This is our prediction on the number of seats for each of the four main national parties with seats assigned to all other parties summed up in "others". For each party we plot a distribution that reflects the uncertainty on the number of seats they will win on Sunday's election. The median of the seats is denoted by a dot while the 90% interval is depicted by a black interval line. For some parties there is a lot of certainty about the number of seats, e.g. IU. For others there is large uncertainty, e.g. C's and PSOE. This distribution has integrated over many sources of uncertainty in our inference machine.
In a future blog post we will provide details on the methodology used to produce such predictive distributions. Basically, we use a Bayesian logit model, estimated with many categorical explanatory variables (age, gender, size of municipality, etc.) as the baseline for post-stratification (allocating votes to political parties depending on the propensity to vote for each party of people with specific age, gender, etc in the population of each province). We avoid using any "cooking" procedure performed by the pollsters since we work with the people who express their vote intention. The training data includes the CIS barometers of January, April, July and October of 2015. The response variable is, as we pointed out before, voting intention. We construct also a multilevel model to aggregate the results of the pollsters. For training we use all the polls published less than 60 days before congressional elections in 2000, 2004, 2008 and 2011 and the European elections of 2009 and 2014. Finally, we synthesize the predictions by updating the post-stratification model with the polls likelihood. Applying D’Hont we simulate the distribution over seats from the distribution over votes. Therefore, our method consists of synthesizing evidence from all available sources of relevant data as national surveys, election polls, census data etc. Our estimation procedure is based on a Bayesian hierarchical model to carry out the synthesis and advanced computational techniques to carry out the calculations, e.g. Hamiltonian Monte Carlo methods (via the STAN software).
We might be interested to see how the parliament would look like in a possible coalition of PP and C's:
The national level seat allocation takes into account the nonlinearity inherent in the seat distribution electoral system. Our probabilistic prediction on the percentage of national vote is as follows.
Our prediction machine is based on predicting the electoral result at provincial level.
