What regression to use to calculate the result of election in a multiparty system? I want to make a prediction for the result of the parliamentary elections. My output will be the % each party receives. There is more than 2 parties so logistic regression is not a viable option. I could make a separate regression for each party but in that case the results would be in some manner independent from each other. It would not ensure that the sum of the results would be 100%.

What regression (or other method) should I use? Is it possible to use this method in R or Python via a specific library?
Robert is right, multinomial logistic regression is the best tool to use. Although you would need to have a integer value representing the party as the dependent variable, for example:

1= Conservative majority, 2= Labour majority, 3= Liberal majority....(and so on)

You can perform this in R using the nnet package. Here is a good place to quickly run through how to use it.