On Sunday 26 September Germans will go to the ballot box to cast several votes in state and federal elections. The Economist and several academics have published their federal election forecasts. But who do Germans think will win the election? Two research teams have used such citizen forecasts to predict the upcoming federal election.
Murr and Lewis-Beck predict the parties’ national vote shares based on citizens’ responses to the question “Who will win the general election?” Their prediction is based on a regression model of historical vote shares on citizen forecasts and whether there was a grand coalition. The historical data goes back until 1980. Combing their regression model with a recent Politbarometer survey from June, they predict CDU/CSU to win 34% of the vote and SPD to win 21%. of the vote. According to them, a CDU/CSU/SPD coalition seems the safest bet statistically, though a CDU/CSU-Greens coalition is not out of the question.
Kayser et al. predict both constituency winners and parties’ national vote shares by simply aggregating citizen forecasts collected in a survey the last two weeks. They collected two different kinds of citizen forecasts. First, they asked citizens to forecast which candidate will win in their constituency. And, second, they asked citizens what vote share each party will win nationally. The authors then simply predict the constituency to be won by the candidate who most citizens say will win. And, they predict the vote share of a party to be the average of citizens’ forecasted vote share. In other words, only survey data and no historical data was used to forecast the election. Citizens collectively predict that CDU/CSU will win more constituencies than the SPD (174 v. 98). However, they also collectively predict that SPD will win a higher national vote share than CDU/CSU (25% v. 23%). The Greens are predicted to win 16%.
Why do the forecasts of the two teams differ? The two teams use different methods and forecast with different lead times. However, we can update the forecast of Murr and Lewis-Beck by using the most recent Politbarometer survey from mid-September. This way the forecasts differ only in method. If we do this, then both forecasts go in the same direction. The Murr and Lewis-Beck model then predicts CDU/CSU to win 25% and SPD to win 31%. In other words, their updated model would also predict the SPD to win a majority of the votes, though a bigger one than predicted by Kayser et al. This said, Murr and Lewis-Beck did some analysis of the optimal lead time of their model: they find that it forecasts more accurately with a lead time of two months (June) than one month (September) on average. Of course, soon we will know which lead time or method forecasted better in this election.
There is speculation about how well various new and small parties will do in today’s elections to the Scottish and Welsh Parliaments. Former SNP First-Minister Alex Salmond has recently established the Alba Party, while George Galloway has created Unity 4 All. Both are contesting regional list seats in Scotland. Meanwhile, Abolish the Welsh Assembly has come fourth, with at least 6% of the regional list vote, in all four polls for the Welsh Parliament (Senedd Cymru) since mid-April. Also, Reform-UK, the renamed Brexit Party, is fielding candidates in both countries. These are just some of the various contenders.
This post explains some of the complications in trying to figure out what share of the vote a party needs to get elected in these institutions. It ends up pointing to past experience as a guide and drawing comparison with and the electoral system for the Greater London Assembly (GLA).
TLDR: The experience of all five elections to the Scottish Parliament suggests that around 5.5% of a regional list vote is usually enough to win a seat. It would be rare, but not impossible, to miss out on a seat with 6%. Winning on 5.2% to 5.4% is not uncommon. The lowest D’Hondt ratio ever to yield a seat in Scotland was 4.6% (equivalent to a single party winning a seat on that share). That was in 2003 when the SNP won 5 seats, including 2 list seats, with 23.0% of the Mid Scotland and Fife list vote. For the Senedd, a share of around 6.5% in a region is likely to be enough, especially in North Wales and Mid and West Wales which have historically been more accessible to small parties. By comparison, the GLA has a 5% legal threshold, without which parties would get seats with 3.8% of the vote.
The Scottish Parliament has 129 seats. The electoral system is sometimes described as proportional, but it is significantly different from pure proportional representation. If it were close then a party would win a seat for roughly every 0.8% of the vote, since 100/129=0.8. More precisely, if all the seats were elected by the D’Hondt method of proportional representation a party would be guaranteed a seat with more than 100/(1+Number of seats) per cent of the vote, that is 100/130 = 0.77% of the vote. As we shall see that is much lower than what is actually required to get elected.
Local election seat gains and losses are hideous to try to predict at the best of times. Various factors make this year especially hard. The Covid-19 pandemic means that the 2020 round of local elections was postponed to today, and there have been various boundary changes and restructuring that mean it is hard to allocate many seats to either the 2016-2020 or the 2017-2021 4-year cycle that my model requires. Nonetheless, and despite the weaknesses of my 2019 forecast (discussed below), I have ploughed on regardless. This is not due to the kind of stoic determination that the Finns call sisu: amusingly summarised by someone as, “chin down and press on to the next disappointment.” Rather, I am still curious as to how much of a guide (on a broad macro level) Westminster vote intention polls are to local election outcomes.
