Monday, 22 February 2010

Alternative Seat Calculator - instructions/link

Seat Calculator – Instructions and Warnings

Firstly – a warning. All models of an event as complex as the General Election will be unavoidably simplified – if for no other reason than the data required to genuinely forecast the outcome (the correct knowledge of opinion in each one of the 650 seats) is unavailable. Treat all models – this one included – with appropriate scepticism. It is intended to inform your opinion of what’s going to happen. Please also remember that by-election victories are not taken into account – so the Conservative performances in Crewe and Nantwich and Norwich North, The Lib Dem performance in Dunfermline and West Fife and the SNP performance in Glasgow East will certainly exceed a model forecast. This model is based on the notional figures provided by Anthony Wells.

The calculator can be found here (

Differences between this model and a UNS swing calculator

Probabilistic nature: In UNS calculators, if the required swing is 6.5% and the polls project 6.4%, hard luck. You missed that constituency (it stays in the original column). In reality, the swings do not go uniformly. Instead of a needle swinging on a semicircle with seats clustered in accordance with their majorities, visualise a kind of fuzzy fan – denser in the centre, wispier towards the sides, a few swing-points wide. This fan covers a lot of the seats, and the density of the coverage corresponds to the chance of the seats there changing hands or being retained. Out of a group of 18 seats 3 points beyond the swing (so with a projected majority of 6 percent after the swing), three should change hands. Similarly, with seats that should be well taken, with majorities for the attacker of 6 points after the swing, a sixth of them will be retained against the tide. (These figures are indicative of typical Lab/Con swing standard deviations). This calculator takes them into account. Those seats that are “one standard deviation” beyond the swing would be counted for the attacker as 1/6th of a seat each (as the attacked should claim a sixth of them). Those that are (for example) one standard deviation inside the swing will only count 5/6ths each for the attacker – as one in six should be retained by the defender.

Adjustability. It’s a probabilistic UNS calculator with knobs on. These knobs can be twiddled to:

- Have different swings in Scotland and Wales

- Adjust for tactical voting and tactical voting unwind

- Allow for the “constituency effect”

- Allow for the differential performance of marginal constituencies

- Specify chances of minor party victories in 6 selected constituencies

Updates/changes/refinements. There won’t be any more – it’s as smooth as I can make it now and has enough knobs on to satisfy everyone (surely?). Changes made since my earlier articles:

- The Speaker is not counted in the numbers of the party from which he came, unlike as shown in the BBC figures for previous elections. In earlier versions of the calculator, I followed the BBC’s convention, but bearing in mind that betting firms will probably insist on actual party counts, I feel this should be more appropriate.

- The SNP and Plaid Cymru are properly modelled – they were more crudely allocated in the earlier model and the battlegrounds in Wales and Scotland followed the GB swing.

- The probabilistic function was made fully continuous, rather than discrete levels using a lookup table. This reduces the amount of “long shots” that could come off. There’s an “effective majority” figure/percentage chance. This assumes 5 Sinn Fein MPs and that the Speaker and 3 Deputy Speakers do not vote other than to break a tie in accordance with Parliamentary procedures.

- The marginal effect rebound for the Conservative/Labour battles was levelled off somewhat and rounded down to half-percentage points.

- A Lib Dem incumbency effect was added.

Instructions for use

The calculator looks complex, but has three distinct areas. As a rule of thumb, faded colours tend to signify information; brighter colours signify areas for you to enter/adjust figures The top section is for input.

Where it says “Current poll”, put in the current polling scores, or the score you want to investigate.

Below that are separate input boxes for Scotland and Wales respectively. If you leave these alone, the calculator uses estimated swing scores for Scotland and Wales, which are displayed. The Conservatives do worse than the national swing would suggest in Scotland and slightly better in Wales. Labour do better than the swing would suggest in Scotland and slightly worse in Wales. The Lib Dems do worse than the swing would suggest in Scotland and a little better in Wales. The SNP and Plaid scores vary so as to keep the total score between the four parties constant.

The “Rewind Factor” boxes control how much the electoral pendulum is assumed to “rebound” as the distorting pressures that produced the electorally distorted effects in the marginals over the 1997 and 2001 elections are removed – if you assume that the rewind effects (constituency factor, tactical voting unwind, marginal effects) for the Conservative-Labour battleground will not be as effective (or will be more effective) in the respective countries, adjust that as you see fit. Note that this control is solely for the Conservative/Labour battleground.

