Business Case: Bayesian forecast model for the German federal elections


The outcome of the Bundestag elections is of great interest to society. In order to gain an insight into the current preferences of voters, various polling institutes regularly publish the results of the so-called Sunday poll. The Sunday poll determines which party respondents would vote for if the Bundestag elections were held next Sunday. However, it is well known that polls have limitations. They are often biased, whether due to unrepresentative samples or other methodological problems. In addition, polls only reflect the current mood and cannot statistically predict the outcome of a future election.

With our election forecasting model we want to meet these challenges. In contrast to conventional election polls, a forecast is made not only for a hypothetical election next Sunday, but also for the election itself. In addition, our model takes into account sources of uncertainty such as sampling errors and biases in the election polls. Another special feature is that, in addition to the actual election result, we also determine probabilities for coalitions and certain events (e.g. "How likely is it that the party Die GrĂ¼nen will be stronger than the SPD?").


As a basis for the model, we use historical election polls from several polling institutes, which are available at We also use the results of past federal elections and data on the parties' government or opposition status. To calculate the probabilities of various coalitions, we derive the "preferences" of the parties from the results and the coalitions formed in the state elections.


We use a Bayesian state-space model to predict the outcome of the election. By simulating a large number of possible election outcomes, it is possible to derive a forecast including a range of uncertainty. The model takes into account the long-term and short-term memory of the electorate, as the parties' vote shares usually return to their long-term trends after major short-term changes. The effect that the vote shares of governing parties often decline is also taken into account, as are the "house effects" (some parties score consistently better or worse with certain institutes) and correlations of the polling institutes.

The probabilities for different coalitions are estimated using a Bayesian multinomial logit model and the simulated election outcomes. The model is based on the results of the last federal and state elections. With the information about all mathematically possible coalitions and the coalition actually in power, the model learns the "preferences" of the parties depending on the election results and the available coalition partners.


Our election forecast not only provides a prediction for a hypothetical election next Sunday, but also for the Bundestag election itself and is able to quantify the uncertainty of the forecast. This means that our forecast not only provides an insight into the current preferences of voters, but also an outlook up to the election and the ongoing coalition formation.