Predictions from Preferences

The way that the Alternative Voting system works is easy to describe but quite difficult to express in logical terms.  One of the trickiest aspects is deciding how the losing party's votes will be distributed to the other candidates.  I've seen some other posts where the 2010 election was "re-run" using AV system, but no detail was provided explaining the assumptions made.

So how should I do it?  Every voter is different, so voter A who voted for Labour might express Lib Dem as their second preference and Conservative as their third, whereas voter B might express Conservative as their second preference, and BNP as their third (a significant shift to the right, I would say!).

My suggested approach is to assume, for each party, their second preference parties only, and the mix.  When a party is eliminated under AV, these votes are transferred to the second preference parties in a pre-set distribution (another assumption needed for that), and from then on those votes "belong" to that party and inherit their second preferences.  In this way I only need to assume the second preferences and the mix.

It might not be too hard to make an educated guess for the second preference parties, but the mix will be a wild guess.  As an example, imagine the following votes in a seat:

Imagine the 100 UKIP voters express their second preferences as follows: 70 to Conservative, 30 to Labour.  The votes become after AV Round 1:

Finally, imagine Labour Party voters prefer Lib Dems to Conservatives in the ratio 70/30.  The 30 votes transferred from UKIP to Labour inherit this preference too, so the second and final round becomes:

So the Lib Dems win under AV, compared with the Conservatives under First Past The Post.



I shall finish the model and we'll see what the election might have been.

Swings and Roundabouts

The 2011 Barnsley Central by-election saw Lib Dem voters desert their party, with their count collapsing by 75%, to just 1,102 - enough to cause panic but hardly enough to set of an intruder alarm.  Having previously split their votes 50/50 with the Conservatives, they slumped to sixth behind Labour, UKIP , the Conservatives, the BNP and an independent candidate.  They even managed to help Labour increase their majority AND increase their share of votes from 47% to 61%.  Whatever the Lib Dems are doing, the Alternative Vote system won't help if allegiances change like this.

I thought I'd put my AV model on hold for a moment whilst I look at a new analysis - second places.  First of all, have a look at this.

This chart looks at how the share of the vote for the winning party was distributed in the 2010 election.  So about 20 seats were won with between 35% and 40% of the vote.  But what happens if you superimpose the share of the vote for second and third place?

There are large overlaps between 3rd and 2nd place votes shares, and between 2nd and 3rd.  For example, in Dorset Mid and Poole North, the Lid Dems won the seat with 45.1% of the vote, and the Conservatives came 2nd with 44.5%.  But in Norwich South the Lib Dems won with just 29.4% of the vote.

In Hamspead and Kilburn, possible the most "even" of the seats, Labour, Conservatives and Lib Dems shared around 97% of the vote between them almost equally.

I get the sense that a collapse of Lib Dem votes of even a fraction of what was witnessed in Barnsley, would change the landscape considerably.  But how?

In Barnsley, there was a swing from Lib Dem to Labour of 13.3%, and from Conservatives to Labour 11.3%.  There were also swings between Lib Dems and UKIP, and probably between Lib Dem and Conservatives although the "maths of swing" doesn't allow it.  In reality, the Lib Dem voters switched to several different parties.  I think that the coalition the Lib Dems are in is a dizzy roundabout that they wish they could get off.  I think they will get thrown off.

In a few weeks time, the Scottish devolved parliamentary elections will be held.  This could be a real litmus test for the Lib Dems and in fact the Conservatives as this is similar to a general election.  Members are elected using a First Past The Post system (73 constituencies)  plus a form of Proportional Representation (56 regional members).  At the moment the Lib Dems and Conservatives hold 17 constituency seats and 20 regional seats.  As they are now in coalition with one another, they could think about coordinating with each other to avoid splitting their votes.  But I don't think this will happen.  Lib Dem supporters already have endured the uncomfortable spectacle of their MPs compromising their beliefs (aka. reneging on manifesto promises) and of their leader actually defending Conservative party policy in parliament.  I think Lib Dem voters will progress from giving them a kicking, to inflicting a bloody nose.

Fun-Size Elections

A fierce debate about the UK’s general election voting system is underway in the media. 

I wonder whether it's possible to produce a meaningful model using historic election results and assumptions about how people might select their 2nd and 3rd preferences, to add some analytical evidence to the debate.

I’m still working on the model.  If and when I finish it (I have to do this in the evening, you know) I’ll post my observations.

Before I look at some numbers that could affect an election result, here's a bit of fun from the 2010 election data...

