A comparison between the methods of apportionment using power indices: the case of the U.S. presidential elections

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 power index and the populations are the ones of the different States of the U.S. We first explain under which conditions this comparison makes sense. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results.Banzhaf index, methods of apportionment, distances, balance population-power.

Real Estate Portfolio Management : Optimization under Risk Aversion

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 function defined on the terminal value of the portfolio. We extend previous results (Baroni et al., 2007, and Barthélémy and Prigent, 2009), established for the quasi linear utility case, where investors are risk neutral. We consider four cases. In the first one, the investor knows the probability distribution of the real estate index. In the second one, the investor is perfectly informed about the real estate market dynamics. In the third case, the investor uses an intertemporal optimization approach which looks like an American option problem. Finally, the buy-and-hold strategy is considered. For these four cases we analyze numerically the solutions that we compare with those of the quasi linear case. We show that the introduction of risk aversion allows to better take account of the real estate market volatility. We also introduce the notion of compensating variation to better compare all these solutions.Real estate portfolio, Optimal holding period, Risk aversion, Real estate market volatility

Some conjectures on the two main power indices

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 are fixed or not.Shapley-Shubik, Banzhaf, power index, power vectors.

Italian Senate apportionment: is the 2007 proposal fair?

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 purpose of this paper is to analyze whether or not the proposed reforms to the apportionment of seats in the Italian senate is fair. We use the theory of power indices to compare different scenarios. We show that the intended reform produces an outcome that is worse than both the ideal situation and the actual situation.power index, Banzhaf, Italian Senate

Which Capital Growth Index for the Paris Residential Market?

In this paper we address the issue of measuring price performance for the Paris residential market. Our main focus is on choosing the appropiate index or indices capable of efficiently capturing capital growth, capital risk, and identifying the main risk factors inherent in this specific market.We identifying three existing indices but show that they may not be completely appropriate to address our main goals. We therefore construct two complementary repeat sales indices: a Case & Shiller (1987) Weighted Repeat sales (WRS) index and a Factorial index using the Baroni, Barthélémy & Mokhrane (2001) approach. We use the CD-BIEN database that contains more than 220 000 repeta sales transactions for residential properties in Paris area covering the period 1983-2001 period.We estimate these two indices for the Paris and close surrounding area and compare them to different existing indices: (I) the square metre index provides by the Chambre des Notaires de Paris and INSEE, (II) the IDP indices, (III) the listed real estate index. OUR conclusions yield interesting implications concerning real estate risk and suggest the construction of jointly using the repeat sales and the factorial approachesReal estate indexes; valuation-based index; repaet sales; risk factors

U.S Presidential Elections and the Referendum Paradox*

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 example of this phenomenon. Can the EC be reformed so that a referendum paradox never arises? We consider vary- ing three natural parameters. First, we consider changing the method of apportioning seats in the House of Representatives to states. Sec- ond, we consider changing the total number of seats in the House. Intuition suggests that as the number of seats approaches the number

On the Likelihood of Dummy players in Weighted Majority Games

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 investigate the conditions that give rise to such a phenomenon and to compute its likelihood. It is shown that the probability of having a dummy player is surprisingly high and some paradoxical results are observed.Cooperative game theory, weighted voting games, dummy player, likelihood of voting paradoxes.

Loi relative aux libertés et responsabilités des universités (loi LRU), élection du président et conseil d’administration : une analyse en termes de pouvoir

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, et en particulier l’indice de pouvoir de Banzhaf, nous montrons que le nombre de représentants d’un groupe, par exemple les professeurs des universités ou les étudiants, et le pouvoir, sont des notions dont les relations sont parfois surprenantes. Nous présentons des exemples où le réel pouvoir de décision n’appartient pas forcément aux groupes auxquels nous pensions intuitivement.conseil d’administration, indice de Banzhaf, pouvoir, universités françaises.

La loi LRU a-t-elle modifié les distributions de pouvoir au sein des universités françaises ?

La loi LRU (loi relative aux libertés et responsabilités des universités) change la structure du pouvoir au sein des universités françaises. Seuls les membres du conseil d'administration (CA) prennent part à l'election du president, alors qu'auparavant, les membres du conseil scientifique (CS) et du conseil des etudes et de la vie universitaire (CEVU) prenaient part au vote. Notre question est alors de savoir si ce changement radical, le nombre de votants est desormais compris entre 20 et 30, alors qu'il etait compris entre 70 et 140, presente souvent comme une reforme majeure du systeme universitaire, a engendre une repartition differente du pouvoir parmi les groupes representatifs tels que les enseignants, les etudiants, les personnels IATOS et les membres exterieurs.Indice de Banzhaf, pouvoir, universites francaises, loi LRU

Transition numérique et pratiques de recherche et d’enseignement supérieur en agronomie, environnement, alimentation et sciences vétérinaires à l’horizon 2040.

Pour citer ce document:Barzman M. (Coord.), Gerphagnon M. (Coord.), Mora O. (Coord.),Aubin-Houzelstein G., Bénard A., Martin C., Baron G.L, Bouchet F., Dibie-Barthélémy J., Gibrat J.F., Hodson S., Lhoste E., Moulier-Boutang Y., Perrot S., Phung F., Pichot C., Siné M., Venin T. 2019. Transition numérique et pratiques de recherche et d’enseignement supérieur en agronomie, environnement, alimentation et sciences vétérinaires à l’horizon 2040.INRA, France, 161pagesTransition numérique et pratiques de recherche et d’enseignement supérieur en agronomie, environnement, alimentation et sciences vétérinaires à l’horizon 2040