Headline forecasts are in the table below together with the range of possible outcomes in the model. The table includes the projections from Michael Thrasher’s second scenario here. He and Colin Rallings would normally calculate an expected National Equivalent Vote (NEV) from the results of local by-elections, but those have not been happening. Instead Michael Thrasher has used adjusted opinion polls to estimate the NEV and then projected the implied changes at the ward/division level. Both mine and his methods use polls this year, but whereas Michael’s is a local projection based on previous ward and division level results, mine is based on regression models of the macro historical relationship between poll changes and net seat changes. (For a really micro, individual-level approach, predicting Labour losses in “red-wall” councils, but not overall net gains and losses, see the analysis from YouGov’s Patrick English here.)
Table 1. Forecasts for English local election net seat changes 2021
-770 to +350
-290 to +430
-50 to +330
It is striking that my forecasts point in different directions from Michael Thrasher’s projections for every party. But with 4630 odd seats up for election, both sets of predictions are for modest net changes. The prediction intervals for my forecasts comfortably include zero for all three parties, so each of them could easily end either up or down when all the results are in.
This post is a revised and updated version of a similar post from 2019 here.
A key summary statistic of the outcome of each year’s annual round of local elections is the so-called Projected National Share (PNS). This is an estimate of the share of the vote that the principal parties would have won in a GB-wide general election if voters across the country as a whole had behaved in the same way as those who actually voted in the local elections. It provides a single, seemingly straightforward measure of party performance that can tell us not only how well or badly a party has done as compared with four years ago (when, typically, most of the seats up for grabs were last contested), but also as compared with any previous local election for which a PNS is available – even though the places in which local elections are held varies considerably from one year to the next.
In this blog we provide some guidance as to how the PNS is being calculated this year by the BBC and how it will be used to project an outcome in terms of House of Commons seats.
Americans are evenly divided in their expectations of who will win today’s presidential election. YouGov found 40% expect Joe Biden to win, 39% think Donald Trump will win and 21% are “Not sure” (see p59 here). By contrast, in 2016 a similar question about expectations of the outcome from New York Times/CBS News polls here had 56% expecting Hilary Clinton to win and just 33% thinking Donald Trump would. Differences in question wording means we should be cautious about detailed comparison, but it appears that Americans collectively are much more unsure of the outcome of this election than they were last time.
They may be more cautious because the majority of them were wrong last time. Then their expectations were in line with the polls and the forecasters, some of whom were clearly over-confident for Hilary Clinton, as I argued before the fact.
The problems of the polls in 2016 were diagnosed and methodology has improved. In particular, many polls are now weighting their samples so that the numbers of people with different levels of education are represented in proportion to their prevalence in the population. Part of the problem with some of the state-level polls last time was that they did not do so. Without that education weighting the polls this year would be showing even bigger Biden leads.
Some of the most over-confident forecasters from 2016 are no longer forecasting (including the Huffington Post), while others, such as Sam Wang, have adjusted their models and de-emphasised the predicted probabilities.
Nate Silver’s FiveThirtyEight forecasts did best in 2016, mainly by having a model with more prediction uncertainty and so a larger probability of Clinton winning. Despite that, one of the most prominent debates about the election forecasts this year has been prompted by the superb statistician Andrew Gelman querying whether the FiveThirtyEight model has included too much uncertainty.
Andrew Gelman is part of The Economist forecasting team. Their model has consistently had more confidence in a Biden win. It now gives Biden a 97% chance, to FiveThirtyEight’s 89% chance, of winning. Their central forecasts are extremely close, it is their uncertainty levels that differ.
More recently, Andrew Gelman has posted this on the effects of using Normal versus t distributions for the tail probabilities, and this on the value of learning from experience as a forecaster, and a fair few interesting posts about election forecasting in between. I can see the case for the modelling choices in The Economist model, but somehow the published level of uncertainty from FiveThirtyEight feels more reasonable to me. Since there will be sources of uncertainty that are not measurable from the polling and historical data, I think it is okay to err on the side of allowing more uncertainty when making choices between different justifiable modelling options.
