Just recently I heard a radio interview with some German professor of math about votes and seats, and the problem to compute the distribution of the seats from the votes. The radio woman correctly identified the problem as the fractions, which occur when you multiply the percentage of votes by the total number of seats. After all, you cannot send 0.2 politician to the parliament. Funny remark, indeed.
The professor started to explain, that these fractions have to be used somehow to divide the remaining seats under the parties, threw in the previously used d’Hondt procedure, and both agreed that it would be too complicated to explain that here and now. The moderator admitted that he would not know exactly anyway.
The professor then continued that we have now a new algorithm which gives each vote the same weight, as he said, as it should be, he said. The surprising solution is to round to the next integer. That, he said, is much more fair than the d’Hondt procedure, which always rounds down. Both did not bother to confront the listener with the problem what to do if the number of seats assigned that way does not happen to be the number needed. But we learned that it is fair, and no longer hurts the small parties more than the bigger ones.
To demonstrate the problem of rounding down small versus large numbers, the professor used a striking example. If we would round down his income to the next million, it would hurt him much more than if we did the same with Bill Gate’s income. I assume the professor makes more than half a million, maybe by radio interviews. For otherwise, a better rounding can only help Bill Gates.
So, if you want to learn how useful math really is, listen to the radio!