Expected electoral result

To begin with, an explanation of how exactly the mechanism used in Poland to distribute seats in the constituency works. Its quotient formula is well known (divide the votes cast for the lists by consecutive integers, etc.). Such a formula confuses an impossibly quite simple matter. In another formula, the method is reduced to one sentence. We need to find such a number that if we divide the votes won by all the lists and round it down, we distribute as many seats as the district is entitled to. J. Flis owes this realization to Dr. Jacek Haman from the University of Warsaw, who described the matter in his book "Democracy, decisions, elections".

This simple mechanism has interesting consequences. Understanding them should start with explaining how to search for the number by which we will divide the votes, which is key to the method. The first step is to calculate the "simple amount", that is, the votes corresponding to one seat in the constituency. We divide the sum of votes cast for all parties participating in the distribution of seats by the number of seats in the constituency and that's it. It is theoretically possible that now it is enough to go the other way to solve the whole task.

If we divide the results of each party by this amount, we will divide all the seats. However, this will only happen if each batch receives a perfect multiple of this amount. This is extremely unlikely. In practice, there are fewer full seats assigned by this method than we are to distribute them all. Each party is left with a fraction - an allowance for the next mandate. This allowance is cut when rounding. The sum of these fractional allowances corresponds to the number of seats we have left to distribute. One thing is only certain - no party will get fewer seats than it has full seats, calculated by dividing its result by a simple amount.