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 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...

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...

This paper deals with real estate portfolio optimization when investors are risk averse. In this framework, we determine several types of optimal times to sell a diversified real estate and analyze their properties. The optimization problem corresponds to the maximization of a concave utility...

In this paper, we compare five well-known methods of apportionment, the ones by 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 Banzhaf...

The purpose of this paper is to present a structural specification of the Shapley- Shubik and Banzhaf power indices in a weighted voting rule. We compare them in term of the cardinality of the sets of power vectors (PV). This is done in different situations where the quota or the number of seats...