We provide an axiomatic foundation of the expected utility preferences over lotteries on roles in simple superadditive games represented by the two main power indices, the Shapley-Shubik index and the Banzhaf index, when they are interpreted as von Neumann-Morgenstern utility functions. Our...

This paper addresses the following issue: If a set of agents bargain on a set of feasible alternatives 'in the shadow' of a voting rule, that is, any agreement can be enforced if a 'winning coalition' supports it, what general agreements are likely to arise? In other words: What influence can...

This paper focuses on the probabilistic point of view and proposes a extremely simple probabilistic model that provides a single and simple story to account for several extensions of the Shapley value, as weighted Shapley values, semivalues, and weak (weighted or not) semivalues, and the Shapley...

We provide a new axiomatization of the Shapley-Shubik and the Banzhaf power indices in thedomain of simple superadditive games by means of transparent axioms. Only anonymity isshared with the former characterizations in the literature. The rest of the axioms are substitutedby more transparent...

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...

Committees are often made up of representatives of different-sized groups of individuals, and make decisions by means of a voting rule which specifies what vote configurations can pass a decision. This raises the question of the choice of the optimal voting rule, given the different sizes of the...

In this paper we revise the probabilistic foundations of the theory of the measurement of 'voting power' either as success or decisiveness. For an assessment of these features two inputs are claimed to be necessary: the voting procedure and the voters' behavior. We propose a simple model in...

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed "natural" postulates that a measure of a priori voting power "should" satisfy, the violations of which are...

In this paper, 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...

This paper deals with the assessment of inequality in the distribution of voting power. As voting procedures are modeled as simple games and power evaluated through power indices, two approaches are possible to deal with inequality in this context, depending on whether the power profiles...