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Based on a general model of the 'quaternary' voting rule, sensitive to voters' choices between four different options (abstaining, voting 'yes', voting 'no' and staying at home), we systematically study different types of majority and quorum. The model allows for a precise formulation of majority rules and quorum constraints. For such rules four types of majority can be defined. We also consider four types of quorum. Then we study the possible combinations of a majority system with a type of quorum and provide examples from rules actually used in parliaments.

Based on a general model of the 'quaternary' voting rule, sensitive to voters' choices between four different options (abstaining, voting 'yes', voting 'no' and staying at home), we systematically study different types of majority and quorum. The model allows for a precise formulation of majority rules and quorum constraints. For such rules four types of majority can be defined. We also consider four types of quorum. Then we study the possible combinations of a majority system with a type of quorum and provide examples from rules actually used in parliaments. [Reprinted by permission of Sage Publications Ltd., copyright holder.]

Committees are often made up of representatives, each of them acting on behalf of a group of individuals or constituency of different size, who make decisions by means of a voting rule which specifies what vote configurations in the committee can pass a decision. This raises the question of the choice of an `adequate' (in a sense to be specified) voting rule, given the different sizes of the groups that members represent. In this article we take a new departure to address this problem, assuming that the committee is a bargaining scenario in which negotiations take place `in the shadow of the voting rule' in search of consensus. That is, a general agreement is sought, but any winning coalition can enforce an agreement. In this context, the notion of a `neutral' voting rule, based on the compromise between equitableness and efficiency (or egalitarianism and utilitarianism) represented by the Nash bargaining solution, is founded, yielding a recommendation that differs from previous ones.

Committees are often made up of representatives, each of them acting on behalf of a group of individuals or constituency of different size, who make decisions by means of a voting rule which specifies what vote configurations in the committee can pass a decision. This raises the question of the choice of an 'adequate' (in a sense to be specified) voting rule, given the different sizes of the groups that members represent. In this article we take a new departure to address this problem, assuming that the committee is a bargaining scenario in which negotiations take place 'in the shadow of the voting rule' in search of consensus. That is, a general agreement is sought, but any winning coalition can enforce an agreement. In this context, the notion of a 'neutral' voting rule, based on the compromise between equitableness and efficiency (or egalitarianism and utilitarianism) represented by the Nash bargaining solution, is founded, yielding a recommendation that differs from previous ones. [Reprinted by permission of Sage Publications Ltd., copyright 2008.]

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 & to compare this rule with an alternative rule, the so-called double majority rule. 5 Tables, 6 Figures, 1 Appendix, 17 References. Adapted from the source document.