England, Scotland and Wales are controlled separately here as it is undeniable that these may have very different reactions to the removal of the earlier effects.

To the right are separate entries for six selected “unmodellable” constituencies, where minor parties (IKHH, Blaenau Gwent People’s Voice, Respect, Greens, UKIP and the BNP) are either defending seats or are making realistic challenges. For these, you have to estimate the chances of each entry winning there (e.g. in Wyre Forest, the chances of Dr Taylor hanging on, of the Conservatives winning, of Labour winning and of the Lib Dems winning). This is not an estimate of polling scores but of the probability of that candidate winning. If the score does not add up to 100% (it’s assumed that one of the parties shown will win), the score to the right will light up in red until rectified.

Below all of this is the output section.

The calculated results are presented. As the model is probabilistic, the central prediction (“Predicted Seat Total”) is usually a number with a decimal point. That is where the centre of the “smeared out” forecast should be. The standard deviation is a measure of the range of the forecast by probability. If the same election were run with the same figures a hundred times, the average scores for each party would be as per the central figure. Sixty-eight of the hundred would fall in the “68% interval”. Ninety five of these hundred alternate universe elections would end up with scores inside those defined by the “95% interval”.

The quoted majority is for the whole number of seats closest to the central forecast. The “effective majority” presumes 5 Sinn Fein MPs and that the Speaker and three Deputy Speakers do not vote on party grounds.

The “% majority” and “% Effective majority” figures estimate the likelihood of the party gaining a majority or effective majority respectively. After all, if the majority forecast is very low, a number of alternate universes will be ones in which the leading party just fails to get across the line – this figure reflects that.

If you wish to see in detail how the parties did in England, Scotland and Wales, look below these results to find:

This shows the central forecast only, for each country. To get the range, use the convention that +/- 1 standard deviation (sd) is a range with 68% likelihood and +/- 2 standard deviations has about a 95% likelihood.

To the right of the output are the core assumptions used. Firstly, the “swing standard deviations”

This is a measure of how variable are the “random” fluctuations about the average swing.

The LabàCon swing, for example, will not be uniform but will vary about the average. This measurement of how variable it is has varied from 2.4 to 3.4% for Lab-Con swing over the past 5 elections. It will probably tend to the higher end for the next election, which is based on notional constituency scores. For Labour-Lib Dem and Conservative-Lib Dem swings, they tend to be fractionally higher (3.6-4.0 and 3.0-3.3 respectively). The swings involving SNP and Plaid Cymru are set to a figure of 3.0 each.

ASSUMPTION: That the swing standard deviation will be the average for the last five elections. As said, a slightly higher figure might be assumed. This will slightly change the forecast.

Next, the specific systematic distortions. A certain level has built up since the election was called in 1997.

The “Constituency adjustment” figure reflects that the average constituency size and turnout is not uniform. In Lab-Con fights, it tends to be that the lower turnout of Labour core voters (and lower changes in their voting patterns) in Labour-held safe seats and higher in Conservative safe seats usually acts to assist the Labour vote when they are improving in the marginals and semi-marginals and detract from it when it is falling. The accumulated effect since 1997 is about half-a-percent.

ASSUMPTION: That this effect will unwind over a national swing sufficient to return the parties to their 1992 position.

This can be adjusted as the user sees fit. There does not appear to be any distinct pattern in the effect in Lab/LD and Con/LD battles, but the facility is there for balance.

The tactical voting adjustment is entered next.

A positive figure in the “Con-Lib” column signifies Conservative voters lending their votes to the Lib Dems to keep out Labour in Lib Dem/labour fights; a negative figure in this column indicates a net transfer from Tories to Labour to keep out Lib Dems.

A positive figure in the Lab-Lib column helps the Lib Dems against the Conservatives on a further winding up of the existing anti-Tory tactical voting; a negative figure helps the Conservatives against the Lib Dems and signifies an unwinding of the tactical voting in Lib Dem/Conservative battles.

A positive figure in the Lib-Lab column would signify that the tactical voting is actually increasing in Labour/Conservative marginals, a negative figure that it is unwinding.

