lost votes in relation to 2001 in
defiance of a national vote swing trend in favour of the
Conservatives. Labour have lost seats in line with the National
trend but they seem to not have been picked up by the
Conservatives. Instead they have been picked up by the Liberal
Democrats and the BNP. Here's a graph of the local vs the
National swing in Dewsbuy:
The swing to the BNP is massive ...and out of line with the National
trend and seems to almost completely correct its self in 2010...? The
only common factor not present in 2001 and 2010 but present in 2005
that I can find is ...erm Lady Warsi. Perhaps voters held a
racial prejudice against the first ever Tory muslim candidate. Or
was it something she said. The battle for Dewsbury seems to have
been extremely hard fought in 2005 and Lady Warsi certainly didn't
enamour herself to the gay rights group Stonewall with her literature
about how nice Section 28 was long after Micheal Howerd had abandoned
And she also managed to come up with this campaign leaflet about
....you want an end to political correctness, an end to yob culture, a
tough stance on crime, a stop to Europe dictating to Britain and
controlled immigration, VOTE CONSERVATIVE, the only party that can
DELIVER and put you FIRST.
Dewsbury is by all accounts an interesting and lively place where
debate is, to borrow a word from Mr Cameron, "robust". After
Shahid Malik won the seat in 2005 and not long after the 7/7 terror
attacks who's protagonists put Dewsbury on the national map for all the
wrong reasons this lively debate escalated into a memorable libel trial
when Mr Malik sued Tory councillor Jonathan Scott and Dewsbury and
District Press editor Danny Lockwood over a letter printed in a 2006
edition which insinuated Mr Malik was complicit in using asian thugs to
Mr Scott claimed that during the local elections Malik's "cohorts" used
"physical intimidation and verbal abuse" at a polling station in
Saville Town. Mr Scott incidentally was Ms Warsi's election
campaign manager. We know this because of a complaint made by
Pink News, Stonewall and a group of Labour Cllrs to David Cameron in
2007 over the continued circulation of the "homophobic
leaflets" used in the 2005 election campaign. The case seems
to have revolved around the principle that while it was in the public
interest for the paper to publish the accusations they should have
contacted Mr Malik ahead of the publication of the letter to allow him
a chance to put his side of the story. Mr Lockwood insisted that
this had been done and wrote a letter to Mr Malik claiming that
attempts had been made to contact him before publication which were
later retracted in court.
"We quite clearly don't have phone records. I trust Martin Shaw
implicitly. If Martin says to me he tried to ring I'm pretty
certain he tried to ring. Yes I was angry, yes I was lashing out.
We do not have phone records. It was a big porky pie." Defending
his decision to publish the letter Mr Locwood went onto add that:
"Dewsbury had severe problems with elections over the last nine
years. We've had stories of postal fraud and intimidation. That's
not specific to Labour but it is specific to the Asian community"
Indeed in 2010 Lady Warsi opined that at the 2010 General Election the
Conservatives lost at
least three seats "based
on electoral fraud”. She refused to identify the seats concerned
but said the problems were “predominantly within the Asian community”
and that Labour had been the beneficiary. “I have to look back
and say we didn’t do well in those communities, but was there something
over and above that we could have done? Well, actually not, if there is
going to be voter fraud". Pressed further on what she meant she
clarified "I am saying there are seats at the last election in
which those constituencies are concerned, quite rightly, that electoral
fraud took place.What I can say to you is that individual
constituencies are raising these issues with the police and with the
Electoral Commission. You'll be surprised to know that 81
complaints were made to the police after the last general election and
I think over 25 of them have now become formal complaints. Yes,
this process is in place; yes, the appropriate authorities have been
informed; yes, it is part of the electoral reform process and
discussions I am having with Nick Clegg. "
Of course the Prime Minister prior to the General Election raised the
idea of severly cutting the funding of the Electoral Commission.
Stating nostalgically that
It is fair to say postal vote fraud is not an exclusively asian
phenomenon - we have previously explored the phenomon of postal voter
fraud by Conservatives in
Guilford. And indeed there have also been allegations of
voter fraud against the Conservative party in Dewsbury and Halifax
which is "a
hot spot for voting fraud".
The Malik libel case eventually went to a fully jury trial, but
unfortunately the Jury was not able to reach a majority verdict.
The Hon. Mr Justice Eady indicated that he would accept a majority
verdict of at least 10-2 but the jury were unable to reach this level
of unanimity. They were not even able to agree that the
publications were defamatory, let alone whether they were substantially
true and requested for permission to “google” the parties on the basis
that they required more information to decide the cases.
