# How can we apply the Bundestag election model to European elections? (model building)

I have looked into electoral systems and am trying to build a model of what the 2019 EU election would have looked like if it had used the Bundestag election system.

Disclaimer: I am fully aware that this is just a model. Since the EU election only has one vote, we cannot directly and precisely infer the results of a two-vote system. Still, here is what I have.

The first 3 tabs deal with the apportionment of seats between Member States, based on Member States' population. I aim at a nominal 800 seats (where the Bundestag has 598) and therefore 400 direct seats. One tab uses Saint-Laguë, another uses Largest Remainder, and the third concludes that the results are actually the same.

The fourth tab is the main one and it uses data and math from the remaining tabs.

For the direct vote, I assume that every Member State is divided into single-MEP constituencies (as for the Bundestag's 299 direct seats). We allocate 400 direct seats. For the results, I used the actual results of European parties in each Member States. For this, I grouped together national parties that are members of the same European parties. Then I arbitrarily changed some figures to introduce some discrepancies with the proportional vote and make it more interesting.

For the proportional vote, I also used the actual results of each European party in each Member State, and used the Saint-Laguë method to apportion the seats to the various parties (see all the numbered tabs). As is done in the Bundestag, I apportioned the total "nominal" number of seats (800 here, 598 for the Bundestag). This gives me the number of seats "owed" to each European party in each Member State.

From this, I derived the number of overhang seats, by taking the number of seats owed to each party and subtracting the number of seats directly gained.

Finally, I end up with a total of seats, resulting from the addition of direct seats and overhang seats. We reach a total of 837 seats, so a mild increase of 37 compared to our nominal 800.

This leads me to two questions:

• For the part of the model that I did, is there anything actually wrong? Is the math correct? (I know, for instance, that I haven't used a threshold as Germany does, but that's on purpose).
• You will also notice that I have not allocated balancing seats (Ausgleichsmandat). This is simply because I am not sure how they are actually attributed; how is this done? The small table (see cell AM35, in the 4th tab) shows that the final "direct+overhang" proportionality is quite close to the ideal proportionality, so this may not be an actual problem in this case, but I would like to understand how this is mathed out in practice (or is it just an agreement between parties?).