Non linearity and elections: How politicians go wrong even when they do not want

The electoral system adopted for the allocation of seats in the Italian Senate utilizes a complex mechanism of awards with the aim of strengthening the winning coalition and so improve overall government stability. We show that in a significant number of cases, the effect of the mechanism is opposite to that desired, to wit, weakening the resultant government by awarding more seats to the minority coalition. Indeed the award to the minority can even be such that the minority coalition becomes the majority and wins the election. The application of the award mechanism is strongly unpredictable as it depends crucially on the precise number of seats independently obtained in each district, a characteristic