Unsurprisingly, the Hon. Mr Justice Eady said :
A retrial was planned but both parties pulled out when they realised
that costs had now reached in excess of £300,000 and avoiding a
retrial would mean avoiding anyone having to cough up any of this
money. Dewsbury's local newspaper continues its unique brand of
Mr Malik lost his seat in 2010 when pro-AV and anti-sealze campaigner
and ex independent MP Martin Bell financed Khizar
Iqbal to stand
against him on an "anti-sleaze ticket"....
...Mr Malik blamed the vote split effect for his losing the seat saying
Mr Iqbal had been "brought forward not to win but to make sure that I
lost". Ironically Mr Bell had actually demonstrated one of the
positive aspects of FPTP. Deeply unpopular MPs and candidates can
lose in defiance of national party trends if they're ...erm...
unelectable. Mr Iqbal has now rejoined the Conservative party and
is back on the local Council.
What really happened in Dewsbury in 2005 I guess we'll never know fully
so let us instead have a look at how FPTP elections could play out
Using data from Croydon Central for 2010 I've done a
basic statistical analysis of the various possibilities. I could
have used 2005 results for this but it makes more sense when
considering if a losing candidate could actually win under AV to take
FPTP results where there is more of a discrepancy between the winner
and loser. This election is more interesting too as for
complicated reasons the
Conservative Party had schismed in Croydon by 2010 and Andrew Pelling
was running against his own party. There was some argument over
whether he had resigned or been sacked by Conservative Central
Office. The payoff for ordinary Conservative Party members now
having a vote in the leadership election is that they have lost
control of their Constitency associations which do not utilise
OMOV to select candidates. Central Office can and does impose
candidates on local party Associations. The old federal
Conservative Party structure was replaced by a more centralised one to
try and resolve some of the bitter disputes above and "modernise the
party". The Conservative
Home website is full of amusing articles on how to circumvent these
rules as the party comes up with new ideas such as open primaries to
excluded the poor who cannot afford to canvass an entire constituency
rather than a few hundred members. The membership at the moment
is 160,000. The membership of the Labour Party is about
250,000-300,000 but has been as low as 180,000 at the tail end of the
Brown years. So why is any of this sillier than say PR with
closed party lists? Some have postulated that Mr Pelling actually
stood order to
"split the vote under FPTP and let Labour in". It has not gone
unnoticed Mr Pelling has
since joined the Labour Party...
It is of
course highly unlikely that any voter would transfer their vote through
every permutation but if they did the results would look something like
This is the case if all the minority candidates redistribute their
votes in order of general candidate popularity. However, it is
more likely that the reallocation would be slightly random. In
which case the results would look more like this
In either case it is the last round that is decisive.
So is there a senario in which the BNP or another such minority group
could "hold the ballence of power"?
Well, statistically the worst case senario to be found would be if
Candidate 9 votes gave all their 2nd preferences to candidate 8 and
these were then ALL transfered to candidate 7 and then Candidate 6 so
that all the minor party candidates all expressed identical second
preferences. This would be an extreme statistical, social and
political freak event and is probably impossible as if they are all of
the same mind why are they all giving their first preferences to
different parties/candidates in the first instance. But as it is
a mathermatical possibility here is what such a senario would look like.
If that looks rather complicated here are the solutions again.
Rounds 1 to 6 are pointless exercise of reallocating votes of one no
hoper to another. The decisive rounds
in an AV election are the
final two. Before these only the candidate who is first in the
first round can win.
At the end of the third to final round the candidate in 4th place's
votes can now push the candidate in 1st place over the 50% finishing
post if they all transfer their votes to the leading candidate.
However, they cannot push the candidate in 2nd place over the finishing
line. As the minor parties collectively seldom poll more than 10%
as a whole it means the 1st place candidate needs to break the 40%
barrier in order to win. Here's an animation in which the Labour
and Conservative percentages go up and down while the Others and the
Liberal Democrat percentages stay fixed...