Another forecaster that has adapted their methods since 2016 is YouGov. Their MRP model forecast has a slightly higher forecast electoral college tally for Biden (364) than does The Economist (356) or FiveThirtyEight (348). The difference is based on a slightly larger predicted Biden lead in votes (9 points for YouGov compared with 8 points for FiveThirtyEight).
YouGov has not published a predicted probability for a Biden win, but from their graph of simulations it seems that they have in the order of a 10% chance of a Trump win. That is roughly the same as FiveThirtyEight despite a lower central forecast for Trump. Moreover, in 2016 the corresponding YouGov model put very little probability on a Trump win despite a much closer forecast for the national vote share margin. The additional uncertainty estimation this time seems like an improvement.
It is worth noting that whereas the FiveThirtyEight, Economist and similar models depend on a plethora of polls funded by others, YouGov build their model on their own polling data. They might do a very large poll, but the YouGov sample size would still pale by comparison with the cumulative sample size of all the other campaign polls at the national and state levels. YouGov’s ability to refine their methodology is important for understanding the potential for getting effective forecasts from more modest amounts of polling data.
Using perhaps the most data of all, PollyVote aggregate not only polls but models, betting markets, citizen expectations and expert forecasts. That website has very helpful descriptions of how the different data sources and models work with links to research on how they have fared in the past. Their overall combined forecast is for a Biden victory, but with a smaller margin than the polls and poll-based models point to. This is largely because citizens suggest the race is close (as discussed above) and the betting markets and experts are cautious about the polls.
One model that points in completely the opposite direction from nearly all others is Helmut Norpoth’s Primary Model. It predicts a comfortable Trump victory because he is an incumbent president (they usually win) and because Biden did not do well in early primary contests, suggesting he is a weak candidate. The Primary Model has a very good track record of successful forecasts. It at least provides a basis for claiming that a Biden win would be remarkable by historical experience.
Overall, the evidence from the (apparently improved) polls is a very strong indication that Biden will win, and win very comfortably. The dearth of media coverage of election forecasts and the cautious coverage of opinion polls this campaign, as a result of their failure to anticipate Trump’s victory in 2016, seems to have led to public uncertainty. If the polls are right, and especially if Biden does a bit better than they suggest, it will come as a shock to many, especially Republican voters who mainly expect Trump to win (see p59 here).
Where has the swing to Biden come from?
Evidence from the polls seems to be that partisan polarization between self-described liberals and Democrats on the one side and conservatives and Republicans on the other has worsened since 2016, with both groups more strongly backing their candidate than they did in 2016. What is helping Biden most is a big swing among those who describe themselves as independent and/or moderate. Since that big swing is mainly among whites and it is towards the Democrats the ethnic divide has narrowed as white vote intention moves closer to the strongly Democratic Latino and solidly Democratic Black vote.
At a macro level it looks like swing at the state level might be fairly uniform. The table below shows my quick calculations for the change in the lead in some of the larger more marginal states. The average lead for Biden in them is a bit bigger for YouGov than FiveThirtyEight, in keeping with the one-point larger lead YouGov expects in the national share of the vote. Relative to Hilary Clinton’s actual lead over Donald Trump in 2016, the predicted change this year is relatively similar in these states. There is variation between states in the extent of the swing expected, but the differences are not huge and they are not all consistent between the two forecasters.
Table: FiveThirtyEight and YouGov predictions for selected swing states
Biden lead – actual Clinton lead
Note: All figures are in percentage points.
That said, both YouGov and FiveThirtyEight expect bigger than average swings in Michigan and Wisconsin, and a smaller than average swing in Florida. This would be the same as in 2016 but in the opposite direction. I have not had time to analyse whether there is a broader pattern of negative correlation between 2012-16 swing and 2016-20 swing, but it would not be surprising if the places that swung most to Trump in 2016 swing most heavily away from Trump today.
House of Representatives
The House is largely expected to stay Democrat controlled. FiveThirtyEight give the party a 97% chance of retaining control. In 2018, the Democrats won 235 seats to the Republicans 199 on an 8.6 point lead in the popular vote, quite a margin to overturn. Currently, the Real Clear Politics generic congressional vote poll average has a Democrat lead of 6.8 points. Similarly, FiveThirtyEight predict a popular vote margin of 6.3 points for the Democrats. Since this is down what it was on 2018 it is remarkable that the Democrats are also predicted to win slightly more seats (239).
If this comes to pass, I for one will be wondering whether the failure of a swing to the Republicans to yield any net seat gain will be due to incumbency advantage, especially “sophomore surges” given that most of the Republican target seats are being defended by first-term Democrat incumbents.
