## 13 new polls show some movement in April

It is four and half months until the September election, and things are getting a little more interesting. Everyone around here is happy that Macron saved the EU and defeated populism in one fell swoop (or maybe not), but I still love a nice parochial state election. And we had a good one: Last Sunday, the small northern state of Schleswig-Holstein went to the polls. The current coalition (SPD, Greens, and the Danish/Frisian minority party SSW) is unusual enough, and they lost their majority of a single seat. The CDU won a bit, the SPD lost a bit more, but for them, it’s a disaster since expectations were high (Schulz effect, anyone?). The Left and the Pirates are out, and both the Greens and the FDP are in double digit territory. Certainly, this is not a federal trend. The AfD made into the Landtag for the 12th (?) time in a row, but barely (5.9%).

Further to the south, North Rhine-Westphalia will have its own election on next Sunday. Here, the red-green coalition is in trouble, because the Greens are doing very poorly, and SPD support is lacklustre. The CDU, which has been trailing the SPD for a long time, is catching up, and both the AfD and the FDP are doing ok, though not great. It’s not quite clear if the Left will make it, and the Pirates (remember?) seem poised to lose their last delegation in a state parliament. What ever happens here will inevitably been read as a bellwether, because of the state’s size (it is home to almost a quarter of Germany’s population), and because it is the last state election before the federal election.

Meanwhile, 13 surveys that poll federal voting intentions have been published. Taken together, there are now 17 polls to track the developments in April (and several that already extend into the first weeks of May).

## The CDU/CSU is the strongest party now, but not very strong

Ever so slowly, the CDU/CSU have managed to pull ahead of the SPD. The Christian Democrats now stand at about 36 per cent. While this makes them the strongest party by far, they polled about 40 per cent four years ago at the same point in the cycle.

For the SPD, the famous Schulz effect has worn off a bit. April was a slow dive that has probably taken them below the 30 per cent threshold once more. While they are still doing much better than they did in January, their support has declined considerably over the last six weeks.

## The Greens and the FDP both move up a tiny bit

The Greens, on the other hand, have probably moved up in April, but only by about a point. Compared to where they stood a quarter ago, they are still performing poorly. The FDP may have gained a point, too, and are now indistinguishable from the Greens: they both hover somewhere just below eight per cent.

## The AfD and the Left remain tied in the same spot

Scandals and quarrels on the one hand (AfD) and non-events (the Left) on the other not withstanding, both parties have remained exactly where they were all through April: tied, and between eight and nine per cent. Move on, nothing to see here.

## Overall estimates and possible coalitions

On the last day of polling so far (May 9), support for all four minor parties is statistically indistinguishable, and they are all safely (though not comfortably) above the electoral threshold. The gap between the major parties is quite pronounced at 8 points (the largest difference in months), with a credible interval of 6-11 points.

Given the weakness of the SPD and the strength of the Christian Democrats, it is hardly surprising that the simulated probability of a red-red-green majority – hotly debated only a two months ago – is zero. The same goes for the “traffic light” option. Let us not even contemplate the prospects for a red-green majority.

But due to the strength of the AfD, a centre-right coalition would also have no majority, CDU recovery or not. Conversely, the probability of a Jamaica (CDU/CSU + FDP + Greens) majority is 99.9%. Put differently, on current levels of polling, every viable coalition would be led by the CDU, and Merkel would have a choice between a) continuing an unhappy marriage with a spouse that wants out or b) entering a risky but also exciting ménage à trois. Which just goes to prove the point that it is impossible to do political analysis without resorting to tiresome sexualised metaphors.

## On the 108th day of polling …

… my true love gave to me: two Dimap polls, two Forsa polls, two INSA polls, one Emnid poll, and one FGW poll. So the total number of polls in the database stands at 59 now. Not too shabby. However, three companies dominate the pool: Insa (11), Emnid (15), and Forsa (15). It would be good to have more polls from Allensbach, Dimap, FGW, and GMS.