We could complicate the animation by making the Liberal Democrats
percentage change, but if it changed much they wouldn't be the 3rd
party any more and then Labour or the Conservatives would be in the
middle of the diagram. The important point to note is that at the
3rd and final round the leading candidate must poll over 40% for the
Others 10% to be able to push them over the finish line - this can only
happen if a very large percentage of the others transfer their votes to
the leading candidate. Even
if ALL the "Others"
only usually poll 2-3% of the others 7-10%)
their votes to the candidate in 2nd place at the penultimate round they
cannot push the candidate in 2nd place over the finish line in any
statistical permutation. Therefore
ballance of power in an AV election resides with the Liberal
response to William Hague's claim that under AV the party that
comes 3rd in the 1st round can win. Yes, but only if the
party in 2nd place gets less than 33% of the vote. The party
that comes 2nd can win on second preference votes of ALL the other
parties. And the
party that comes 1st in the first round can win with the 2nd preference
votes of the 4th, 5th, 6th to nth votes or with the 2nd preference votes of
the 4th, 5th, 6th to nth votes. Here's another diagram
showing all the permutations possible where parties A and B are neck
and neck and we vary the percentages of C and D In any NON
1st round winning senario, for A,B,C,D to be 1st, 2nd, 3rd & 4th
place the following conditions MUST be true: A + B + C +D
= 100% A <= 50% (if A is greater than 50% then A
wins on the first round and there's no point in calculating anything) A > B B > C C > D
A (1st in the 1st round) + D (votes redistributed in the penultimate
round) are just capable of causing the 1st round winner to win without
going to a final round
B (2nd in the 1st round) + D (votes redistributed in the penultimate
round) are NOT
of causing the 1st round loser to win without
going to a final round
If the Substantial portion of D's votes are transfered to C in the
penultimate round B (the second
place candidate in the 1st round) can be eliminated by C if they poll
A gridding program like Surfer can give us a better ideal of the
interdependency of A+D, B+D and C+D as B approaches A. It looks
like this. The blue area of the grid represents > 50%.
Viewing from the side we can see how D votes can just push the leading
candidate A over the finishing line...
...and viewing from the top we can see how the gird never extends quite
up to or beyond the 50% mark of the C + D and B + D axes because it is
impossible for candidate B or C to cross the finish line with the help
of candidate D.
If voting goes to the penulitmate round where all the minor party votes
have been redistributed and we only have three candidates left A, B
& C where A + B + C = 100% A <= 50% A > B B > C
then, of course either A or B can win with the help of C. The
possible vote share permutations here
are much easier to visualise and looks like this:
However, the No Campaign still managed to come out with some stand out
nonsense graphs. Here's probably their best example which shows
BNP candidate E (not even D) pushing candidate B over the finishing
line - mathematical impossibility...
After I pointed this out to them they gave up on that particular con
trick and tried creating graphs that conceal the starting point.
However, being very good at Maths we have managed to take the
Conservatives Race poster and back calculate the starting point...
that the "athletes" have run less than 9 Metres and this picture too is
they have a point that "the person in 3rd place can win" - not by the
margin shown. Actually (B and C)
and (C and D) must both be within 15% of each other and (B and D)
within 22% of each other to generate a valid senario and B must poll
< 33%. Since this is a Conservative No to AV poster it
must have been approved by the Prime Minister. Erm ... not
inspiring. To be fair to the NO campaign though - this is not "as
simple as 1,2,3". Interestingly although there is quite a large
statistical window it's only happened once in Australian Electoral
history. And not under the AV system that was suggested for the
UK but under a full preferential system by which as Lord Ashcroft points
out Henry Arthur Hewson was elected to the Australian House of
Representatives in 1972.
After bringing in AV the Australian politicians got the hump that not
enough people used their preferences and made voting compulsory.
Since an AV election is a simulation of a series of runoff ballots this
effectively made using all your preferences compulsory too and in the
end this resulted in "donkey voting":
Donkey voting is
you when you simply vote in the order the candidates appear on the
ballot paper as a form of abstention 1,2,3,4,5 ... etc. Because
there's no ability to spoil the ballot paper or abstain this resulted
in there effectively being a 2% advantage to be gained from being the
person at the top of the ballot paper. So in the tradition of
Malcolm Hardee who always called his shows
something like Aaaaaaaaaargh! in order to be the first listing in the
Fringe program parties actually started selecting people purely for
having names that began with A and B. The most famous example was in
the NSW Senate election in 1937 where Labor's ticket featured four
candidates named Amour, Ashley, Armstrong and Arthur - all of the "Four
A's" were duly elected. Eventually it was decided that the ballot
paper name ordering should be made random to the eternal dissapointment
of all Australians with names like Anthony.
Then again the person in 3rd place winning might not be as silly as it
sounds after all. Particularly if you live in Norwich South :
...which thanks to
the the Green party taking a leaf out of Lord Ashcroft's target seats
tactics is now Britain's most divided Constituency where the Liberal
Democrats won with 29.4% and a majority of just 310. Norwich
voted against AV with a margin of 71%. One of the few places that
did vote for AV was Camden which just happens to contain Britiain's
most 3 way split constituency with the highest 3rd party vote:
Hampstead & Kilburn.
This is the sort of
place where the FPTP model is clearly starting to break down.
However, the Yes to AV campaign never really bought such arguments
Concentrating on the argument that AV would end safe seats.
