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.

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

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.

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

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.

eISP, une architecture de calcul programmable pour l'amélioration d'images sur téléphone portable.

4 pagesToday's smart phones, with their embedded high-resolution video sensors, require computing capacities that are too high to easily meet stringent silicon area and power consumption requirements (some one and a half square millimeters and half a watt) especially when programmable components are used. To develop such capacities, integrators still rely on dedicated low resolution video processing components, whose drawback is low flexibility. With this in mind, our paper presents eISP {--} a new, fully programmable Embedded Image Signal Processor architecture, now validated in {TSMC~65nm} technology to achieve a capacity of {16.8~GOPs} at {233~MHz}, for {1.5~mm$^2$} of silicon area and a power consumption of {250~mW}. Its resulting efficiency ({67~MOPs/mW}), has made eISP the leading programmable architecture for signal processing, especially for {HD~1080p} video processing on embedded devices such as smart phone

Identification des unités de mesure dans les textes scientifiques

National audienceIdentification of units of measures in scientific texts. The work presented in this paper consists in identifying specialized terms (units of measures) in textual documents in order to enrich a onto-terminological resource (OTR). The first step permits to predict the localization of unit of measure variants in the documents. We have used a method based on supervised learning. This method permits to reduce significantly the variant search space staying in an optimal search context (reduction of 86% of the search space on the studied set of documents). The second step uses a new similarity measure identifying automatically variants associated with term denoting a unit of measure already present in the OTR with a precision rate of 82% for a threshold above 0.6 on the studied corpus.Le travail présenté dans cet article se situe dans le cadre de l'identification de termes spécialisés (unités de mesure) à partir de données textuelles pour enrichir une Ressource Termino-Ontologique (RTO). La première étape de notre méthode consiste à prédire la localisation des variants d'unités de mesure dans les documents. Nous avons utilisé une méthode reposant sur l'apprentissage supervisé. Cette méthode permet de réduire sensiblement l'espace de recherche des variants tout en restant dans un contexte optimal de recherche (réduction de 86% de l'espace de recherché sur le corpus étudié). La deuxième étape du processus, une fois l'espace de recherche réduit aux variants d'unités, utilise une nouvelle mesure de similarité permettant d'identifier automatiquement les variants découverts par rapport à un terme d'unité déjà référencé dans la RTO avec un taux de précision de 82% pour un seuil au dessus de 0.6 sur le corpus étudié

eISP: a Programmable Processing Architecture for Smart Phone Image Enhancement

4 pagesToday's smart phones, with their embedded high-resolution video sensors, require computing capacities that are too high to easily meet stringent silicon area and power consumption requirements (some one and a half square millimeters and half a watt) especially when programmable components are used. To develop such capacities, integrators still rely on dedicated low resolution video processing components, whose drawback is low flexibility. With this in mind, our paper presents eISP {--} a new, fully programmable Embedded Image Signal Processor architecture, now validated in {TSMC 65nm} technology to achieve a capacity of {16.8 GOPs} at {233 MHz}, for {1.5 mm$^2$} of silicon area and a power consumption of {250 mW}. Its resulting efficiency ({67 MOPs/mW}), has made eISP the leading programmable architecture for signal processing, especially for {HD 1080p} video processing on embedded devices such as smart phone