## The CDU is leading, but by a small margin

Following the surprise candidacy of Martin Schulz, the SPD made enormous strides, and the two major parties have been neck-on-neck for more than two months. But over the last couple of weeks, the Christian Democrats finally managed to regain a lead over their current coalition partner, although it is a tenuous one compared to their previous standing in the polls. For April 18, the model estimates support for the Christian Democrats at 36 per cent (with a 34-37 per cent credible interval), and support for the SPD at 31 per cent (CI: 30-33).

## The FDP and the Greens are still struggling

The Greens have not recovered from the drop they suffered in January. Quite to the contrary, support for them seems to have fallen a bit further during the last four weeks or so. But this movement is well within the margin of error. The FDP, on the other hand, may have recovered a little bit, but again, they are still within the CI they were two, four, or even eight weeks ago. Statistically speaking, support for both parties is indistinguishable at the moment.

## The Left and the AfD are remaining neck-on-neck

And the same goes for the Left and the AfD. Support for both parties is estimated at 8 per cent, with a 7-9 per cent credible interval. Infighting within the AfD has reached new heights (lows?), and the party may even split again (by the way, I’m really looking forward to the Hunger Games of this weekend’s party conference), but so far, this has had relatively little effect on their polling results, which are still within the (lower) bound of the credible intervals for March. Conversely, support for the Left may have risen a bit but is still within the (upper) bound of their credible interval for March.

## Overall estimates and possible coalitions

From this final graph, it is clear that the credible intervals for all four minor parties overlap at the moment: in all likelihood, they are all somewhere above the electoral threshold and below the ten per cent mark, but there is insufficient evidence for determining how exactly voters rank them at the moment.

For the two major parties, the uncertainty regarding the exact levels of their support is even larger, but the probability that the Christian Democrats are enjoying higher levels of support than the SPD is more than 99 per cent. However, due to the uncertainty about the parties’ standing, the uncertainty regarding the size of this gap is substantial: the credible intervals stretches from 2 to 7 per cent.

Given these estimated levels of support, neither a “civic” (FDP/Christian Democrats) nor a classic leftist (SPD/Green) coalition would be possible. As a consequence of the Christian Democrats’ rising popularity, even a red-red-green coalition would be possible in fewer than 2 per cent of the simulated draws from the posterior joint distribution. A “Jamaica” coalition of Christian Democrats, FDP, and Greens, on the other hand, would command a parliamentary majority in 71 per cent of the simulations. Having a choice between two coalitions would obiously strengthen Merkel’s hand considerably. But once more, remember that these are not predictions but rather (hopefully) plausible estimates of the current state of public opinion.

## What’s the matter with the AfD?

Over the last couple of weeks, the mainstream media (or as the AfD would have it, the “lying press”) have begun to write off the AfD as past its sell-by day (btw, did you realise that we won the battle against populism when Wilders performed slightly less well than expected after some early polling?). There are basically three reasons for that:

1. New lows of infighting
2. The Saarland election
3. A modest slump in the polls

Let’s look at them in turn.

## More infighting in the AfD

I cannot remember how often I have used the phrase “fear and loathing” by now, but hey, it still fits. Frauke Petry and her supporters in the national and state-level leadership are still trying to expel regional leader Björn Höcke over his Holocaust comments. Höcke’s own chapter, however, have just selected him as a delegate for the upcoming party conference. Within her own chapter, Petry is under pressure because she is seen as a) too moderate and b) too obsessed within her own agenda. Just yesterday, the Stern magazine leaked a draft resolution for the party conference which aims at re-defining the AfD as a “moderate”, “civic” outfit that would in principle form coalitions with other parties. This is particularly funny once you remember that this is exactly what Petry’s predecessor Lucke had in mind before Petry ousted him with a little help from the less-than-moderate elements in the party. And the list goes on …

## What about the Saarland election?

In the election for the Saarland state parliament, the AfD won six per cent of the vote, which is a bit of a comedown after the party’s performances in the last round of state elections in 2016. The media read this as an omen for the Bundestagswahl in September, which is nonsense for a number of reasons: First, the AfD tends to do better in the eastern states. Second, and more importantly, state elections tend to be affected by federal politics, but only up to a point: first and foremost, they are regional affairs. In the case of the Saarland, this means (amongst many other things) that the regional chapter of the AfD is so closely enmeshed with right-wing extremists that the national leadership tried to disband the chapter only last year.

