Nigel Marriott's Blog

An independent statistician using data to understand our world and to predict the future

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By-Elections #1 – How to predict outcomes in the Brexit era

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Since the UK voted to leave the EU on 23rd June 2016, there have been 3 contested parliamentary by-elections (Witney, Richmond Park, Sleaford & North Hykeham) and one uncontested by-election (Batley & Spen which was the late Jo Cox’s seat).  Many commentators have analysed these results to see how the referendum result has impacted on parliamentary voting intentions.  Whatever voter dynamics are revealed, it is reasonable to assume that they are likely to influence future by-elections.  In late October 2016 just after the Witney result, I realised it could be possible to build a by-election model by combining two sources of data.

  1. My own estimates of the Leave & Remain votes in each of the 650 parliamentary constituencies where I calculated that 400 out of 650 seats voted Leave.
  2. My interpretation of the Lord Ashcroft “exit poll” carried out on 21st to 23rd June 2016 and published immediately after the results were announced. 

At the time, I described my by-election modelling approach in a youtube clip and that is worth listening to.  I have made some changes to my model since then so this post is the most up to date version of my model. I will illustrate the basic principle using the Witney by-election (David Cameron’s former seat) of 20th October 2016 where the top line numbers are:

The first two rows show the general election results & turnout for 2010 & 2015.  The EU 2016 row shows the actual turnout in Witney was 7 points higher than the General Election in 2015 which tells us there were people who voted in 2016 but not in 2015.  I have recast the 2015 results into what would have been the vote shares had these additional voters been able to tick a box in 2015 which said “None of the above but I will vote in the referendum in 2016” as shown by the Non-GE black column. 

This is important to do because in any future election or by-election, these Non-GE voters may be inspired to vote having not done so in 2015.  For the sake of completeness, I have assumed that if people did not vote in either the referendum or the General Election then they will never vote in any future by election.

We then have the Remain & Leave vote shares of 54% & 46% respectively in the next two rows.  In the case of Witney, these are actual results since the results were declared for West Oxon district council which happens to be the same geographical area as the Witney seat.  We now have actual data for 172 of the 650 seats in the UK and so for some by-elections, I do not need to estimate these figures but for most by-elections I will use my Leave vote share model to make these estimates.

I have split the Leave & Remain votes by political party in 2015 including the Non-GE voters.  So of the 55% (after allowing for Non-GE voters) who voted Conservative in 2015, I estimate a small majority voted Remain with a 28:27 split.  These splits are derived from the Ashcroft “exit poll” where he found that Conservative voters split 58:42 Leave in the referendum based on the UK result of 52:48 Leave.  Using those party splits as a starting point, I have then adjusted the proportions equally across all parties until I end up with numbers that reconcile with the known 54:46 remain vote in Witney.

The question for any by-election in the post-Brexit era is how will these voting segments behave in any future election?  Will Conservative Remainers switch to the Lib Dems?  Will Lib Dem Leavers switch to the Conservatives?  I am sure you can imagine many possible scenarios and there is a danger that you end up picking scenarios that fit your narrative.  To avoid this bias and add some rigour, I paid particular attention to question 24 of the Ashcroft “exit poll” and my interpretation of this question was that Leave & Remain voters can be split into 5 Voter Segments within each party.

  1. REMAIN Pro-EU – Someone who believes in the ideal of the European Union and will fight to stay in.   An Anti-Brexit party will surely appeal to such people
  2. REMAIN Best of Both – Someone who likes being in the EU but wants to stay out of the Euro and other integrationist policies.  Unlikely to be enthusiastic about the EU but will listen to an Anti-Brexit party if the leaving process runs into big problems.
  3. REMAIN Economic Risks – Someone who doesn’t like the EU and agrees with Leave regarding sovereignty/immigration issues but doesn’t want to take the economic risk of leaving the EU.  Very much “devil you know” but are most likely to accept the referendum result and will only listen to an Anti-Brexit party if their economic fears come to fruition otherwise they will be unimpressed with an Anti-Brexit party that appears to be defying the democratic will of the people.
  4. LEAVE Potential Begret – Someone who accepts there are economic risks in leaving but voted leave on sovereignty/immigration grounds.  Can be persuaded to switch if economic outcomes are worse than they expected.
  5. LEAVE Brexiteer – Someone who believes that life will be better outside the EU regardless of any initial uncertainty and is not going to change their mind.

The chart shows the size of each segment based on my reading of the Ashcroft “exit poll”. Note the Economic Risks segment is larger and the Pro-EU segment is smaller among Conservative Remainers compared to Labour and Lib Dem Remainers.

Using this chart I can allocate each parties’ remain and leave voters into the 5 referendum segments which results in additional rows to the table I have already shown.  For Non-GE voters, there is a clear correlation between Leave voting and increased turnout so these voters are assumed to be disproportionately Leave.