While a swing to the Republicans in the House without net Republican seat gains would seem to be a sign of problematic unresponsiveness of the electoral system, it would represent a partial unwinding of a pro-Republican bias in the distribution of seats given votes and so arguably a sign of the system working more fairly.
There is much more uncertainty as to whether the Senate will flip from Republican to Democrat. Of the 35 Senate seats up for election this time 21 are begin defended by Republican incumbents, and incumbency effects in US Senate elections are very strong. However, the seats up this time were last fought in 2014, which was a midterm year when Obama was president. The big c.9.7 point swing to the Republicans then appears to be being partially undone. Also, the Democrats have more of the seats not up for election: 35 out of 65 including two independents caucusing with the Democrats.
Sam Wang’s Princeton Election Consortium is predicting the Senate to go 53 D 47 R, while Fivethirtyeight’s central prediction is 51.5 D 48.5 R, with a 75% chance of Democratic control.
Overall, based on the polling evidence the Democrats are likely win control all three branches of government, with the Senate the least certain to go their way.
By Stephen Fisher, John Kenny and Rosalind Shorrocks
Since our first combined forecast at the start of the campaign, the number of forecasts for this general election has grown substantially. All of the combined forecasts – seats, vote shares, and probabilities – are pointing to a Conservative majority. However, some individual forecasts do predict a hung parliament, and there is variation within each forecast type over how certain this majority is, and how large it is predicted to be.
Seat projections from the betting markets, complex models, and simple models are all very similar, forecasting a Conservative majority of between 343 and 351 seats. The average number of seats across all forecasts that the Conservatives are expected to win – 341 – is slightly lower but ultimately very similar to the forecast last week.
Since last week the Political Studies Association have published their Expert Survey, in which the average expected number of Conservative seats suggests a hung parliament with the Conservatives just shy of a majority. It is interesting that the experts surveyed by the PSA predict the Conservatives will win fewer seats than is currently suggested by the polls. Perhaps they are factoring in the same kind of late-campaign changes as observed in 2017 – although it should be noted that when a similar kind of survey was run for the EU referendum in 2016, the average predicted vote share for Remain and Leave amongst experts was the furthest away from the actual result than any of the other types of forecast. They also predicted a Conservative majority in 2017, although that prediction was made much more earlier in the campaign when the Conservatives had considerable leads over Labour in the polls.
The similarity between the seat projections from most sources hides considerable variation within one particular forecast type – complex models. These models range from predicting 311 Conservative seats to 366 – the difference between a hung parliament and a healthy Conservative majority. They also range between 190 and 268 for Labour. It is particularly noteworthy that the voter expectation model, from Murr, Stegmaier, and Lewis-Beck, which uses citizen forecasts to predict the number of seats, forecasts one of the highest number of Conservative seats (360) and the lowest number of Labour seats (190). This is in contrast to our implied probability calculated from the citizen forecasts, which suggest that citizens are in general the least convinced about the likelihood of a Conservative majority compared to other forecasting methods. This suggests these surveys also suffer from being open to multiple interpretations and methods of analysis, as well as the question wording effects we discussed last week.
Every May local election results are analysed as indicators of the state of the political parties and scrutinised for what they tell might tell us about the outcome of the next general election. That general election is tomorrow. Although a lot has happened in politics since May 2019, and especially since May 2018, it might be worthwhile reminding ourselves of what happened in the local elections then and what those results portend for the outcome this week.
In 2015, when the polls failed to anticipate a Conservative majority, one of the more successful forecasting models was Chris Prosser’s one based on the 2013 and 2014 rounds of local elections. Unlike the polls – which showed the Conservatives and Labour neck and neck – that model forecast a four point Conservative lead in vote share. Using a uniform change projection, the forecast shares predicted a Conservative tally of 296 seats for 2015, short of an overall majority but better than a uniform projection from the final opinion polls and the best of a set of twelve academic forecasting models for that election.
Applying the same method again, the table below shows that both the 2018 and 2019 rounds of local elections point to a clear lead for the Conservatives in a subsequent general election. However, the forecast shares of the vote from both rounds do not suggest a big enough lead for the Conservatives to be sure of an overall majority. On the average of the two set of vote shares, coupled with a uniform change projection (also using last night’s YouGov MrP projected SNP and PC vote shares) points to a very narrow Conservative majority of 8.
Forecast share based on 2018 results
Forecast share based on 2019 results
Average forecast share
Standard Error of share forecast
The fact that a forecast based on local elections 7 and 19 months ago should be so close to last night’s YouGov MrP projection of Con 339, Lab 231, LD 15 is remarkable. There is just a difference of 10 seats for the Tories and none for Labour.