Actually AV does nothing to Large majorities. AV is an attempt to
put an end to small majorities. One thing neither campaign asked
was how many such Constituencies there are. The answers are
displayed further down the page. That all said AV with it's person in 3rd
place can come 1st is obviously just too random for most ordinary
people - unlike FPTP where a Liberal Democrat vote increase of
1,000,000 between 2005 and 2010 translated into 6 less seats which
makes a mockery of the Nick Cleggs entreaties that "if people want more
Lib Dem policies the way to make that happen is to vote for them".
Although there maybe some truth in the theory that all the places that
voted Yes to AV are filled with Liberal Elites and Guardian readers it
is interesting to note from the IPPR Worst of Both worlds study that
Metropolitan areas score the worst in terms of the "disproportionality
quotient" DV.This is highest in London. And as we can see above
is absolutely at its highest in Camden.
The statement that the person in 4th place can win ...
...is of course nonsense too -although at least the No campaign tried
some statistical analysis no matter how ridiculous.
To be fair they did eventually get an image which correctly explained
the AV worst case senario
But then they underlined it with a mathematically untrue statement.
The votes of the least popular candidate cannot mathematically decide
unless there are less than 4 candidates... which there aren't in the
Also careful viewers will notice that it's not until Round 4 that any
of the piles get any taller.
If we give them the benefit of the doubt and the diagrams of rounds
1,2,3 and 4 were not meant to be to exactly the same scale
Then this is what they're trying to display. Still, it's within
an acceptable boundary of error - this is after all
a leaflet condemning a form of proportional representation so one would
expect the graphs to ...erm... not be in proportion.
To be fair to the
No campaign they did actually provide some diagrams (all be they mostly
wrong). The Yes campaign avoided providing any mathematical
Anyway who cares about Mathematical truth? FPTP is better
because it is SIMPLE. We know it is simple because
every time there's a general election we recieve a lot of literature
containing dodgy statistics telling us how to do runoff calculations in
our heads because
"ONLY WE CAN WIN
How inspiring. These tactics
however, are very effective in
keeping the 3rd placed party very low in any marginal constituency:
If you order that in terms of the marginality of each seat (A-B) +
(B-C) + (C-D) you see this:
Although the margin of A and B over C and D looks big it has of course
got lower over time as voters who used to be put off from voting for
fringe parties with the inference that their votes were wasted and that
a "wasted" vote is somehow immoral dont seem to give as much of a toss
about this any more...
So it's not impossible that Britain actually will abandon FPTP one day
but it wont happen until the number of 3rd party and other votes
increases a little further. Winning majorities have consistently
fallen since the 30s to below 60%. The further the fall the more
random election outcomes become and the more the FPTP model will break
If we create some
grids of the data (i.e. attempt to put a mathematical function across
it to build some surfaces) we can see in 3 dimensions the effect of the
3rd and other party votes adding up to much more than the first party
votes in some constituencies.
The crosses ( + ) on the grid mark real data points - everthing else is
extrapolation (in case you're wondering how some grids can cross others
where in real life this would be impossible). However, the
purpose of the grids is to try and view the overall trend rather than
create an exact representation of reality. The further away a
grid point is from the crosses displayed the more likely it is to be
nonsense. If we blank out the extrapolated parts of the grids
beyond our input data limits we see the 20 constituencies where
tactical voting becomes important because the 3rd and other paries
share of the vote is now > the winner's share. There are about
110 marginals at any election so this represents about 18% of all
Anyway all of this statistical analysis is silly anyway as all that was
really needed to
win the referendum was this picture:
Chris Huhne, of course got very cross at Cabinet about the use of this
picture causing George Osborne to retort that "This is cabinet not a
Jeremy Paxman interview". Mr Huhne was, of course, Mr Clegg's
rival for the leadership of the Liberal Democrats back in
2007. A contest that was so close it was decided by a
margin of only 1%.
Devotees of the late Right Honourable Francis Urquhart MP can do
nothing but admire the speed with which tabloid newspapers wheeled out
his ex-wife. Huhne won his seat in 2005 with only 568 votes ...
...and shortly after
being elected again with a slightly increased majority....
...revealed to the press that actually he was divorcing his wife for
his mistress Carina Trimingham (a technique often employed by MPs
wanting to dump "loyal" wives at the optimum point of the electoral
cycle known as "doing a Pelling"). Ms Trimingham is also
campaigns director at the Electoral Reform Society making the
referendum loss by such a large margin a personal as well as political
failure for Mr Huhne.