The end result is that I have now split Witney into 35 voting segments.  A number of these are tiny such as UKIP Remainers (almost an oxymoron!) but doing this allows me to identify the largest segments which are likely to be key in any by-election.  In Witney, the largest segment is Conservative Brexiteer which accounts 23% of 2016 voters followed by Conservative Economic Risks with 15%.

To arrive at a forecast for a by-election we have to answer these questions. 

  1. What % of each segment will bother to vote in a by-election?
    • On average, by-election turnout tends to be around 2/3 of that seen in a General Election but it can be lower.
    • For non-GE voters, turnout will probably be much lower than for the parties since these voters didn’t vote in the General Election so will they be motivated to vote in a by-election?
  2. For each segment that votes, will they remain loyal to their 2015 party or will they switch to another party?
    • If they do switch, to which party will they switch to and in what proportion?
  3. Are there any national trends in addition to local switching that we should add or subtract?

By now, I am sure you will be thinking that you could come up with pretty much any figure you want and you would be right to say so.  So the way to get around any potential cherry picking, I have devised hundreds of potential scenarios (528 to be precise) and by examining the distribution of outcomes generated by these scenarios, I can draw conclusions.  For example, if all scenarios point to a Conservative win say, then it doesn’t matter too much scenario is the correct one.  Alternatively, you may find half the scenarios point to a Labour win and the other half point to a UKIP.  At that point, you can seek to identify what are the common factors behind Labour victories, what are the common factors behind UKIP victories and then compare and contrast the specific factors that drive the differing outcomes.  With this information, you can then choose to give more weight to some factors than others if you think that is worth doing.

For by elections that have already taken place, my approach is different.  This time, I want to identify the scenarios that best explain the actual results.  With 3 by-elections, this gives me the chance to see if there is any consistency in the best fit scenarios that could be used to predict future by-elections.  It turns out that there is some consistency.

Witney 20th October 2016 – Conservative Remain seat

I have colour coded each of the 35 voting segments to indicate where I think the votes went and the following scenario generates a forecast close to the final result.  All is consistent with my reading of the political mood at the time.

  1. Turnout is higher among Lib Dem & Labour voters
  2. Non-GE voters did not vote
  3. No additional national swing is needed.
  4. All Pro-EU voters defect to the Lib Dems
  5. Half of the Potential Bregret voters defect to the Lib Dems
  6. All Conservative Best of Both voters defect to the Lib Dems
  7. All Lib Dem Brexiteer voters defect to the Conservatives

This scenario does tend to overestimate the UKIP vote but since UKIP got less than 10% of the vote in 2015, I am not so bothered about getting the smaller parties correct.  The main thing is to find the scenarios that best fit the larger parties.

Richmond Park 1st December 2016 – Conservative Remain seat

In this by-election, Zac Goldsmith actually stood as an independent Conservative candidate.  Both UKIP and the Greens decided not to stand.  Richmond Park was one of the strongest Remain seats in the country coming in at #36 out of 650.  Among Conservative seats it was the 4th most Remain seat with the other 3 also in South West London.

By now, the political mood had started to change following the strong showing by the Lib Dems in Witney and so the following scenarios appear to be consistent with my perceptions at the time.  Those statements coloured in blue bold also apply to Witney, other statements differ from Witney.

  1. Turnout is broadly similar among the parties
  2. Turnout among Non-GE voters is 1/3 that of the main parties
  3. There is an additional national swing away from Labour of 2% which is split between the Conservatives & Lib Dems.
  4. All Pro-EU voters defect to the Lib Dems
  5. Half of the Potential Bregret voters defect to the Lib Dems
  6. All Conservative & Labour Best of Both voters defect to the Lib Dems
  7. All Lib Dem Brexiteer voters defect to the Conservatives

So in two Conservative Remain seats in the London/South East area, some similarity of scenarios is now apparent.

Sleaford & North Hykeham, 8th December 2016 – Conservative Leave Seat

This by-election was the first since the referendum to take place in a Leave seat.  Compared to Richmond Park though, turnout was considerably lower and an Independent candidate made a strong showing.  This time, the following scenarios apply with those in blue common to both Richmond Park & Witney and those in red common to Richmond Park.

  1. Turnout is higher among Lib Dem voters
  2. Turnout among Non-GE voters is 1/3 that of the main parties
  3. There is an additional national swing away from Labour of 2% which is split between the Conservatives & Lib Dems.
  4. All Pro-EU voters defect to the Lib Dems
  5. All Lib Dem Brexiteer voters defect to the Conservatives

Unlike Richmond Park, there was little evidence of Potential Bregret & Best of Both switching to the Lib Dems.  Whether this was because the Lib Dems focused on Richmond Park or because the seat was a Leave area or because it was outside the London/South East area is unclear. 

Two assumptions do now seem to be solid ones, namely that all Pro-EU voters have swung behind the Lib Dems but the Lib Dems have lost their Brexiteers to the Conservatives.  Six weeks on from Witney, it now appears that Non-GE voters are starting to turn out to some degree and that there is a small national swing away from Labour that needs to be taken into account.  Going forward, my by-election forecasts will tend to favour these scenarios.