Annick Laruelle

Shapley-Shubik and Banzhaf Indices Revisited

We provide a new axiomatization of the Shapley-Shubik and the Banzhaf power indices in the domain of simple superadditive games by means of transparent axioms. Only anonymity is shared with the former characterizations in the literature. The rest of the axioms are substituted by more transparent ones in terms of power in collective decision-making procedures. In particular, a clear restatement and a weaker alternative for the transfer axiom are proposed. Only one axiom differentiates the characterization of either index, and these differentiating axioms provide a new point of comparison. In a first step both indices are characterized up to a zero and a unit of scale. Then both indices are singled out by simple normalizing axioms.

Assessing success and decisiveness in voting situations

Abstract.In this paper we propose a simple model for measuring ‘success’ or ‘decisiveness’ in voting situations. For an assessment of these features two inputs are claimed to be necessary: the voting rule and the voters’ behavior. The voting rule specifies when a proposal is to be accepted or rejected depending on the resulting vote configuration. Voting behavior is summarized by a distribution of probability over the vote configurations. This basic model provides a clear common conceptual basis for reinterpreting different power indices and some related game theoretic notions coherently from a unified point of view.

Voting and collective decision-making : bargaining and power

List of figures Preface 1. Preliminaries 2. Seminal papers, seminal ambiguities 3. Take-it-or-leave-it committees 4. Bargaining committees 5. Application to the European Union Index.

SUCCESS VERSUS DECISIVENESS: CONCEPTUAL DISCUSSION AND CASE STUDY

In this article, we vindicate the relevance of the notion of success or satisfaction for the normative assessment of voting rules. We provide arguments in support of this view and emphasize the conceptual and analytical differences between this notion and that of decisiveness. The conclusions are illustrated in the case study provided by three different voting rules that have been proposed for the Council of Ministers of the European Union.

Inequality among EU citizens in the EU's Council decision procedure

Abstract This paper provides a normative assessment of the inequality among EU citizens imputable to the decision-making rule used by the European Council of Ministers. To this end, the EU decision-making process is modeled by a compound two-stage game among the EU citizens, whose respective voting power is evaluated by their Banzhaf index in the years 1958–1999. Two inequality indices measure the resulting inequality in the distribution of power among citizens. This permits us to evaluate the actual qualified majority rule and to compare this rule with an alternative rule, the so-called double majority rule.

Inequality in voting power

This paper deals with the assessment of inequality in the distribution of voting power. Voting power is evaluated through a general concept of power measurement based on both the voting rule and the probability distribution over vote configurations. This general concept includes as particular cases the most usual power indices and other extensions of this traditional concept. Thus no particular power index is privileged in our approach. An inequality index over the class of all power profiles with a given number of voters generated by this general measure is then singled out by requiring reasonable properties. In order to compare profiles with different numbers of voters, two alternative principles are considered, which extend the said index consistently in two ways.

Different least square values, different rankings

Abstract. The semivalues (as well as the least square values) propose different linear solutions for cooperative games with transferable utility. As a byproduct, they also induce a ranking of the players. So far, no systematic analysis has studied to which extent these rankings could vary for different semivalues. The aim of this paper is to compare the rankings given by different semivalues or least square values for several classes of games. Our main result states that there exist games, possibly superadditive or convex, such that the rankings of the players given by several semivalues are completely different. These results are similar to the ones D. Saari discovered in voting theory: There exist profiles of preferences such that there is no relationship among the rankings of the candidates given by different voting rules.

On The Difficulty Of Making Decisions Within The Eu-25

In this paper we measure the effect of the quota on the difficulty of making decisions in the EU-25 Council after the next enlargement. We compute the probability of a proposal being rejected in the Council. This probability depends on the voting rule (and therefore on the quota) and on the probabilities of the different vote configurations. Here we do not consider that all vote configurations are equiprobable, the classical implicit or explicit assumption. We assume that vote configurations with a minority of members states in favour of the proposal have a null probability, with other vote configurations being equiprobable.