In this paper we analyze the fairness of the 2007 reform proposal concerning the apportionment of the seats between the regions for the Italian Senate. Theory of power indices is used to compare the actual case with the proposed one. Two scenarios are proposed, senators belonging to the same...

The spatial analysis of power indices is commonly used in the literature to study the importance of ideological criteria. Our purpose is to show, through the example of some french groupings of local cities, the importance of the geographical situation of the players when considering power...

In this paper, we compare the five more famous methods of apportionment, the methods of Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the well-known...

How can we count and list all the Banzhaf or Shapley-Shubik index of power configurations for a given number of players? There is no formula in the literature that may give the cardinal of such a set, and moreover, even if this formula had existed, there is no formula which gives the...

L’objet de cet article est de mesurer le pouvoir des membres des conseils d’administration des universités françaises tel qu’il est défini par la loi relative aux libertés et responsabilités des universités (loi LRU). A l’aide d’outils issus de la théorie des jeux coopératifs,...

Since the political collapse of the 90’s, and in particular since the bicameral commission experience of 1997, Italian governments have always tried to face the need for wide constitutional reform. Reductions in the number of deputies and senators have been planned on several occasions. The...

When the number of players is small in a weighted majority voting game, it can occur that one of the players has no influence on the result of the vote, in spite of a strictly positive weight. Such a player is called a “dummy” player in game theory. The purpose of this paper is to...

In the United States, the president is elected by the Electoral Col- lege (EC) and not directly by individual voters. This can give rise to a so-called referendum paradox in which one candidate receives more popular votes than any other, but this candidate is not elected. The 2000 election is an...

According to a given quota q, a candidate a is beaten by another candidate b if at least a proportion of q individuals prefer b to a. The q-Condorcet efficiency of a voting rule is the probability that the rule selects a q-Condorcet winner (q-CW), that is any candidate who is never beaten under...

This paper analyzes a sequential voting mechanism that eliminates at each round one candidate, until only one of them is left (the winner). The candidates are the voters and they only differ across their skill level. The payoff allocated to the winner depends on the sequence of elimination of...