1.        No one took the Kevin Phillips Bong prize by polling no votes at all (by the way, I saw this sketch live at the Drury Lane Theatre in London in the 1970s)

2.        Parties I’ve enjoyed spotting include:

a.        Animals Count, which is a new use for them which will be needed if AV is brought in

b.       The Bus-Pass Elvis Party, who clearly believe he’s alive and living in Kettering

c.        Get Snouts Out Of The Trough, possibly a porcine reference to the expenses scandal?

d.        I’ve always expected “None Of The Above” to appear on the ballot at some stage, but the closest I’ve seen is the No Candidate Deserves My Vote party, which ironically polled 327 in Stevenage

e.        Strangely, the Go Mad And Vote For Yourself Party struck a chord with 233 voters in Dorset South who didn’t realise they were voting for someone other than themselves

f.        The Reduce Tax on Beer Party is clearly the organisation most happy to declare its self-interest

g.       I can’t ignore the Monster Raving Loony Party, who continue to field multiple candidates, and as a result appear in my list of “large parties”

h.       Finally, there’s the wonderfully named Fancy Dress Party who probably have no policies at all but always look good

Anyway, down to the model.  Here’s some of the current output using data from the May 2010 election results.  It shows that in my home constituency of Birmingham Edgbaston, Labour got elected with just over 40% of the vote using the “First Past The Post” (FPTP) system.  Under the “Alternative Voting” (AV) system, the Christian Party’s 127 votes are split according to each voter’s 2^nd preferences.  All other voters’ ballots are amended to remove this Party if they’ve been selected.   This re-assignment of votes goes on until one party emerges with 50% or more of the votes.  You can see that even if all the “smaller” parties’ votes were transferred to Labour this way, they would still not reach 50%.  Eventually, in Birmingham Edgbaston, it’ll be Lib Dem voters’ preferences that’ll decide who wins.

You can also see that there are 650 constituencies (seats), contested by 138 parties.  But 80 of these parties only contest one seat, and 125 of them contest fewer than 10.   Here’s some basic analysis of parties which fought 10 or more seats, plus "smaller" parties who actually won.

Party	Seats fought	Seats won	Seats won 50%+ of vote	Votes cast	% of vote in seats fought	% vote Min	% vote Max
Conservative	631	306	126	10,703,654	36.95	4.40	62.80
Labour	631	258	76	8,606,517	29.71	2.25	71.96
Liberal Democrats	631	57	12	6,836,248	23.60	5.03	61.97
UK Independence Party	558	-	-	919,471	3.56	0.65	17.38
British National Party	338	-	-	564,321	3.70	0.40	14.60
Green Party	335	1	-	285,612	1.81	0.51	31.33
English Democrats	107	-	-	64,826	1.28	0.14	5.18
Christian Party	71	-	-	18,622	0.60	0.19	1.77
Scottish National Party***	59	6	-	491,386	19.93	7.66	45.68
Plaid Cymru**	40	3	-	165,394	11.28	2.10	44.33
Trade Unionist and Socialist	37	-	-	11,913	0.80	0.29	2.93
Monster Raving Loony Party	27	-	-	7,510	0.56	0.187	1.77
Socialist Labour Party	23	-	-	7,196	0.77	0.28	1.72
Alliance Party of NI*	18	1	-	42,762	6.35	0.59	37.23
SDLP*	18	3	-	110,970	16.47	1.06	48.58
Christian Peoples Alliance	17	-	-	6,276	0.76	0.11	2.83
National Front	17	-	-	10,784	1.45	0.28	4.87
Sinn Fein*	17	5	2	171,942	26.88	0.75	71.08
UCUNF UUP and CON*	17	-	-	102,361	16.32	3.11	30.44
Democratic Unionist Party*	16	8	-	168,216	28.34	7.58	49.81
Respect	11	-	-	33,251	6.84	0.39	25.12
Scottish Socialist Party***	10	-	-	3,157	0.81	0.51	1.41
Traditional Unionist Voice	10	-	-	23,300	7.26	3.54	16.78
Independents	235	1	-	175,604	1.63	0.10	63.26
Speaker	1	1	-	22,860	47.29	47.29	47.29

* Northern Ireland; **Wales; ***Scotland

These are my observations:

1.   Out of 650 seats, 214 were won with 50%+ of the vote, which means that 436 would have required transferring votes under AV

2.   Even the Speaker didn’t have a majority.  Traditionally, no-one is supposed to stand against the Speaker, but this time  it was contested by 10 other smaller parties/independent candidates.  If these others are objecting to the Speaker personally, perhaps because of his parliamentary expenses record, under AV it is entirely possible that he would not have won his seat

3.   The thinnest margin on the record is in Fermanagh & South Tyrone (Northern Ireland) where Sinn Fein beat an Independent candidate by just 4 votes, each polling 45.52% and 45.51% respectively.  This seat could easily flip but would not affect which of the main parties would rule in the UK– this is because the main parties do not field candidates in Northern Ireland and could not benefit from AV

4.   Northern Ireland, Scotland and to a lesser extent Wales constituencies have seats which have multiple candidates that each polled strongly, implying that these results would also be easily affected by AV

5.   There are also a number of constituencies in England where local issues have either unseated a mainstream party, or have split the vote; these also would be affected by AV.  Examples include:

a.   Birmingham Hall Green; Poplar & Limehouse; and Bethnal Green & Bow, where a Respect candidate probably took votes away from mainstream parties

b.   Barking; and Dagenham & Rainham, where a BNP candidate pushed the Lib Dems into 4^th place

c.   In Norwich South, the three main parties each polled between around 23% &  29%, but the Green Party took over 14%.  So only a small % of Green voters choosing differently could have flipped the seat

d.   In Wyre Forest, the 1-seat Independent Community and Health Concern party polled a stunning 31.7% of the vote, taking 2^nd place.  The same could be said of the 1-seat Independent Save Our Green Belt party who polled over 27% in Castle Point

I'm planning to do some more thinking and then adapt the model to enable an AV system.  

What assumptions should I make?