Unfortunately by the time of the referendum this affair was rather old
news and all Mr Huhne's children now seem to be grown up making the
"leaves wife to bring up family" angle a no goer ... but fortunately
his ex-wife was able to revive a claim that he had asked people to take
points from him to prevent him losing his licence. Mr Huhne lost
his driving licence eventually anyway due to speeding a
lot while trying to cover the enormous distances ....
When the driving points story and the fact Ms Trimingham is bisexual
failed to ignite anyone's imagination the Sunday
Times ran an story about Mr Huhne somehow incriminating himself in
a "secret tape" that was "obtained legally". We were not informed
who was on the other end of the phone by Mr Huhne (according to the
Telegraph it was his ex-wife) but he apparently said “I
honestly don’t think, I really don’t think, that it is sensible to have
these sorts of conversations over the phone,” as “the last thing” the
witness wants is a “half-baked story” appearing in The Sunday
Times. An official complaint has been made to Essex police by
Simon Danczuk, a Labour MP about the diriving points matter and they
are now very busy reviewing 8 year old speed camera footage which I'm
sure is a very sensible use of police time and resources. Inside
the paper regular columnist Jeremy Clarkson was very busy opining that
is a need for Super injuctions and Privacy laws to prevent people like
himself becoming the victims of malicious tittle tattle and
unsubstantianted claims. Then again maybe Mr Huhne is just a bad
man. The accusations and counter accusations are complicated so
we asked a detective what he thought.
"cost of AV" proposed by the No campaign was beyond satire. But
it has to be said the Nick Clegg chose his words carefully when he
replied that the votes would be counted "in the normal way" without
counting machines. This is not a denial that it would have taken
more time or money.
Of course cost is a ridiculous argument. Particularly from the
likes of David Blunkett who's abandoned ID card scheme cost £260,000,000
and was expected to have cost £800,000,000 if it had gone to
completion. Blunkett even admitted this himself when
cornered. Gamely responding that during an election campaign
people just make figures up. While there are laws about telling
lies about individual candidates personal character... statistical lies
and outright mathematical lies are pretty much regarded as simply all
part of the free debate... so tell as many outright provable lies as
you can. It doesn't matter if it gets votes in the box.
If you want other examples to scale £250,000,000 to
The Labour Government, of course, also spent over £4.5 billion on
the Iraq War.
The Conservative 1992 Black Wednesday debacle cost the country an
estimated £3.3 billion.
On the other hand
it is fair to point out the the Yes campaign assiduously avoided giving
any costs for their proposal. "Votes would be counted in the
usual way" is not a costing. And while it is true you can count
an AV election manually it would doubtless be long term more time and
cost efficient to deploy counting machinery.
Of course the other accusation against AV is that it's not full blown
PR. There's a reason for this. In order to approximate the
number of seats to the number of votes in the most mathematically
rational way so that number of seats = proportion of the votes you have
to use multi-member constituencies. The larger you make these the
nearest you can get an equal correlation of the votes to seats.
The oldest and most common system is STV.
Under STV a candidate must poll above a set "winning"
threashold. If not all seats are filled on the first count the
winner's "extra" votes are reallocated to a second preference. If
still no one passes the threashold then the candidate in last place is
eliminated and their votes are reallocated. As soon as there is
a second winner if there is another seat to fill this winner's "extra"
votes are reallocated to a second preference. The process
repeats till all seats are filled. There are different ways
of course of setting the threashold but usually the "Droop quota" is
used which is:
It's not a complicated as it looks. What it means is if there is
1 seat the threashold is 50% +1 votes,
2 seats 33.3% +1 votes,
3 seats 25% +1 votes etc
of the total valid poll.
It's really an attempt to refine AV for multi-member constituencies by
allowing extra votes from a constituency where the winning candidate
got > 50% flow into one where they got < 50% by taking the two
constituencies and melding them into one big one and using a formula to
calculate proportional vote transfer... if you follow that.
The difference between STV over closed list PR is that under STV the
voter can chose for their votes to be re-allocated along non-party
lines if they have a strong personal dislike for an individual
Candidate. In order to make this easier to visualise here's a
theoretical example that I have made up showing what might happen if
you merged Croydon Central, North and South into one STV constituency...
If you only have a one member constituency then the winner's extra
votes reallocation proceedure is meaningless and thus a 1 seat STV
election is simply an AV election.
However there wont be a
referendum on this as the maths really is hard and politicians dont
anyone would vote for multi memeber constituencies ... although the UK
actually had them until as late as 1950 which used the Bloc vote system
electors could cast a vote for up to as many candidates as there were
seats to be filled. The elector could not vote more than once for any
candidate, but was free not to use all the possible votes. This
was abandoned as it was even more non-proportional than FPTP ...which
is quite hard.