Yes, you read that right. The move was blocked by the AfD’s highest internal court, which ruled that the evidence against the chapter was insufficient. The national leadership then asked the state party to clean up their act and not to take part in the election. The state party declined that request. Their frontrunner candidate was caught on camera selling Nazi devotionalia in his shop only weeks before the election. And they still got six per cent of the vote in a high turnout election. Not too shabby, I would think.

## What do the polls say?

### How strong is the AfD? Depends on whom you ask

Repeat after me: “It’s just a single poll” … which is not entirely true any more. The last nine days have brought the same number of new polls (pushing the total to 51), the last of which seem to indicate a further slump of AfD support. Just today, FGW published findings from another Politbarometer survey, which has the AfD at six per cent (that’s the mood, i.e. weighed but not otherwise adjusted data), even worse than the seven per cent Forsa gave them after the Saarland election. Even INSA, who are always rather bullish on the AfD, reported a mere nine per cent support on Monday. But another Forsa poll as well as an Emnid poll which both gave the AfD nine per cent again went largely unnoticed. And FGW always generates huge negative outliers (which still might represent public opinion accurately) when it comes to the AfD. My model, which aims at factoring in these things, currently puts them at eight per cent – definitely less support than they had in January, but sufficiently far away from the electoral threshold

For all purposes and intents, the Left and the AfD are currently indistinguishable.

But the same can not be said for the FDP. For the first time since I began pooling the polls in January and less than six months before the election, support for the FDP may have fallen below the electoral threshold. As of Wednesday (the mathematical midpoint of the FGW poll), the estimated probability of the FDP having exactly five per cent support or more was 64 per cent. As one of the great political philosophers of our time is apt to say: SAD. Losers?

Support for the Greens, on the other hand, is lower than it was in January but has been stable at this level for the last two months.

And finally, the major parties. According to their political preferences, the media have variously reported an ongoing Schulz effect, the Christian democrats catching up with the SPD, or Merkel pulling far ahead. The latest polls seem to support any of these views. They look rather noisy, and estimated levels of support are still overlapping: the Christian democrats could be anywhere between one point behind or five points ahead of the SPD.

In sum, the overall estimates have not changed much over the last two weeks. The two major parties are more or less neck-on-neck, with the CDU/CSU still struggling to re-establish a clear lead. The AfD, Left, and Greens are all well below ten and well above five per cent. The only relevant change is that the FDP has slipped back a bit, which brings them perilously close to the electoral threshold.

This, in turn, rules out a “civic” coalition: in 60,000 simulated draws from the posterior, not a single one indicated that on current levels of polling, the FDP and the Christian Democrats could be able to form a government. Neither is there a red-green majority. A red-red-green coalition (vastly unpopular with most voters) is a mathematical possibility in 63% of all draws. Unsurprisingly, it becomes much more likely (99%) if the FDP is out. A “Jamaica” coalition (FDP, Greens, Christian Democrats) is not even mathematically likely (11%), and the odds for a “Trafficlight” coalition (FDP, Greens, SPD) are even worse (2%). On the other hand, unless the AfD makes a massive recovery, there is no chance that a Grand Coalition would not have a crushing majority. Watch this space

The other day, someone on twitter suggested that the polls on the upper margins of my latest model-based estimates of AfD support were conducted by the “notoriously AfD-friendly INSA company”.

This view is not uncommon in Germany. INSA, who do polling for Germany’s premier tabloid Bild, want to prop up support for the AfD via a band waggon effect, because there is an alleged business and ideological link between their CEO and the AfD’s notorious Thuringia chapter (in German) – or so the story goes. A more innocent explanation is that INSA polls are based on internet access panels, and that the AfD is probably the most internet-savy party in Germany and hence overly popular with heavy users.