The Lib Dem voters who lent their votes to Labour in order to “keep out the Tories”, or “kick out the Tory” are assumed not to be as motivated to vote for their formerly second-choice party. The national swing starts from a point assuming that they will repeat their tactical vote. For the Lib Dem à Labour tactical voters, the baseline amount left voting Labour in 2005 was calculated to have the same effect as about a 0.5% distortion of the national swing in favour of Labour, in Conservative/Labour fights.

ASSUMPTION: That the “detoxification” of the Conservative party, as evinced by “forced choice” questions, has unwound this effect.

The next effect is the most crucial: The marginal battleground boost.

Since the advent of Tony Blair and New Labour, the Labour Party have tended to outperform the national swing in the seats they most needed. The potential reasons are manifold: particular attraction to the centrist and floating voters most found in marginals and semi-marginals (“Mondeo Man” and “Worcestor Woman”), concentration of the tactical voting effect where it is most needed, more money spent in the most important seats, higher activist usage, etc), but the outcome is that in these seats, since 1997, the distortion of the UNS has built up considerably. The forces acting to hold this distortion in place have been arguably removed – the “forced vote” question and other polling questions have demonstrated that the Conservatives are no longer seen as being so repellent to centrist/floating voters (and indeed seem to have reversed the effect slightly). Tactical voting should unwind, and the concentration in the marginals should also unwind. Activist levels, party targeting and money spent in marginals now definitely do not benefit the Labour party as they did before. The effect is most pronounced in the most marginal seats and recedes as the swing required increases. All of these figures can be adjusted by the user.

In LD v Con marginals, LD-held seats are at the bottom of the table; Con-held seats at the top. Positive is good for Lib Dems; negative is good for Conservatives.

In Lab v Con seats, Lab-held seats are at the bottom of the table; Con-held seats at the top. Positive is good for Labour; negative is good for Conservatives.

In Lab v LD seats, Lab-held seats are towards the bottom of the table; LD-held seats at the top. Positive is good for Labour; negative is good for Lib Dems.


Note that only the relevant figures for the Conservative-Labour battles are included in detail The other figures have not been produced due to small sample size and minimal pattern emerging – although the Liberal Democrats do seem to do better in their relevant marginals and have a definite trend of performing well in close incumbent battles. Therefore a boost has been assumed for defending Lib Dem MPs. The user may enter whatever figures he/she deems appropriate. There is also a possibility of Conservative -> Liberal tactical voting.

Historically, Lib Dem MPs have been reportedly hard to shift when they have won their seats. This effect seems borne out by the data, and so a “defence boost” for Lib Dem held seats (against both other parties) is assumed.

ASSUMPTION: That there will be a “defence boost” to Lib Dem-held incumbent seats.

Please note that all of these assumptions should be carefully weighed by the user. If you feel that the effect is too large to be unwound in a single election (or even that it has been countered or will remain), the easiest thing to do is to adjust the grey “rewind factor” boxes next to the polling scores. Reducing these to zero will eliminate the Conservative-vs-Labour rewind effect completely (although not the Lib Dem defence boost). If you ensure that all of the assumptions are set to zero, this spreadsheet can be used simply as a probabilistic UNS calculator.

(Edit - these instructions have been uploaded as a Word document here on Google Docs)


Plato said...

Great stuff - must have taken ages.

James said...

Having trouble opening this. Can we have some help for a technophobe.

Anonymous said...

Andy, is there any chance of getting the Instructions as a Word document or similar? I am scared that I am going to lose the link, and my (lack of) maths means that my use of this magnificent resource is not going to be intuitive...I will need reminding as to what to do!


Andy Cooke said...

Right - caught up on main site, now here.

Plato - thanks. I think it (including all previous incarnations over the past 3 years) and the analysis that gave the figure for rewind took probably a little over 300 hours over 3 years. But I did it because it was fun to solve a problem (like sudoku or crossword puzzles :) )

James - can you say what the problem is? One thought - Google Docs can't handle the spreadsheet to present itself - you have to click "Download" to download it to your computer.

Anonymous - sure. I'll put it into a Word file and upload it.

Augustus Carp said...

Thanks, Andy - I should have explained that I am not "Anonymous" as such, more pseudonymous really, but I couldn't work out how to get my name to appear. (Office computer, pressure of work etc.)

Thanks again - it's going to be a really valuable resource to many many people.

Andy Cooke said...

Augustus - Word Document uploaded: