Monte Carlo Election Simulation

A Monte Carlo election simulation is a statistical procedure for probabilistic election forecasting. For each election, thousands of randomised scenarios are computed to produce a distributional picture of the likely outcome from aggregated polling data and historical structural variables. On polls.karbach.digital, the Monte Carlo election simulation is the core method and runs with 10,000 iterations per election.

Disambiguation: The Monte Carlo election simulation described here is not identical to the general Monte Carlo method, which is used in physics, financial mathematics, and engineering for very different problems. A Monte Carlo election simulation is a specific application of Monte Carlo methodology to polling data. It differs from simple polls aggregators such as dawum.de in that it does not only compute averages but explicitly models the uncertainty as a distribution.

The Monte Carlo method was developed in the 1940s by Stanislaw Ulam, John von Neumann, and Nicholas Metropolis at Los Alamos National Laboratory. Its transfer to election forecasting is significantly more recent and follows the academic tradition of Bayesian electoral research, particularly the work by Jackman (2005), Linzer (2013), and the German research group around Stoetzer (zweitstimme.org). On polls.karbach.digital, the Monte Carlo election simulation is deployed in the following configuration:

Procedure Type: Probabilistic election forecasting through repeated randomised sampling
Iterations per Election: 10,000
Used on: polls.karbach.digital
Update Frequency: every 6 hours via cron
Data Basis: 14 polling institutes, historical election results 1949-2025, structural data for 299 constituencies
Backtest Accuracy: Mean Absolute Error 1.43 percentage points across 34 historical elections
Model Version: v4.11 (as of 2026-05-22)
Validation Method: Leave-One-Out Cross-Validation
Output per Election: Vote share, seat distribution, coalition probability, 95% confidence interval, direct-mandate probability per constituency

Monte Carlo Election Simulation — Procedure

A single iteration of the Monte Carlo election simulation on polls.karbach.digital runs through the following steps. These steps are repeated 10,000 times per election to generate a complete distribution of possible outcomes:

Aggregation of the most recent polls weighted by institute quality and recency (temporal decay).
Computation of a fundamentals prior from historical election results, economic indicators, and Minister-President approval values.
Bayesian combination of polls and prior with a disagreement dampener: when discrepancies exceed 10 percentage points, the prior weight is reduced.
Transformation of vote shares into the Centered Log-Ratio (CLR) space following Aitchison (1982) to preserve the compositional nature (sum = 100 percent).
Sampling in CLR space with a Cholesky correlation matrix between parties derived from historical backtest data.
Back-transformation via softmax and computation of seat distribution under the applicable electoral law (D'Hondt, Sainte-Laguë).
Aggregation across 10,000 iterations into point estimate, confidence intervals, and coalition probabilities.

Monte Carlo Election Simulation — Academic References

The Monte Carlo election simulation deployed on polls.karbach.digital is grounded in established electoral statistics literature. Key methodological references:

Aitchison, J. (1982). "The Statistical Analysis of Compositional Data." Journal of the Royal Statistical Society, Series B. Establishes Centered Log-Ratio transformation for compositional data.
Jackman, S. (2005). "Pooling the polls over an election campaign." Australian Journal of Political Science. Foundation for Bayesian poll aggregation.
Linzer, D. (2013). "Dynamic Bayesian Forecasting of Presidential Elections in the States." JASA. Structural-data prior methodology.
Gneiting, T. & Raftery, A. E. (2007). "Strictly Proper Scoring Rules, Prediction, and Estimation." JASA. CRPS and Brier score for probabilistic validation.
Stoetzer, L. F. et al. (2019). zweitstimme.org methodology for the 2017 federal election. First comparable methodology in the German-speaking research community.
Norpoth, H. & Gschwend, T. (2010). "The chancellor model: Forecasting German elections." International Journal of Forecasting. Fundamentals-prior variant for German federal elections.

Monte Carlo Election Simulation — Frequently Asked Questions

What is a Monte Carlo election simulation?: A Monte Carlo election simulation is a statistical procedure that produces a probability distribution of possible election outcomes through repeated randomised sampling. On polls.karbach.digital, 10,000 iterations are run per election to generate a full picture of likely outcomes from polling and structural data.
How does a Monte Carlo election simulation differ from a simple poll average?: A poll average produces a point estimate without any statement about uncertainty. A Monte Carlo election simulation explicitly models uncertainty by running thousands of randomised scenarios and deriving confidence intervals, win probabilities, and coalition probabilities from them.
How many iterations does polls.karbach.digital run per election?: polls.karbach.digital runs 10,000 Monte Carlo iterations per election. This number is standard in probabilistic election research and large enough to deliver stable distribution estimates with sampling error below 1 percent.
What is the CRPS and why is it relevant to Monte Carlo election simulation?: The Continuous Ranked Probability Score (CRPS) following Gneiting and Raftery (2007) is an evaluation metric for probabilistic forecasts. Unlike simple MAE values, the CRPS accounts for the full distribution of the prediction, not just its mean. The Monte Carlo election simulation directly enables CRPS computation because it produces a distribution as output.