But is there any evidence of overreporting? As you can see here, INSA’s average estimate of AfD support is just one percentage point above the grand mean of all measurements – not such a huge difference. Also, they have only contributed seven polls to the total pool of 43 major polls whose results have been published since January.

Pollster n  AfD % (average)
Allensbach 2 10
Dimamp 6 12
Emnid 11 10
Forsa 11 10
GMS 2 10
INSA 7 11
Poba 4 7
All 43 10

And perhaps these polls were conducted earlier in the year, before the model suggested that the AfD’s support fell by a couple of points? But no, this is not the case. INSA polling goes back until the first week of February. (In fact, there are even some INSA polls from January, which are not in the database because of a glitch in the script that I use to pull the data from the interwebs.) More importantly, each and every of the seven INSA polls is well above the credible interval around the model-based estimate:

So yes, INSA’s readings of AfD support are clearly unusually positive. But so are the Dimap polls, whereas FGW (Poba) are taking a distinctly bearish view.

Avid readers will remember that the model tries to account for party-specific house effects, under the overly optimistic assumption that these sum to zero across all firms. Given the small overall number of polls, and given that Allensbach and GMS have only published two polls each so far, I wouldn’t trust these estimates too far, but just for fun I’ve pulled them out of the mountain of simulated draws. According to the model, INSA overreports AfD support by 2 points (CI 1.5-2.6), Dimap by 1.8 points (CI 1.1-2.5), whereas FGW underreports AfD support by 2.5 points (CI -3.2-1.8). It will be interesting to see how the numbers develop over the coming months, and whether these estimates will square with the actual result. For the time being, take them with an appropriately large dose of salt.

## Eight new German polls

Over the last fortnight, eight new polls have been published: two by Insa, two by Forsa, and one apiece by Dimap, Emnid, GMS, and FGW. For GMS, it is only the second poll conducted since the beginning of this year (a third one was published early in January, with fieldwork partly carried out in late December). As usual, there is quite a bit of variation in the data (hence the pooling), although there is no such shocker as the (unweighted) FGW poll done in mid-February which put the SPD at 42 per cent, twice of what they had been polling in early January.

## The SPD and the Christian Democrats are in a dead heat, but …?

Probably no “but” so far. Back in late January, the SPD’s fortunes began to rise rapidly thanks to their new candidate Martin Schulz (aka St Martin), and by early February, support for the two major parties had become statistically indistinguishable. For the last ten days or so, the model has put the CDU about a percentage point ahead of the SPD, but that does not mean a thing: the credible intervals are still more or less identical. The SPD’s rise and rise in the polls has stopped in March, but the Schulz effect is still very much a thing.

## The Left and the AfD

Since January, the AfD has lost a bit of steam (i.e. about 2 points) in the polls, but it is still the strongest opposition party at just under 10 per cent. The model-based line in the graph suggests that over the last couple of weeks, the party has recovered a wee bit, but that movement is negligible (have a look at the scale), just a teensy-weensy wiggle well within a wide credible band. Similarly, the Left is basically where it was two (and four, and six) weeks ago at 7.5 per cent.

## The Greens and the FDP

The Greens had a bad start into the campaign. Just when they had selected two Spitzenkandidaten from the more conservative wing of the party (signalling that they might enter a CDU/CSU/Green coalition), the SPD pulled a Schulz on them by choosing a leader who would attract leftist voters and would at least ponder the prospects of an SPD/Left/Green coalition. The Greens lost a couple of points in January and early February but have been perfectly stable since. Conversely, the FDP may or may not have won a point since February. Like with the AfD, the wiggling is not impressive, given the width of the credible intervals. But importantly, this interval has not touched the electoral threshold of five per cent during the last three months, though the threshold is never that far away.

## Conclusion

The polls are noisy as ever, but the model, which tries to account for house effects and random errors, suggests that the noise is just that, and that so far there was no real movement in political support in March. This picture is at least plausible: Apart from the AfD, all parties have selected their respective Spitzenkandidaten by now, it’s still six months to go,  and there have been no major domestic events.

At current levels of support, the Bundestag would have two (relatively) major parties that could continue the Grand coalition, although it’s not quite clear which one would hold the chancellorship, and four almost identically-sized minor parties, commanding between six and ten per cent of the vote. In such a relatively fragmented parliament, the chances (in a purely statistical sense) for forming a SPD/Left/Green coalition are slim: Only in 15 per cent of all draws from the (simulated) joint distribution of support is there a sufficient red-red-green majority. At 12 per cent, the chances of a numerical majority for a “Jamaica” coalition (Christian Democrats, FDP, Greens) are even lower. In none of the the simulations is either a SPD/Greens or Christian Democrats/FDP coalition feasible. It would be Grand Coalition, or new elections, or minority cabinet rule (a first). But remember the mantra: It’s six months to go, we’re very much talking about political mood, not firm intentions here, and this is just a model that tries to average over many different noisy and potentially biased polls.

With just six months to go until the 2017 Bundestag election, this is perhaps the ideal time to reflect on the rather remarkable 2013 election. Perhaps there is also a very fine line between Political Science and Contemporary History, and the German electoral studies community has a particular gift to step exactly on that line without ever quite crossing over? Either way, German Politics (the journal) published a fine Special Issue on the 2013 election in Germany. The articles focus on a number of highly specific research questions: Ben Christian employs the Rolling Cross Section-component of the GLES to study how voters learn to identify what would be the “correct” electoral choice for them over the course of the campaign. Martin Elff and Sigrid Roßteutscher show that the link between dealignment and party decline (of the SPD in particular) is more nuanced than previously thought. Marc Debus demonstrates that – female Chancellor or not – gender had little effect on voting for the Christian Democrats in recent Bundestag elections.

Katsunori Seki and Guy D. Whitten pit various economic voting models against each other. Robert Rohrschneider and Stephen Whitefield show that as far as mainstream parties are concernend, “Europe” is still largely a non-issue in German Politics, even in these troubled times. Sascha Huber looks at motivations for coalition voting to explain the decline of the FDP in the last weeks preceding the 2013 election. Rüdiger Schmitt-Beck dissects the AfD’s 2013/2014 electorate into two groups: euro-sceptics and xenophobes. Heiko Giebler and Bernhard Weßels demonstrate that good campaigns made voters remember local candidates. Finally, yours truly casts another long and dirty look at partisan dealignment, which has almost come to a halt in Germany. And since German Politics is a somewhat arcane journal, you may want to have a look at the nearly identical author’s (pre-publication) version.

Almost exactly four years ago, the “Alternative für Deutschland” party (AfD) began its life as a moderately eurosceptic outfit that brought together right-wingers of various stripes. Even back in 2014, the party did not qualify as radical right-wing populist. Quite to the contrary: The leadership went to great lengths to present a “civic” front of professors, business persons, and concerned citizens. However, their 2015 de facto split was a critical juncture in the young party’s history. The part’s most prominent face, economist and former CDU member Bernd Lucke, and many of his supporters left the party.

The AfD’s central command is very active on Facebook, and so a quantitative analysis of their posts is a reasonable means for tracking their ideological trajectory. For a presentation I gave last week, I have updated and somewhat streamlined my 2015 analysis of their social media activities. I’m only looking at posts by the AfD on their own (federal) fan page. Over the last four years, the party has accumulated no less than 3482 of them. Their text is lightly normalised and stemmed, and I’m looking for substrings pertaining to four issues: Europe and the Euro, Greece, Islam/Muslims, and Migration/Refugees. Obviously, a post can refer to two or more of these issues, so the numbers may sum up to more than 100%. The result is this:

It’s quite clear that in 2013 and early 2014 (think European elections), a large chunk of their posts made reference to the Euro, the EU, and so forth. In the first half of 2015, Greece (remember the long nights and that funny finance minister) and Euroscepticism were back on the agenda. But when the economic liberals left the AfD around June and the refugees emerged as a dominant issue in European politics later that year, Greece was forgotten. In 2016, the AfD was all about migrants, refugees, and Muslims. I really need to find the time to dig deeper into this.