Given that since the 2018 local elections we’ve had May’s Deal and the first missed Brexit deadline, and since the 2019 local elections we’ve seen Brexit Party and Lib Dem success in the European parliament elections, a new prime minister, a new Brexit withdrawal agreement, and another missed Brexit deadline, it is even more surprising that most opinion polls now do not differ profoundly from what previous local elections suggested would happen.
Two years ago Andrew Adonis wrote a piece in Prospect arguing that Labour should ditch Jeremy Corbyn because of the importance of party leadership for electoral success. The piece claimed that “the best leader wins and nothing else matters,” and in Lord Adonis’s view Mr Corbyn is the worst Labour leader since Michael Foot. So, Adonis concluded already in September 2017, that regarding the next election “Corbyn will lose it decisively if he contests it.”
In response to Adonis’ claims many, including Danny Finkelstein, expressed skepticism about the power of leadership and pointed out that it is difficult to properly evaluate the quality of leaders in retrospect. Once we know who won and who lost we have a tendency to convince ourselves that the winner was a better leader than the loser. But there are ways of producing measures of leadership quality prior to elections which have historically been useful for forecasting election outcome.
The Party Leadership Model, was devised by Andreas Murr in the run up to the 2015 general election. It successfully anticipated David Cameron’s victory unlike the vast majority of other forecasts at the time. Murr has elaborated the model further for this election to produce a seats forecast, not just a prediction as to who will emerge as prime minister. His new model forecasts that the Conservatives will win an overall majority this week with 342 seats, and that Labour will win 254 seats.
On average the polls have had a fairly consistent and comfortable lead for the Conservatives in this general election campaign. However, around that average there are substantial differences between polls. Some suggest the Conservatives might fail to win a big enough lead to secure a majority, while others point to a Tory landslide with a majority over a hundred. What’s going on?
In short, since this is a long and complicated blog, our tentative conclusion is that the big systematic differences between pollsters are due primarily to systematic differences in the kinds of people they have in their samples, even after weighting. Some of the sample profile differences translate straightforwardly into headline differences. For instance, having more 2017 Conservatives in a sample means there will be more 2019 Conservatives. In other areas there are more puzzling findings. Polls vary in the extent to which women are more undecided than men and in the extent to which young adults are less certain to vote, but neither source of variation has the effect on headline figures that we would expect. Nonetheless for most of the aspects of the poll sample profiles we have inspected, it is remarkable the extent to which polls differ primarily between pollsters, with relatively little change over time for each pollster. This suggests that the way different pollsters have been going about collecting responses has yielded systematically different kinds of respondents for different pollsters. With a couple of exceptions, it seems as though it has been the process of data collection rather than post-hoc weighting and adjustment that may be driving pollster differences in this campaign.
As the graph below shows, a large part of the variation between polls is between pollsters. The pollsters have shown a similar pattern of change in the Conservative-Labour lead over time, most with a peak in mid-November and a slight decline since. The headline Conservative-Labour lead – the basis for the swingometer – is the main guide to seat outcomes. So an important question is why pollsters differ systematically in the size of their published Conservative leads.
In this blog post we use data from the standard tables that pollsters have to publish as part of the requirements of British Polling Council membership. They contain a wealth of information about the profiles of the different survey samples both before and after weighting and adjustment. We collected data from such tables for all polls between the 30th of October (when parliament voted for an early general election) to the 4th of December (just over a week before the end of the campaign). There have been more polls since then but so far as we can tell they do not substantially change the issues we raise here.
By Stephen Fisher, John Kenny and Rosalind Shorrocks
Since our update last week there have been several new forecasts, most notably including the YouGov MRP (multilevel regression and post-stratification) model. That was a nowcast rather than a forecast, but the same is true of most of our “forecasts”. More on differences between forecasting models below, along with some observations about intriguing question wording effects for citizen forecasts.
But first, overall, the seats projections overall have tightened for the Conservatives, who are down from a 353 average last week to 346 this week, while Labour are up from 209 to 218. The Liberal Democrat forecast total has dropped yet again (from 23 to 19). Now they are estimated to return fewer MPs than they had going into the election (20), but still more than the number of seats they won in 2017 (12).
There is now remarkably little difference between the betting markets, complex and simple models in the expected size of the Conservative majority. Particularly striking is that on average the complex models differ by only a seat for each party from the simple uniform change projections based on the average of the opinion polls.