Anyway the problem with STV is that proportionality
effectiveness is a function of constituency size and number of seats.
could go into some quite complex mathematics to prove this but
here's the back of a fag packet explanation instead. 3rd party
and minor party votes are spread about geographically over a wide area
patches and this is why small parties do very badly under FPTP and only
a little bit better under AV. The STV mathematics is an attempt
to reintroduce proportionality but because of the wide geographical
spread of 3rd and small party voters there is no mathematical way of
doing this without delocalising MPs to some extent. On the plus
side both AV and STV negate the inherant gerrymandering problems of
FPTP. Under FPTP as MPs are highly localised where you actually
constituency boundaries can have an extremely disproportionate effect
on proportionate representation This can result in the party with most
not actually having the most seats in parliament as happened 3 times in
the 20th century. The last was 1974.
The alternative to AV or STV is PR using open or closed party lists and
a largest remainder method of calculating how many MPs of each party
there should be. The European elections utilise the D'Hondt
method of PR from closed party lists with its easy to comprehend
The total votes
cast for each party in the electoral district is divided, first by 1,
then by 2, then 3, then 4, then 5, right up to the total number of
seats to be allocated for the district/constituency. If the district
contains 8 seats, the highest 8 numbers are chosen from all the numbers
resulting from the divisions. The parties under which each of these 8
highest numbers were produced get the seat.
**** = 4 seats won
*** = 3 seats won
* = 1 seat won
No * = no seats won
....using a closed party list system that creates very large ballot
...that makes an AV
one look simple.
Unless you're in Northen Ireland where they use STV because they are
special. And the resuts look a bit like this
Or one can use the the fudge between AV and PR known as AV+ whereby the
bulk of MPs are elected using AV from single member constituencies with
the remainder needed to achieve statistical proportionality chosen from
party lists to "top up" the legislature. Again this leaves some
MPs without physical constituencies.
AV+ was the invention of the
1998 Jenkins Commission into all the different forms of Proportional
Representation set up by Tony Blair. Mr Blair wanted to woo
Liberal Democrat voters with promises of reform, but fortunately as
there are multiple forms of Proportional Representation he could spend
a long time getting Jenkins to investigate them all and thereby avoid
Aware that all forms of PR for the Westminster Parliament are not in
their immediate self interest the Labour Leaderships have long played
cat and mouse with the Liberal
Democrats over Electoral Reform. Claiming to be committed to it
in some form but never enough to do anything about it - just enough to
pick up Lib Dem voters. Fortunately AV+ with its "two types of
MP" invented by Jenkins has certain logistical problems to be resolved
and no history of
implementation so it can never be implemented. For example what
if a candidate is rejected by a constituency but ends up in Parliament
anyway to achieve proportionality...? Such questions have never
been fully clarified. Arguably STV is
more logical than AV+ (a form of Additional Member system) which is a
best of both world solution and so likely to satisfy nobody... but it
would require quite large constituency regions to achive proper
That said the Blair government did experiment with Additional Member
systems in the Scottish Parliament and Welsh and London Assemblies so
this wasn't a compete dead end. Of course the reason for using
these systems was to stop any of these regional bodies getting single
party government that could lead to a referendum on Independence.
A policy that has spectacularly failed now the SNP have a majority in
Parliament. Which just goes to show if you think about
winning and not the system ... then you're not the 3rd party.
Aditional Member systems do have the advantage of the greatest
statistical proportionality. Obviously because you can vary the
number of aditional members to achieve this. Here's a picture I
stole off wikipeda
of relative proportionality for voting systems...
Based on Patrick Dunleavy (London School of Economics and Political
Science), Helen Margetts (Department of Politics and Sociology,
Birkbeck College, London), Report to the Joseph Rowntree Foundation, 15
April 1999. As we can see AV actually is more proportional than
FPTP but that didn't stop the No to AV campaign claiming it both was
and was not.
Of course in regards to the AV referendum the Party Political question
is who would have benefited and most
analysis would seem to suggest that in general Labour and the
Conservatives would lose seats to Liberal Democrats under AV while the
very small parties are frozen out. The Conservatives would lose
more seats which is probably why they are almost totally against it,
while the Labour party would lose a few which explains why they are
split on it. If you're wondering how the party split on it here's
a histogram of Yes/No/Dont know Labour MPs vs Majority showing that
...it's a pretty random split. At least it is independent of
majority. The input data is taken from Labour
List's list. ...Of course, AV is a statisticians wet dream as
are so many potential permutations as variables.
attempt at the most basic simulation can be achieved by downloading the
2010 election results off the Electoral Commission website and doing
some cell operations to try and figure out what happens when you divide
all the minor party votes up equally between the top three polling
parties in each constituency and then divide up the 3rd parties votes
between the 1st and 2nd place parties for various percentages.