With just under seven months to go until the German federal election, I have recently begun once more to pool the pre-election polls from seven major survey firms. Since January, when the date for the election was set and the Spitzenkandidaten were selected, results from 35 polls with a median sample size of about 1900 have been published: nine apiece by Emnid and Forsa, five by Dimap, five by Insa, four by FGW, two by Allensbach, and a single one by GMS.

Easily the most exciting event in the (long) campaign so far has been the #Schulzzug: the mostly unexpected leak/announcement on January 24 that Sigmar Gabriel would be replaced as party leader and (presumptive) candidate by Martin Schulz, the former president of the European Parliament. Support for the SPD in the polls had hovered at historically low levels of just over 20 per cent for months, but the Schulz candidacy re-energised party members and resulted in lots of (mostly positive) media coverage so far. Subsequently, support for the party leaped up in the polls, even overtaking support for the Christian Democrats in some of them.

But most movement in the polls is noise, and so we would like to know if the Schulz bounce is real. The data basically say: yes.

[]

The figure shows that support for the SPD begins to rise a couple of days before Schulz’s candidacy was announced, but this is probably an artefact. The model assumes that true support normally changes very little from one day to the next, but these are unusual circumstances, and so the ascent was probably steeper than the graph suggests. At any rate, the estimated level of support for the SPD in February was somewhere between 30 and 35 per cent, whereas it was between 20 and 24 per cent early in January. The model’s priors may play a role here (though they should be quickly overwhelmed by the data), but it is obvious that there was a gap of at least 10 percentage points between the two major parties in January that has essentially closed now. Support for the CDU and the SPD is virtually indistinguishable, and the Christian Democrats are rightfully worried.

What this means for the election is a different question. Estimated levels of support for both parties have been essentially constant for the last four weeks or so. The SPD has unexpectedly closed the gap, but it has stopped gaining. The Christian Democrats are not doing much worse than at the same point in the cycle four years ago. And once voters learn more about Schulz (who is a known unknown in Germany), the Schulz effect may wear off.

It’s that time of the electoral cycle again: With just under seven months to go until the federal election in September, I feel the urge to pool the German pre-election polls. I’ve burnt my fingers four years ago when I was pretty (though not 100%) sure that the FDP would clear the five per cent threshold (they failed for the first time in more than six decades), but hey – what better motivation to try it again?

## Why bother with poll-pooling?

Lately (see Trump, Brexit), pre-election polls have been getting a bad rap. But there is good evidence that by and large, polls have not become worse in recent years. Polls, especially when taken long before the election, should not be understood as predictions, because people will change their mind on how to vote, or will not yet have made up their mind – in many cases, wild fluctuations in the polls will eventually lead to an equilibrium that could have been predicted many months in advance. Rather, polls reflect the current state of public opinion, which will be affected by campaign and real-world effects.

Per se, there is nothing wrong with wanting to track this development. The problem of horse race journalism/politics is largely a problem of over-interpreting the result of a single poll. A survey of 1000 likely voters that measures support for a single party at 40% would have a sampling error of +/- 3 percentage points if it was based on a simple random probability sample. In reality, polling firms rely on complicated multi-stage sampling frames, which will result in even larger sampling errors. Then there is systematic non-response: some groups a more difficult to contact than others. Polling firms therefore apply weighs, which may hopefully reduce the resulting bias but will further increase standard errors. And then there are house effects: Some quirk in their sampling frame or weighing scheme may cause polling firm A to consistently overreport support for party Z. So in general, if support for a party or candidate rises or drops by some three or four percentage points, this may create a flurry of comments and excitement. But more often than not, true support in the public may be absolutely stable or even move in the opposite direction.

