Entropic Analysis of Votes Expressed in Italian Elections between 1948 and 2018

In Italy, the elections occur often, indeed almost every year the citizens are involved in a democratic choice for deciding leaders of different administrative entities. Sometimes the citizens are called to vote for filling more than one office in more than one administrative body. This phenomenon has occurred 35 times after 1948; it creates the peculiar condition of having the same sample of people expressing decisions on political bases at the same time. Therefore, the Italian contemporaneous ballots constitute the occasion to measure coherence and chaos in the way of expressing political opinion. In this paper, we address all the Italian elections that occurred between 1948 and 2018. We collect the number of votes per party at each administrative level and we treat each election as a manifestation of a complex system. Then, we use the Shannon entropy and the Gini Index to study the degree of disorder manifested during different types of elections at the municipality level. A particular focus is devoted to the contemporaneous elections. Such cases implicate different disorder dynamics in the contemporaneous ballots, when different administrative level are involved. Furthermore, some features that characterize different entropic regimes have emerged.