Anyway after running all the various permutations I came up with this
As we can see the Labour party could push the Conservatives out of
power if they got more than 60% of 3rd party votes. However, they
could also find that they had 80% of 3rd party votes but did
worse...? Bear in mind that the 1st, 2nd and 3rd placed parties
are not always
the main three parties and to some extent this explains the extremely
interesting graph shape. As we can see the Liberal
Democrats have a lot to gain...
If you divide up the all the 3rd, 4th, 5thm 6th to nth party votes and
generate a similar percentage plot (i.e. dont share out the minor party
votes equally) you see this:
...which looks very good for the Labour and Liberal Democrats ...or
does it look like a Conservative Lib Dem Coalition? Certainly the
average voter in the street might say we had a Coalition before and we
had one after - so what's changed?
Of course this assumes people would vote the same way under FPTP as AV
so round in a circle?
One might imagine that given it's been their biggest policy plank to
which everthing has been sacrificed to implement the Liberal Democrats
should be as happy as a manic
depressive in the manic stage by the prospect of AV but in reality
they've been so committed to full blown STV PR systems that would give
them even more seats that given the
chance to actually change something they're not happy either.
There's even a No to AV because it's not PR campaign spearheaded by the
one and only Mr Principles-over-Power himself Dr David Owen...
In order to see why the Liberal Democrats are such big fans of PR one
need only look at how seats would be distributed under a fully
... of course AV is
not a fully proportionate system so it would not increase their seats
to the same extent. However, as well as giving the Liberal
Democrats an extra 92 seats... PR would give the BNP 12 seats and
UKIP 20 seats. So it is not a surprise that many people are
quietly of the opinion that full proportionality might not be a good
idea...? Still, that's democracy for you... after all the old
system of having two main parties that are regularly split over the
issues of Immigration and Europe trying to constantly glue their
enormous spectrums of opinion together using internal AV election
processes in order to heal the disproporionality of FPTP is obviously
much more sensible than not using AV to start with in an attempt to
brush extremist opinions under the carpet. Interestingly one of
the deals Nick Clegg has done to win an AV referendum is to reduce the
total number of Westminster seats by 50 to 600. So at the next
election if we don't have AV it will be even harder for the Liberal
Democrats to win any seats at all - particularly since all the
constituency boundaries will be totally redrawn to favour the
Conservative party just as for the past 10 years they've been redrawn
in favour of the Labour Party.
Of course memories of David Owen and the SDP Liberal Alliance raise the
wider question that although in the 1980s it is (as Neil Kinnock and Ed
Miliband opine) techincally possible for their combined votes
to have beaten Mrs
Thatcher if it hadn't been for vote split effects .........one has to
what a coalition of Labour and the SDP Liberal Alliance would have
looked like. Particularly given that the latter was so internally
divided its two
leaders David Steel and David Owen obviously didn't get along with each
other let alone Neil. There's an old saying about politics.
It's split ...
...because it is shit. Anyway we have the result for the
Referendum now it was ...
...like this. Yes, the Yes campaign was so bad that it failed
even to engage the support of its main supporter base (the Liberal
Democrats and the minor parties). It's interesting too how the
Referendum Result is almost an exact mirror of how people vote at a
General Election...? Funny that. This is why it will never
happen... at least not until the Liberal Democrat vote share comes to
challenge the 2nd place party. So probably never. In a
million years. Ever.
I could explore further such things as Duverger's law of 2-party
domination which attempts to explain how the number of viable political
parties is a function of the type of voting system you use but really,
at this point I got a bit bored and adapted my program to
analyse the mathematical solution to Deal or no Deal. Deal or no
Deal like First Past the Post involves guessing what's inside a box
before it is opened so as to make a seemingly important choice.
First one must consider the number of ways of arranging 22 boxes.
This is fairly simple it is 22 factorial. The number of ways of
arranging 2 things is 2, of 3 things 6, of 4 things 24 ...don't
understand why? Neither do I it's just a mathematical fact that
the number of ways of arranging two things = 1 X 2 = 2, of three things
= 1 X 2 X 3 = 6, of four things 1 X 2 X 3 X 4 = 24. This
function is called a "factorial". With it we can calculate the
"decrease in possible box arrangements with each round". From
1,124,000,727,777,610,000,000 at the start of the game to 0 at the end.