Creating a poll of polls can alleviate these problems somewhat. By pooling information from many adjacent polls, more accurate estimates are possible. Moreover, house effects may cancel each other out. However, a poll of polls will not help with systematic bias that stems from social desirability. If voters are generally reluctant to voice support for a party that is perceived as extremist or otherwise unpopular, that will affect all polls in much the same way.

Moreover, poll-pooling raises a number of questions to which there are no obvious answers: How long should polls be retained in the pool over which one wants to average? How can we deal with the fact that there are sometimes long spells with no new polls, whereas at other times, several polls are published within a day or two? How do we factor in that a change in polling that is reflected across multiple companies is more likely to reflect a true shift in allegiances?

## The method: Bayesian poll-pooling

Bayesian poll-pooling provides a principled solution to these (and other) issues. It was pioneered by Simon Jackman in his 2006 article on “Pooling the polls over an election campaign”. In Jackman’s model, true support for any given party $P$ is latent and follows random walk: support for $P$ today is identical to what it was yesterday, plus (or minus) some tiny random shock. The true level of support is only ever observed on election day, but polls provide a glimpse into the current state of affairs. Unfortunately, that glimpse is biased by house effects, but if one is willing to assume that house effects average out across pollsters, these can be estimated and subsequently factored into the estimates for the true state of support for any given day.

The Bayesian paradigma is particularly attractive here, because it is flexible and because it easily incorporates the idea that we use polls to continuously update our prior beliefs about the state of the political play. It’s also easy to derive other quantities of interest from the distribution of the main estimates, such as the probability that there is currently enough support for the FDP to enter parliament, and, conditional on this event, that a centre-right coalition would beat a leftist alliance.

In my previous misguided attempt to pool the German polls, I departed from Jackman’s model in two ways. First, I added a “drift” parameter to the random walk to account for any long term trends in party support. That was not such a stupid idea as such (I think), but it made the model to inflexible to pick up that voters were ditching the FDP in the last two weeks before the election (presumably CDU supporters who had nursed the idea of a strategic vote for the FDP). Secondly, whereas Jackman’s model has a normal distribution for each party, I fiddled with a multinomial distribution, because Germany has a multi-party system and because vote share must sum up to unity.

The idea of moving to a Dirichlet distribution crossed my mind, but I lacked the mathematical firepower/Bugs prowess to actually specify such a model. Thankfully, I came across this blog, whose author has just done what I had (vaguely) in mind. By the way, it also provides a much better overview of the idea of Bayesian poll aggregation. My own model is basically his latent primary voting intention model (minus the discontinuity).

The one thing I’m not 100% sure about is the “tightness” factor. Like Jackman (and everyone else), the author assumes that most movement in the polls is noise, and that true day-to-day changes are almost infinitesimally small. This is reflected in the tightness factor, which he arbitrarily sets to 50000 after looking at this data. Smaller numbers make for more wiggly lines and wider confidence intervals, because more of the variability in the data is attributed to true change. Unfortunately, this number does not translate to a readily interpretable quantity of interest (say a true day-to-day change of 0.5 per cent).

After playing with smaller and even larger values, I came up with a cunning plan and made “tightness” a parameter in the model. For the first six weeks of polling data, the estimate for tightness is about an order of magnitude lower in a range between 3500 and 10000. Whether it is a good idea to ask my poor little stock of data for yet another parameter estimate is anyone’s guess, and I will have to watch how this estimate changes, and whether I’m better of to fix it again.

## The data

Data come from seven major polling companies: Allensbach, Emnid, Forsa, FGW, GMS, Infratest Dimap, and INSA. The surveys are commissioned by various major newspapers, magazines, and TV channels. As far as I know, Allensbach is the only company that does face-to-face interviews, and INSA is the only company that relies on an internet access panel. Everyone else is doing telephone interviews. The headline margins are compiled and republished by the incredibly useful wahlrecht.de website: http://www.wahlrecht.de/umfragen/index.htm, which I scrape with a little help from the rvest package.