As you can see the rate at which the available choices drop is very
rapid. Even on a logarithmic scale it looks like this:
The chance of correctly guessing which box is going to be opened next
is 1 / the factorial number for each round above which is:
FIVE BOXES 0.83333333333333300000%
THREE BOXES 50.00000000000000000000%
To find out how the boxes behave and the passages from all boxes to 1p
or £250,000 is a simple matter of writing an iterative program to
select 22 random numbers and use these to randomly chose a box opening
order. After 100 iterations I started to see a pattern
As expected the
average amount of money in the game diverges rapidly from the
start. There are also possibe sudden drops at every point along
the box opened axis. Not very helpful...? Well, that's
probably because we're looking at it in XY space and the board is of
course arrange with the £s increasing on a logarithmic
scale. So let's change the Y axis to logarithmic space to refect
the playing board.
This is what
confuses many players that the amounts on the board go up
logarithmically - making it difficult to estimate how far your average
will drop if you eliminate a high box. We can simplify this down
a bit by averaging all 100 iterations and calculating a standard
As you can see if you calculate a standard deviation for the data
scatter in linear space then by box 19 the Mean - the standard
deviation < 0. It is of course impossible to win negative -
£s so what this means in practice is that by box 19 there's a
very high probability of dropping down to less than £100 and
never recovering. In log space the deviation looks like this.
If you run 60,000 iterations and sort them in order of maximum money
remaining in the grame from box 22 down to box 1 so that 0 stands for
the unluckiest iteration and 60,000 winning the £250,000 you see
something like this:
Of course most people stand in a TV studio in Birmingham for up to four
weeks in the hope of winning the £250,000. The
chances of having either 1p or £250,000 if you go right to the
final box are approximate 4.55%. And of course as the financial
scale is logarithmic it's the top five boxes that control the average
within the game. The rate at which these boxes drop out of the
game over the course of the 22 rounds and 60,000 random iterations is
a bit like this... If you want to see the average for all boxes it
is of course a straight line...
Weird. It's almost as if the game were completely
Postscript : Letter from America Of course while referendums are a
rarity in the UK this is apparently not the case abroad... Our US correspondents Pete Peterson
and Pooh write that :
There are 2 things we are involved
here in Idaho politically: 1) Referendums. 2) A Recall of Tom
Luna. First, a referendum is used by
voters to repeal a law that has already been passed by our state
legislature. There are currently 3 referendums that citizens are
collecting signatures on. All 3 referendums are designed to repeal the
3 education "reform" laws that our chief education official (Tom Luna),
pushed through against strong opposition from students, parents, &
teachers. If citizens can gather 18,000 valid signatures on each
referendum before June 1, 2011, then citizens vote in November of 2012
whether to repeal the laws or not. A simple majority vote against each
law results in its repeal.
Second is the recall of Tom Luna
(our chief education official). The recall of Mr. Luna (an elected
state official) is what I am focusing my time & energy on. To
recall Mr. Luna, we must gather 160,000 valid signatures by July 3,
2011. This is a Herculean effort, but it is only the first step. If we
gather the 160,000 valid signatures then there is a special election
held on November 8, 2011. To toss Mr. Luna out of office takes 250,000
votes (that's right Mr. Miller, a quarter of a million votes). I checked with our election
officials & the recall election (if we get the 160,000 valid
signatures) will be held on August 30, 2011 instead of in November of
2011. This makes the recall election even more difficult as August is
an unusual time for an election & most folks are focused on end of
summer activities. One thing that helps the recall effort is that Mr.
Luna is as well liked currently in Idaho as Hitler was in the United
Kingdom in 1944. I hope this clears things up a
little bit. I was @ a hostel in Amsterdam once & the little Dutch
reception girl asked me to explain American politics to her. I told her
that someone would have to explain American politics to me first.
By the way, I have still not received my invitation to the Royal
Wedding (probably a problem with the U.S. Mail). The next time you
happen to see the Queen could you ask her to send me another one?
We'd like to thank the following
for getting close to the many scarey people portrayed on this page so
that we dont have to. Ted Heath photographed by Allan
Warren. Margaret Thatcher photographed by the Margaret Thatcher
John Major United States Federal Government. William Hague photographed
by United States Federal Government.
Iain Duncan Smith photographed by Brian Minkoff - London Pixels
Howard photographed by Mholland
David Cameron from 10 Downing Street
Michael Portillo by Regents College London
Kenneth Clarke by
About Yup David Davies by Robert Sharp
Michael Heseltine by
the Financial Times
Roy Jenkis by Herry Lawford
Baroness Warsi by the UK Home Office and
Particular thanks to Mastro Biggo for the
picture of his cat Malliwi for the photo of Mr
With thanks to Golden Software for help
with 3D visualisation software